Neural Network Control

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29 papers5 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Oct 26, 2026

Learning Direct Control from Optimization for Dynamic Target Tracking

Dynamic target tracking requires a mobile robot to maintain target visibility while navigating obstacles with smooth, feasible controls. Online trajectory optimization explicitly encodes these objectives but requires repeated numerical solving, whereas waypoint-based neural policies separate geometric prediction from control execution. We introduce LECO, a framework that transfers tracking optimization into offline learning of a direct-control policy. LECO predicts control sequences and maps them to trajectories through a differentiable kinematic model, allowing trajectory-level objectives to directly guide control learning. A decaying expert-guidance curriculum initializes effective tracking behavior and progressively shifts learning toward these task objectives. At deployment, a predictive safety lock checks short-horizon obstacle clearance and invokes a classical planning and control fallback when the predicted motion is unsafe or the target prediction is invalid. Across three simulated obstacle densities, LECO reduces root-mean-square linear jerk by 14.1--31.2% relative to the best competing method for this metric and achieves the highest tracking success rate, with per-cycle computation times of 4.25--5.63,ms. Experiments on two robot platforms further demonstrate tracking through indoor narrow passages and outdoor forest environments. These results demonstrate that learning direct control from optimization enables smooth and robust dynamic target tracking.

Bing Sun, Yue Lin, Canhui Wen +4

Robot Policy Learning Neural Network Control

Oct 21, 2026

Certified Neural Approximation of Robust Nonlinear Model Predictive Control

Model predictive control is a high-performance control method, but it incurs comparatively high online computational costs across many control tasks and is challenging to realize in low-level hardware settings. To address this, we present a framework for generating neural network controllers that provably inherit the safety and stability guarantees of a robust model predictive policy. In contrast to approaches based on post-verification or additional online safety filters, our method provides constructive, a priori design conditions that ensure preservation of recursive feasibility and stability before deployment. We treat the approximation error as a bounded input disturbance, which is addressed in the MPC design. This allows the neural network controller to directly inherit robustness from the underlying model predictive controller, which enables the transfer of guarantees to the approximation. The design process is an offline, constructive synthesis pipeline and can be implemented once Lipschitz bounds are specified. We further demonstrate in simulation that the learned controller reproduces the closed-loop behavior of the original controller while reducing online computation.

Hendrik Alsmeier, Maik Pfefferkorn, Rolf Findeisen

Control and Cyber-Physical Systems Laboratory, Technical University of Darmstadt, Landgraf-Georg-Str. 4, 64283 Darmstadt, Germany

Neural Network Control Nonlinear MPC Neural Network Stability Robust Control

Oct 16, 2026

Distributed Performance Boosting through Neural Control for Plug-and-Play Networks

We address the problem of improving the performance of pre-stabilized networked systems subject to plug-and-play (PnP) operations, namely additions or removals of subsystems. While distributed baseline controllers can preserve stability after a PnP transition, augmenting them with expressive neural policies can invalidate the formal stability guarantees. To overcome this issue, we build on recently proposed Performance Boosting controllers based on the Internal Model Control (IMC) principle, which reduce closed-loop stability to a finite

\ell_2

-gain requirement on an auxiliary operator. In the distributed setting, this operator is formed by interconnecting local neural operators that exchange information only between neighboring subsystems. We then derive free parametrizations of this interconnection, namely explicit maps from unconstrained trainable variables to interconnected neural operators satisfying a prescribed network gain bound for every parameter value. The obtained distributed neural controller can therefore be trained by unconstrained gradient-based optimization without stability constraints or projection steps, while retaining the prescribed gain bound at every training iterate. We develop two complementary parametrizations. A neighbor-based compositional parametrization uses local coupling bounds, so that after a PnP event only subsystems whose bounds change need to update their gain parameters. A network-norm parametrization instead uses a bound on the overall coupling matrix and can reduce conservatism, at the price of requiring network-wide information. A PnP DC-microgrid case study shows that the proposed neural layer improves voltage transients under topology changes and load variations while preserving nominal closed-loop stability.

Danilo Saccani, Leonardo Massai, Giancarlo Ferrari-Trecate

Ecole polytechnique federale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

Neural Network Control Distributed Control Neural Network Stability Neural Operators

Oct 9, 2026

History, Adaptation, and Hidden Gain: Two Prospective Tests of Learned Predictive Control in a Synthetic Neural Population

We study learned one-step predictive control of a synthetic population of 64 leaky integrate-and-fire neurons whose light sensitivity is scaled by a hidden factor s, using two prospective confirmations on plants simulated only after the analysis was frozen. In the first (50 plants, 11 conditions), removing the 200-ms input-output history substantially worsened a parameter-count-matched neural predictor at low and moderate gain (s = 0.6, 0.8; RMSE rose by 2.47 Hz at s = 0.6, 97.5% CI 2.43-2.51). In secondary comparisons, recursively adapted ARX had the lowest mean error of the deployable controllers in 10 of 11 conditions, tuned PI with anti-windup matched or beat the network for s >= 0.7, and training for 10,000 rather than 900 epochs lowered prediction error but worsened control. Development work suggested the network's learned action sensitivity did not track the hidden gain. A second protocol (50 new plants, 9 sensitivities, 2 noise levels) confirmed three pre-specified predictions at the primary noise level. Re-estimating a single multiplicative input gain recovered 87% (95% CI 86-88%) of the benefit of full adaptive ARX. Supplying that online estimate to the network as an extra input reduced high-gain tracking error by 1.84 Hz [1.81, 1.88]. Longer training worsened the plain network by 1.09 Hz but improved the gain-input network by 1.07 Hz, a differential of 2.16 Hz [2.13, 2.20]. Under high process noise (sigma = 2.0) the effects shrank to about 0.04 Hz or less and gain-only adaptation recovered only 24% of the adaptive-ARX benefit. In this synthetic plant, at the primary noise level, one-parameter online gain estimation accounts for most of the gap between a history-based network and full adaptive ARX, and for its prediction-control mismatch.

Mahesh Reddy Pagadala

Aston University, Birmingham, UK

Neural Network Control Adaptive Control Dynamical Systems Online System Identification Neural Surrogate Modeling

Oct 6, 2026

Micro Neural Policies for Safe Real-Time Robotic Control

In this paper, we investigate the synthesis of Micro Neural Policies (MNP) to enable safe and robust real-time robotic control on computationally constrained embedded devices. We demonstrate that integrating Evolution Strategy (ES) and Statistical Model Checking (SMC)-based verification for policy search can drastically reduce neural network size without compromising safety and robustness. We conduct a large-scale training and evaluation of MNP on Cartpole and Quadrotor control tasks, varying control frequencies and network architectures. After validating these policies in simulation, we evaluate their deployability through zero-shot transfer to physical systems. Our experiments show that MNP can successfully achieve safe sim-to-real transfer without sacrificing control performance. We then show that the policies' memory footprint, ranging from 0.5 to 7.5 kB, allows deployment on microcontrollers, where they achieve real-time inference latency with under 25 ns of jitter while leaving the chip idle for over 97% of the time for additional workloads. This makes them a highly practical solution for severely resource-constrained robotic systems.

Hongpeng Cao, Riccardo Curcio, Daniele Ottaviano +1

School of Engineering and Design, Technical University of Munich, Boltzmannstraße 15, 85748 Garching b. München, Germany · Department of Computer Science, Sapienza University of Rome, Via Salaria 113, 00198 Rome, Italy

Robotic Control Statistical Model Checking Robot Safety Neural Network Control

Oct 5, 2026

Interleaved Projected Gradient Descent for Safe Imitation Learning

We propose an imitation-learning design for neural-network control policies under state and input constraints. Training alternates a standard imitation gradient step with a block of

k

safety steps that pull the network's actions toward their projection onto the safe set; at run time, the controller is the trained network alone, with no safety filter. We analyze this scheme as inexact projected gradient descent in the space of policy actions. When the projected actions are recomputed at every safety step and each step moves the actions consistently toward the safe set, letting

k

grow logarithmically yields asymptotic constraint satisfaction on the training states and bounds the distance to the constrained optimum of the imitation loss; with the projected actions held fixed, the same holds only if they are exactly representable by the network. On a nonlinear autonomous racing task, we compare our method with adding a weighted constraint-violation penalty to the imitation loss. With a sufficiently large weight, our method matches the lap time of unconstrained imitation while reducing the fraction of violating episodes from

15\%

to

1\%

, about six times fewer than the penalty approach at its best weight. Its lap times are less sensitive to the weight, which instead sets how quickly violations vanish during training. In racing, the safety corrections are sparse and the conditions of the analysis do not hold; the gain arises instead through the data collected during training. These gains come at the cost of additional training computation.

Shengfan Cao, Francesco Borrelli

University of California, Berkeley

Gradient Descent Imitation Learning Neural Network Control

Sep 21, 2026

Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian

The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degree based conditions into the learning process. This enables the conventional feedback controller components to be replaced by neural Lie derivatives, thereby facilitating a fully data-driven feedback linearization framework. Furthermore, practical closed-loop stability is established by deriving sufficient conditions under which bounded identification errors lead to bounded tracking errors. The derived theoretical results are validated through their application to an armature controlled DC motor.

Lakshmi Priya P. K., Andreas Schwung

Department of Automation Technology and Learning Systems, South Westphalia University of Applied Sciences,Lübecker Ring 2, Soest, 59494, Germany

Data-Driven Control Feedback Control Feedback Linearization Optimization Neural Network Control

Sep 18, 2026

Scalable Incremental Robustness Analysis of Neural Network Feedback Systems

Semidefinite programming (SDP) certificates for feedback systems containing deep neural networks (NNs) typically scale with the total number of neurons, whereas small-gain tests are scalable but can be highly conservative. This paper develops a unified and scalable framework for incremental robust stability and performance analysis of feedback interconnections involving high-dimensional NNs and unmodeled dynamics. By combining a structured decomposition of the full-order SDP condition with scalable Lipschitz constant estimation algorithms, we derive reduced verification conditions that certify incremental convergence and incremental

\ell_2

-gain bounds. The dimensions of the resulting control-analysis linear matrix inequalities (LMIs) depend only on the widths of the last two network layers and are independent of network depth. The framework preserves the coupling between the plant and the NN, with the incremental small-gain condition recovered as a special case. To further reduce conservatism, we develop a multi-round alternating update scheme that iteratively refines the coupling variables while preserving scalability. Numerical experiments show that the proposed framework achieves state-of-the-art incremental

\ell_2

-gain bounds for large-scale NN feedback systems.

Zichen Wang, Peter Seiler, Geir Dullerud +1

Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois Urbana–Champaign · Department of Electrical Engineering and Computer Science, at the University of Michigan · Electrical and Computer Engineering Department at the University of Minnesota

Neural Network Control Neural Network Robustness Feedback Control Neural Network Verification

Aug 19, 2026

Learning the Right Abstraction: Neural Reduced Dynamics for Complex Robot Control

High-fidelity embodied AI simulators provide realistic evaluation of complex robotic systems, but their computational cost limits their direct use for large-scale reinforcement learning campaigns. We advocate the use of less accurate but more expeditious simulations, which might draw on data-driven, e.g., neural dynamics, models. This contribution argues that the practical value of a neural dynamics model for complex robot control lies in learning the right abstraction: a reduced state that preserves the control-relevant physics of the high-fidelity system while enabling high-throughput policy learning. We develop a neural reduced dynamics (NRD) framework that separates the state the model propagates from what can be supplied as an input or recovered analytically, trains policies entirely inside the frozen learned model, and validates them back in the high-fidelity simulator. Two case studies instantiate it across three control tasks: terrain-aware HMMWV trajectory tracking on rigid, bumpy and deformable Continuum Representation Model (CRM) terrain; and goal reaching for a stock tracked vehicle and its front-mounted articulated arm. Every policy transfers back to the high-fidelity simulator. A single policy trained inside the terrain-conditioned dynamics model, and given no terrain input of its own, attains lower median and mean tracking error than both single-terrain specialists on all three terrains, including zero-shot bumpy terrain. Quantitatively, the tracked vehicle reaches 100 of 100 goals and the arm 97 of 100, with zero contacts or joint-limit violations. The NRD models advance roughly four orders of magnitude faster in simulated time than the high-fidelity simulator scenes they replace, making iterative on-policy learning practical and supporting neural reduced dynamics as a bridge between accurate but expensive physics simulation and scalable robot learning.

Harry Zhang, Dan Negrut

Department of Mechanical Engineering, University of Wisconsin–Madison, Madison, 53706, WI, USA

Robotic Control Robot Dynamics Learning Robotics Simulation Reduced-Order Modeling Model-Based RL Neural Network Control

Jul 15, 2026

Conditional Invertible Neural Networks for Data-Driven UAV Control: A 2-D Proof of Concept

We investigate conditional invertible neural networks (cINNs) as probabilistic inverse-dynamics models for multirotor control. For a planar X8 coaxial multicopter, we learn

p(u \mid s_t, c_t)

from an incremental nonlinear dynamic inversion (INDI) teacher using rational-quadratic spline coupling and invertible linear mixing. Open-loop reproduction reaches

R^2 = 0.944

, mean CRPS 0.0915, and log-probability-error correlation

ρ= -0.60

. Over 15 closed-loop scenarios, position RMSE matches INDI (9.7 vs. 9.5 m), with 47 percent tracking acceptably; failures separate into attitude divergence under aggressive steps and phase lag under high-frequency references, isolating command bandwidth and data coverage as dominant failure mechanisms.

Christian Wittke, Stephan Myschik, Oliver Niggemann

Computer Science in Mechanical Engineering, Helmut Schmidt University, Hamburg, Germany. · Institute for Aeronautical Engineering, University of the Bundeswehr Munich, Bavaria, Germany

Invertible Neural Networks Quadrotor Control Inverse Dynamics Neural Network Control

Jul 13, 2026

Implicit Neural Networks as Static Controllers: Certificates and Performance Separation

Implicit neural controllers (INCs) are static feedback laws that are evaluated through an algebraic fixed point {equation}; they include as special cases neural network controllers. We propose a so-called implicit representation of neural networks as a key enabling device that exposes the controller as a trainable linear interconnection closed through a known static activation map, thereby making well-posedness and Lyapunov/IQC analysis mathematically easy to handle. For finite-dimensional LTI plants, we first develop a rigorous analysis theory for a given INC, including Perron--Frobenius and norm conditions for well posedness, LMI/IQC certificates for exponential stability, and LMIs for discounted infinite-horizon quadratic performance. We then formulate synthesis as a certification-compatible heuristic search: training is carried out under explicit well-posedness constraints, implicit-differentiation formulas provide gradients, and the resulting controller is accepted only after independent post-training LMIs or regional admissibility checks are feasible. Finally, we establish constrained-control separation results: for a specific scalar unstable plant with hard actuator bounds, an INC achieves a strictly smaller discounted infinite-horizon cost than any admissible finite-order dynamic linear controller. Additional results cover quadratic state-input costs, comparison with linear static output feedback, and computable upper/lower-bound certificates. Numerical examples illustrate the mechanism and the resulting certified performance.

Giuseppe C. Calafiore, Laurent El Ghaoui

Implicit Neural Representations Neural Network Control Feedback Control

Jul 7, 2026

Neural-ESO: A Dual-Pathway Architecture for Provably Robust Learning-Based Control

A learning-enabled disturbance-rejection framework based on a Neural Extended State Observer (Neural-ESO) is presented in this letter. Unlike existing learning-based control methods that largely rely on the learned model once deployed, Neural-ESO adopts a dual-pathway architecture: a predictive pathway uses a neural network to provide a feedforward disturbance estimate that accelerates convergence, while a corrective pathway employs a conventional ESO to compensate prediction errors and prevent over-reliance on the neural component. Using Lyapunov theory and a small-gain analysis, we show that enforcing a Lipschitz bound on the learning component guarantees uniform ultimate boundedness of the closed-loop error dynamics. The proposed framework is validated on a quadrotor landing task subject to strong ground-effect disturbances across normal and out-of-distribution scenarios, demonstrating accuracy-robustness trade-off and greater operational reliability during training, deployment, and transfer compared with state-of-the-art baselines.

Fan Zhang, Richie Suganda, Jinfeng Chen +4

Department of Engineering Technology, University of Houston, USA · Department of Electrical and Computer Engineering, University of Houston, USA · Department of Electrical Engineering, Rice University, USA

Robust Control Neural Network Control Disturbance Rejection

Jun 29, 2026

ShardNet: Training Neural Controllers with Hard, Non-Convex Constraints

While neural network control policies are powerful, their deployment on safety critical systems depends on ensuring that they obey strict constraints. Existing work often treats safety as a metric to optimize for, which competes with other performance objectives, if training converges at all. Instead, we introduce ShardNet, a neural network architecture that strictly enforces unions of polyhedral constraints by construction, using a differentiable projection layer parameterized by a classification network. The key insight is to embed safety into the neural network's structure, allowing performance to be optimized independently because formal safety guarantees are always given. In contrast with existing neural architectures that can only enforce simple convex constraints, ShardNet enables the first safe-by-construction synthesis of forward-invariant neural network controllers on closed-loop systems where safety constraints are expressed as nonconvex unions of polyhedras or learned value function level sets. To support this, we also introduce a technique to verify and train such value functions correctly as rectified linear unit (ReLU) networks, which has not previously been possible. On double integrator benchmarks drawn from the literature, ShardNet policies maintain 100% safety on verified sets and achieves significantly lower objective loss compared to existing formal methods. Furthermore, our value function training technique also produces safe sets more than 3 times larger than existing verification approaches.

Long Kiu Chung, Shreyas Kousik

Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA.

Neural Network Verification Safety-Critical Control Neural Network Control

Jun 11, 2026

Neural Architectures as Functional Priors in Physics-Informed Control Problems

In this work we investigate the role of neural architectures as implicit functional priors in control problems governed by ordinary differential equations. Rather than focusing on highly complex problems, our objective is to investigate architecture-dependent effects in controlled dynamical systems within the simplest physically interpretable settings possible. In particular, we study a controlled linear RLC electrical circuit and a nonlinear Duffing-type dynamical system. Both systems are analyzed first through classical optimal-control formulations and later through PINN-based approaches. We compare different combinations of multilayer perceptrons (MLPs) and Fourier-based KAN-like architectures, and analyze their influence on the resulting controls. The numerical experiments suggest that different architectural choices systematically generate qualitatively distinct controls, even under identical governing equations, loss functionals, initial and target states, training parameters and physical constraints. Significant differences appear in the spectral structure, smoothness, energy distribution, and phase-space behavior of the learned solutions. A central observation of this work is the emergence of a functional specialization phenomenon when the neural architectures are allowed sufficient freedom to shape the structure of the learned controls. More specifically, in the systems considered here, Fourier-based architectures tend to produce trajectories with richer oscillatory content, whereas smoother low-frequency-biased architectures tend to generate more regular and energetically efficient controls. This suggests that different functional components of the control problem may be handled more efficiently by different neural architectures, leading to an implicit specialization between state representation and control generation.

Sonia Rubio Herranz, Fernando Carlos López Hernández, Antonio López Montes

Department of Statistics and Operations Research (EIO), Universidad Complutense de Madrid, 28040 Madrid, Spain · Department of Software Engineering and Artificial Intelligence, Universidad Complutense de Madrid, 28040 Madrid, Spain · Department of Analysis and Applied Mathematics, Universidad Complutense de Madrid, 28040 Madrid, Spain

Dynamical Systems Ordinary Differential Equations Physics-Informed ML Optimal Control Neural Network Control

Jun 4, 2026

Amortized Nonlinear Model Predictive Control

Nonlinear Model Predictive Control requires solving a constrained nonlinear program (NLP) in real-time at every sampling instant, a computational bottleneck that limits deployment on resource-constrained hardware or at high sampling rates. We address this challenge for the broad class of input-affine nonlinear systems to show that the optimal control move can be approximated by a state-dependent quadratic program (QP) whose cost parameters depend on the current state and reference. We propose a single-network residual-corrector architecture: a state-dependent analytic baseline provides initial QP parameters, and the network learns only the corrections needed to match the full NLP solution; the QP is solved by a differentiable interior-point layer, guaranteeing constraint satisfaction for the first control action. The network is trained offline on data generated by an NLP solver using a hybrid loss that combines supervised imitation and KKT-residual penalties. We validate the approach on a three-link planar robotic arm with Cartesian end-effector tracking, demonstrating orders-of-magnitude speedup over the NLP solver while maintaining comparable tracking performance.

Francesco Pillitteri, Alberto Bemporad

IMT School for Advanced Studies, Lucca, Italy

Robotic Control Nonlinear MPC Learning to Optimize Model Predictive Control Optimal Control Neural Network Control

May 26, 2026

Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorial

Learning-based methods for synthesizing controllers have gained popularity due to their high expressiveness and strong empirical performance. However, in safety-critical scenarios such as autonomous driving, robotics, and power systems, empirical performance alone is insufficient, and formal verification of controller properties such as stability and safety is highly desirable. Unfortunately, many prior verification approaches are either tied to specific structural assumptions on the system or the certificate, making them difficult to transfer across settings, or suffer from poor scalability on higher-dimensional neural network systems. In this tutorial, we present a unified framework that aims to mitigate this gap via bridging control with the state-of-the-art neural network verifier

α,\!β

-CROWN (alpha-beta-CROWN). At its core,

α,\!β

-CROWN is a general-purpose bounding engine for nonlinear functions represented as computation graphs: given an input domain, it can produce certified bounds and explicit linear relaxation of the nonlinear function. These certified bounds are useful on their own for tasks such as reachability analysis, and they also provide the foundation for more complex routines that perform satisfiability checking and optimization. More specifically, many control problems reduce to verifying real-valued inequalities over a state domain (e.g., Lyapunov theory). Consequently,

α,\!β

-CROWN enables scalable verification of such conditions by computing tight bounds and recursively partitioning and pruning subdomains based on the bounds. Thanks to GPU parallelization, this pipeline demonstrates superior scalability on verification and optimization problems that are challenging for traditional approaches. In this tutorial, we discuss the basics of

α,\!β

-CROWN and introduce its application to various control-related tasks.

Haoyu Li, Xiangru Zhong, Hao Cheng +2

Department of Computer Science · Department of Electrical and Computer Engineering, University of Illinois Urbana-Champaign, Urbana, IL 61801, USA

Neural Network Verification Neural Network Control

May 25, 2026

Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers

Neural network (NN) dynamics models and control policies achieve strong performance in robotics, but providing sound guarantees under uncertainty remains difficult, especially for closed-loop NN systems. Existing reachability tools provide formal over-approximations, yet are often non-differentiable, overly conservative, or too slow for modern learning and online planning pipelines. To address this, we present a parallelizable, differentiable reachability framework in JAX for continuous- and discrete-time systems with analytical and NN-based dynamics and controllers. Our framework combines Taylor-model flowpipe construction with CROWN-style linear bound propagation through a unified representation that preserves affine dependencies while supporting GPU-batched computation and automatic differentiation. Building on this reachability primitive, we develop (i) a certified training method that encourages reachability-friendly dynamics models and controllers, and (ii) a reachability-aware sampling-based MPC scheme with gradient-based refinement. Experiments on non-prehensile manipulation and quadrotor tasks, including hardware and higher-dimensional evaluations (up to 72D), demonstrate practical online planning while maintaining certified reachable-set over-approximations under bounded uncertainty.

Keyi Shen, Glen Chou

Georgia Institute of Technology, Atlanta, GA 30308

Robotic Control Neural Network Verification Reachability Analysis Robot Policy Learning Model Predictive Control Neural Network Control

May 6, 2026

Bilinear Mamba-Koopman Neural MPC for Varying Dynamics

Koopman-based neural MPC models generate time-varying dynamics from historical data, but preserve convexity by enforcing that the system operator is independent of the current control input. This conditional independence constraint limits adaptation to changing dynamics within a single MPC horizon, particularly under time-varying conditions and under stale-plan execution. We propose Bilinear Mamba-Koopman Neural MPC, a minimal extension that introduces control-dependent coupling in the latent dynamics, allowing the effective operator to adapt to the current input. The resulting model is a strict generalization of the standard linear, conditional-independence formulation, adds less than 1% parameters through a low-rank structure, and admits exact model Jacobians that enable efficient Sequential Convex Programming (SCP) with monotone-descent and KKT convergence results under standard trust-region assumptions. Across CartPole and RSCP benchmarks in time-invariant and time-varying regimes, the proposed model matches or improves forecasting accuracy on every cell when training noise is averaged out, with strict gains where control-state coupling is structurally present. Its main closed-loop gains appear in the RSCP TV task, where iterative SCP improves adaptation within the horizon and substantially stabilizes training; in CartPole TV, the gains are modest but consistent. In delayed re-planning experiments on the time-varying variants, the bilinear model degrades more gracefully under stale-plan execution, maintaining a consistent advantage on CartPole TV and a substantially larger robustness margin on RSCP TV. These results show that control-dependent latent dynamics provide a simple and effective mechanism for robust MPC under varying conditions.

Matan Pagi, Zohar Sorek

Psistar AI

Optimal Control Dynamical Systems Koopman Operator Learning Nonlinear MPC Robust Control Model Predictive Control+2

May 5, 2026

Neural Control: Adjoint Learning Through Equilibrium Constraints

Many physical AI tasks require sequential implicit computation: at each step, boundary controls are applied, and the resulting configuration is obtained by solving an equilibrium problem. This setting arises naturally in deformable object manipulation, where even bending a deformable linear object (DLO) to a target shape can be nonlinear and multistable: identical boundary conditions may produce different configurations depending on actuation history. Unlike explicit transition models, the control-to-configuration relation is implicit and history-dependent, making long-horizon learning and control brittle; backpropagating through iterative solves is also memory- and compute-intensive. We propose Neural Control, a boundary-control framework that propagates gradients through branch-dependent sequences of equilibrium solves rather than a single fixed point. Neural Control computes trajectory-dependent proxy gradients by differentiating equilibrium conditions with an adjoint formulation, avoiding solver unrolling while keeping forward rollouts on converged equilibria. Combined with receding-horizon continuation, Neural Control re-anchors optimization to realized equilibria and mitigates basin switching. We validate Neural Control on simulated and real DLO manipulation, compare against SPSA and iCEM, and demonstrate applicability to a learned DEQ-style implicit equilibrium model.

Dezhong Tong, Jiawen Wang, Hengyi Zhou +3

The Robotics Department, University of Michigan, Ann Arbor, US · The Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, US

Robotic Control Dynamical Systems Implicit Differentiation Deformable Object Manipulation Neural Network Control

Apr 18, 2026

Neural Network-Based Adaptive Event-Triggered Control for Dual-Arm Unmanned Aerial Manipulator Systems

This paper investigates the control problem of dual-arm unmanned aerial manipulator systems (DAUAMs). Strong coupling between the dual-arm and the multirotor platform, together with unmodeled dynamics and external disturbances, poses significant challenges to stable and accurate operation. An adaptive event-triggered control scheme with neural network-based approximation is proposed to address these issues while explicitly considering communication constraints. First, a dynamic model of the DAUAM system is derived, and a command-filter-based backstepping framework with error compensation is constructed. Then, a neural network is employed to approximate external frictions, and an event-triggered mechanism is designed to reduce the transmission frequency of control updates, thereby alleviating communication and energy burdens. Lyapunov-based analysis shows that all closed-loop signals remain bounded and that the tracking error converges to a neighborhood of the desired trajectory within a fixed time. Finally, experiments on a self-built DAUAM platform demonstrate that the proposed approach achieves accurate trajectory tracking.

Yang Wang, Hai Yu, Wei He +3

Institute of Robotics and Automatic Information System, College of Artificial Intelligence, and Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300350, China. · Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University, Shenzhen 518083, China.

Robot Trajectory Tracking Aerial Robotics Neural Network Control Feedback Control Quadrotor Control Event-Triggered Control+1

Apr 16, 2026

A Nonlinear Separation Principle via Contraction Theory: Applications to Neural Networks, Control, and Learning

This paper establishes a nonlinear separation principle based on contraction theory and derives sharp stability conditions for recurrent neural networks (RNNs). First, we introduce a nonlinear separation principle that guarantees global exponential stability for the interconnection of a contracting state-feedback controller and a contracting observer, alongside parametric extensions for robustness and equilibrium tracking. Second, we derive sharp linear matrix inequality (LMI) conditions that guarantee the contractivity of both firing rate and Hopfield neural network architectures. We establish structural relationships among these certificates-demonstrating that continuous-time models with monotone non-decreasing activations maximize the admissible weight space-and extend these stability guarantees to interconnected systems and Graph RNNs. Third, we combine our separation principle and LMI framework to solve the output reference tracking problem for RNN-modeled plants. We provide LMI synthesis methods for feedback controllers and observers, and rigorously design a low-gain integral controller to eliminate steady-state error. Finally, we derive an exact, unconstrained algebraic parameterization of our contraction LMIs to design highly expressive implicit neural networks, achieving competitive accuracy and parameter efficiency on standard image classification benchmarks.

Anand Gokhale, Anton V. Proskurnikov, Yu Kawano +1

Center for Control, Dynamical Systems, and Computation, UC Santa Barbara, Santa Barbara, CA 93106 USA · Department of Electronics and Telecommunications, Politecnico di Torino, Italy, 10129 · Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan

Dynamical Systems Contraction Theory Recurrent Neural Networks Neural Network Stability Neural Network Control

Apr 3, 2026

Neural Operators for Multi-Task Control and Adaptation

Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose solution is a mapping from task description (e.g., cost or dynamics functions) to optimal control law (e.g., feedback policy). We approximate these solution operators using a permutation-invariant neural operator architecture. Across a range of parametric optimal control environments and a locomotion benchmark, a single operator trained via behavioral cloning accurately approximates the solution operator and generalizes to unseen tasks, out-of-distribution settings, and varying amounts of task observations. We further show that the branch-trunk structure of our neural operator architecture enables efficient and flexible adaptation to new tasks. We develop structured adaptation strategies ranging from lightweight updates to full-network fine-tuning, achieving strong performance across different data and compute settings. Finally, we introduce meta-trained operator variants that optimize the initialization for few-shot adaptation. These methods enable rapid task adaptation with limited data and consistently outperform a popular meta-learning baseline. Together, our results demonstrate that neural operators provide a unified and efficient framework for multi-task control and adaptation.

David Sewell, Xingjian Li, Stepan Tretiakov +2

The University of Texas at Austin

Neural Network Control Optimal Control Neural Operators

Apr 1, 2026

Neural Robust Control on Lie Groups Using Contraction Methods (Extended Version)

In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce contraction conditions on the Lie group manifold. Sufficient conditions are derived for the existence of such an RCCM and neural controller, ensuring that the geometric constraints imposed by the manifold structure are respected while establishing a disturbance-dependent tube that bounds the output trajectories. As a case study, a feedback controller for a quadrotor is designed using the proposed framework. Its performance is evaluated using numerical simulations and compared with a geometric controller.

Yi Lok Lo, Longhao Qian, Hugh H. T. Liu

The authors are with the Institute for Aerospace Studies, University of Toronto, 4925 Dufferin St, North York, ON M3H 5T5, Canada

Neural Network Control Robust Control

Mar 23, 2026

Hebbian Attractor Networks for Robot Locomotion

Biological neural networks continuously adapt and modify themselves in response to experiences throughout their lifetime - a capability largely absent in artificial neural networks. Hebbian plasticity offers a promising path toward rapid adaptation in changing environments. Here, we introduce Hebbian Attractor Networks (HAN), a class of plastic neural networks in which local weight update normalization induces emergent attractor dynamics. Unlike prior approaches, HANs employ dual-timescale plasticity and temporal averaging of pre- and postsynaptic activations to induce either co-dynamic limit cycles or fixed-point weight attractors. Using simulated locomotion benchmarks, we gain insight into how Hebbian update frequency and activation averaging influence weight dynamics and control performance. Our results show that slower updates, combined with averaged pre- and postsynaptic activations, promote convergence to stable weight configurations, while faster updates yield oscillatory co-dynamic systems. We further demonstrate that these findings generalize to high-dimensional quadrupedal locomotion with a simulated Unitree Go1 robot. These results highlight how the timing of plasticity shapes neural dynamics in embodied systems, providing a principled characterization of the attractor regimes that emerge in self-modifying networks.

Alexander Dittrich, Fuda van Diggelen, Dario Floreano

Laboratory of Intelligent Systems, EPFL, Switzerland

Hebbian Learning Neural Network Training Dynamics Neural Network Control Robot Locomotion

Mar 23, 2026

Stability-Preserving Online Adaptation of Neural Closed-loop Maps

The growing complexity of modern control tasks calls for controllers that can react online as objectives and disturbances change, while preserving closed-loop stability. Recent approaches for improving the performance of nonlinear systems while preserving closed-loop stability rely on time-invariant recurrent neural-network controllers, but offer no principled way to update the controller during operation. Most importantly, switching from one stabilizing policy to another can itself destabilize the closed-loop. We address this problem by introducing a stability-preserving update mechanism for nonlinear, neural-network-based controllers. Each controller is modeled as a causal operator with bounded

\ell_p

-gain, and we derive gain-based conditions under which the controller may be updated online. These conditions yield two practical update schemes, time-scheduled and state-triggered, that guarantee the closed-loop remains

\ell_p

-stable after any number of updates. Our analysis further shows that stability is decoupled from controller optimality, allowing approximate or early-stopped controller synthesis. We demonstrate the approach on nonlinear systems with time-varying objectives and disturbances, and show consistent performance improvements over static and naive online baselines while guaranteeing stability.

Danilo Saccani, Luca Furieri, Giancarlo Ferrari-Trecate

Institute of Mechanical Engineering, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland. · Department of Engineering Science, University of Oxford, United Kingdom

Neural Network Control Feedback Control Neural Network Stability Adaptive Control

Mar 16, 2026

Generalizable Optimal Control with Transformers: One Policy Across Diverse Systems

Classical optimal control designs a separate controller for each plant. Even for the Linear Quadratic Regulator (LQR), every new model must be identified and its Riccati equation re-solved. We ask whether a single learned policy can instead serve an entire family of systems, and we show that one transformer can. We train the policy to imitate optimal LQR state feedback across a collection of heterogeneous Multiple-Input, Multiple-Output (MIMO) Linear Time-Invariant (LTI) systems that differ in their state and input dimensions and in their cost objectives. A shared representation lets the same parameters control every member of the family. It combines system-wise standardization, zero-padding and masking across dimensions, and an explicit encoding of the cost matrices. At run time, the policy maps a short window of recent states and the specified cost to a control action. It uses no plant matrices and identifies the dynamics implicitly from the state history. We evaluate on

28

simulated systems over

9{,}675

closed-loop rollouts, and no unstable rollout was observed in any of them. On the systems seen during training, it attains a median relative sub-optimality of

0.022\%

, even under parameter perturbations of up to

\pm10\%

. It transfers to unseen systems with lightweight fine-tuning, reaching a median sub-optimality of

0.19\%

. These results support transformers as generalizable near-optimal controllers for structured families of linear systems.

Turki Bin Mohaya, Maitham F. AL-Sunni, John M. Dolan +1

Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, USA

Optimal Control Neural Network Control Policy Learning

Mar 15, 2026

Data-Driven Physics Embedded Dynamics with Predictive Control and Reinforcement Learning for Quadrupeds

State of the art quadrupedal locomotion approaches integrate Model Predictive Control (MPC) with Reinforcement Learning (RL), enabling complex motion capabilities with planning and terrain adaptive behaviors. However, they often face compounding errors over long horizons and have limited interpretability due to the absence of physical inductive biases. We address these issues by integrating Lagrangian Neural Networks (LNNs) into an RL MPC framework, enabling physically consistent dynamics learning. At deployment, our inverse dynamics infinite horizon MPC scheme avoids costly matrix inversions, improving computational efficiency by up to 4x with minimal loss of task performance. We validate our framework through multiple ablations of the proposed LNN and its variants. We show improved sample efficiency, reduced long-horizon error, and faster real time planning compared to unstructured neural dynamics. Lastly, we also test our framework on the Unitree Go1 robot to show real world viability.

Prakrut Kotecha, Aditya Shirwatkar, Shishir Kolathaya

the Robert Bosch Center for Cyber-Physical Systems, Indian Institute of Science, Bengaluru. · the Robert Bosch Center for Cyber-Physical Systems and the Department of Computer Science & Automation, Indian Institute of Science, Bengaluru.

Lagrangian Neural Networks RL for Legged Locomotion Physics-Informed RL Robot Dynamics Learning Neural Network Control Model Predictive Control

Sep 30, 2025

Learn2Drive: A neural network-based framework for socially compliant automated vehicle control

This study introduces a novel control framework for adaptive cruise control (ACC) in automated driving, leveraging neural networks and physics-informed constraints. As automated vehicles (AVs) adopt advanced features like ACC, transportation systems are becoming increasingly intelligent and efficient. However, existing AV control strategies primarily focus on optimizing the performance of individual vehicles or platoons, often neglecting their interactions with human-driven vehicles (HVs) and the broader impact on traffic flow. This oversight can exacerbate congestion and reduce overall system efficiency. To address this critical research gap, we propose a neural network-based, socially compliant AV control framework that incorporates social value orientation (SVO). This framework enables AVs to account for their influence on HVs and traffic dynamics. By leveraging AVs as mobile traffic regulators, the proposed approach promotes adaptive driving behaviors that reduce congestion, improve traffic efficiency, and lower energy consumption. Numerical results demonstrate the effectiveness of the proposed method in adapting to varying traffic conditions, thereby enhancing system-wide efficiency. Specifically, when the AV's control mode shifts from prioritizing its own energy conservation to optimizing collective traffic flow efficiency, the controlled AV proactively adapts its acceleration profile. This prosocial behavior yields at least a 38.39% improvement in the average speed of downstream vehicles and effectively dampens traffic oscillations, demonstrating significant enhancements in system-wide dynamics. The implementation code is available https://github.com/lilab2024/Learn2Drive-SVO_v1.git.

Yuhui Liu, Samannita Halder, Shian Wang +1

Department of Civil Engineering Saint Louis University · Department of Electrical and Computer Engineering Saint Louis University · Department of Civil, Environmental, and Architectural Engineering The University of Kansas

Intelligent Transportation Systems Autonomous Driving Neural Network Control

Aug 2, 2024

Certified Robust Invariant Polytope Training in Neural Controlled ODEs

We propose a framework for training neural network controllers with certified robust forward invariant polytopes. First, we parameterize a family of lifted control systems in a higher dimensional space, where the original neural controlled system evolves on an invariant subspace of each lifted system. We use interval analysis and neural network verifiers to further construct a family of lifted embedding systems, carefully capturing the knowledge of this invariant subspace. If the vector field of any lifted embedding system satisfies a sign constraint at a single point, then a certain convex polytope of the original system is robustly forward invariant. Treating the neural network controller and the lifted system parameters as variables, we propose an algorithm to train controllers with certified forward invariant polytopes in the closed-loop control system. Through two examples, we demonstrate how the simplicity of the sign constraint allows our approach to scale with system dimension to over

50

states, and outperform state-of-the-art Lyapunov-based sampling approaches in runtime.

Akash Harapanahalli, Samuel Coogan

School of Electrical and Computer Engineering, Georgia Institute of Technology

Neural Controlled Differential Equations Robust Control Neural ODEs Neural Network Control