Optimal Control

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Overview

Optimal control asks how to steer a system over time toward goals while minimizing costs such as energy, time, or tracking error and respecting limits on actions and states. Classical approaches include Pontryagin’s maximum principle, dynamic programming and Hamilton–Jacobi–Bellman equations, and numerical methods such as direct collocation, differential dynamic programming, and model predictive control. Recent work also uses reinforcement learning, differentiable simulators, and neural surrogates to speed up planning or handle complex models, with applications ranging from robotics and aerospace to energy systems and PDEs. A central challenge is making these methods fast enough for real-time, high-dimensional tasks without losing reliability when models are uncertain or safety guarantees are needed.

Latest papers

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139 papers11 papers in the last four weeks, up 22% on the four weeks before. 0.1% of all new papers.

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 2828 simulated systems over 9,6759{,}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%0.022\%, even under parameter perturbations of up to ±10%\pm10\%. It transfers to unseen systems with lightweight fine-tuning, reaching a median sub-optimality of 0.19%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 ControlNeural Network ControlPolicy Learning
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Mar 13, 2026

State-space models through the lens of ensemble control

State-space models (SSMs) are effective architectures for sequential modeling, but a rigorous theoretical understanding of their training dynamics is still lacking. We formulate continuous-time SSM parameter-path optimization as an ensemble optimal control problem: each input sequence generates a corresponding state trajectory in the ensemble, while the trainable parameter path forms a common control shared by all trajectories. Within this formulation, model evaluation is represented by the forward state equation and backward sensitivity propagation by the corresponding adjoint equation. We show that the Hamiltonian gradient with respect to the control variable represents the negative first-variation density of the reduced ensemble objective. Using this representation, we analyze a Bregman mirror-descent scheme for the continuous-time ensemble objective; in Euclidean geometry this reduces to functional projected gradient descent. State-adjoint and Hamiltonian-gradient stability yield two-sided relative curvature of the reduced objective and relative convexity under sufficient regularization. We further show that in the relatively convex regime the optimal-control problem admits a minimizer, which is unique under relative strong convexity. For SSMs, the explicit stability-generated defect κstabSSMκ_{\mathrm{stab}}^{\mathrm{SSM}} gives an O(1/k)O(1/k) objective rate at τ=κstabSSMτ=κ_{\mathrm{stab}}^{\mathrm{SSM}} and geometric convergence to the unique minimizer for τ>κstabSSMτ>κ_{\mathrm{stab}}^{\mathrm{SSM}}, under the stated stepsize condition.

Ye Feng, Jianfeng Lu

Mirror DescentOptimal ControlState Space Models
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Mar 11, 2026

Parallel-in-Time Nonlinear Optimal Control via GPU-native Sequential Convex Programming

Real-time solution of nonlinear optimal control problems remains challenging on embedded robotic hardware, where conventional solvers often rely on global sparse linear algebra or sequential recursions that are difficult to map efficiently to massively parallel processors. This paper presents ucenter, a GPU-native Sequential Convex Programming (SCP) framework for nonlinear optimal control. At each SCP iteration, nonlinear dynamics are linearized around a nominal trajectory, and the resulting convexified subproblem is solved by a consensus Alternating Direction Method of Multipliers (ADMM) scheme. The temporal splitting replaces global sparse Karush-Kuhn-Tucker factorizations with independent per-node dense solves, closed-form dynamic consistency updates, and analytical projections onto convex constraint sets. Both the outer SCP loop and the inner ADMM subproblem are executed entirely on the GPU, enabling efficient optimization. The proposed solver is evaluated on quadrotor obstacle avoidance and Mars powered descent problems using an NVIDIA Jetson AGX Orin edge platform. Benchmarking against a CPU-parallel iLQR baseline in randomized environments reveals that the GPU implementation achieves over 100 Hz batched planning throughput, a 4.1x speedup, and a 51% reduction in energy consumption, while consistently maintaining low nonlinear dynamics defects. The framework exposes reusable GPU-parallel optimization primitives that can be specialized to a wide variety of complex nonlinear optimal control settings, as demonstrated by the scenario-based robust MPC and batched Monte Carlo generation tasks.

Yilin Zou, Zhong Zhang, Maxime Robic +1

School of Aerospace Engineering, Tsinghua University, 100084 Beijing, China. · Department of Aerospace Science and Technology, Politecnico di Milano, 20156 Milan, Italy.

Optimal ControlGPU AccelerationNonconvex OptimizationModel Predictive Control
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Mar 10, 2026

An Optimal Control Approach To Transformer Training

In this paper, we develop a rigorous optimal control-theoretic approach to Transformer training that respects key structural constraints such as (i) realized-input-independence during execution, (ii) the ensemble control nature of the problem, and (iii) positional dependence. We model the Transformer architecture as a discrete-time controlled particle system with shared actions, exhibiting noise-free controlled McKean--Vlasov dynamics, and we show that lifting the dynamics to probability measures produces a fully-observed Markov decision process (MDP). Positional encodings are incorporated into the state space to preserve the sequence order under lifting. Using the dynamic programming principle, we establish the existence of globally optimal policies under mild assumptions of compactness. We further prove that closed-loop policies in the lifted problem is equivalent to an initial-distribution dependent open-loop policy, which are realized-input-independent and compatible with standard Transformer training. To train a Transformer, we propose a triply quantized training procedure for the lifted MDP by quantizing the state space, the space of probability measures, and the action space, and show that any optimal policy for the triply quantized model is near-optimal for the original training problem. Finally, we establish stability and empirical consistency properties of the lifted model by showing that the value function is continuous with respect to the perturbations of the initial empirical measures and convergence of policies as the data size increases. This approach provides a globally optimal and robust theoretical alternative to gradient-based training without requiring smoothness or convexity.

Kağan Akman, Naci Saldi, Serdar Yüksel

Department of Mathematics, Bilkent University, Ankara, 06800, Turkey · Department of Mathematics and Statistics, Queen’s University, Kingston K7L 3N6, ON, Canada

TransformerTransformer Training DynamicsOptimal Control
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Mar 6, 2026

Receding-Horizon Nullspace Optimization for Actuation-Aware Control Allocation in Omnidirectional UAVs

Fully actuated omnidirectional UAVs enable independent control of forces and torques along all six degrees of freedom, broadening the operational envelope for agile flight and aerial interaction tasks. However, conventional control allocation methods neglect the asymmetric dynamics of the onboard actuators, which can induce oscillatory motor commands and degrade trajectory tracking during dynamic maneuvers. This work proposes a receding-horizon, actuation-aware allocation strategy that explicitly incorporates asymmetric motor dynamics and exploits the redundancy of over-actuated platforms through nullspace optimization. By forward-simulating the closed-loop system over a prediction horizon, the method anticipates actuator-induced oscillations and suppresses them through smooth redistribution of motor commands, while preserving the desired body wrench exactly. The approach is formulated as a constrained optimal control problem solved online via Constrained iterative LQR. Simulation results on the OmniOcta platform demonstrate that the proposed method significantly reduces motor command oscillations compared to a conventional single-step quadratic programming allocator, yielding improved trajectory tracking in both position and orientation.

Riccardo Pretto, Mahmoud Hamandi, Abdullah Mohamed Ali +3

Tampere University, Finland · New York University Abu Dhabi, Abu Dhabi, UAE

Aerial RoboticsOptimal ControlModel Predictive Control
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Mar 5, 2026

Accelerating Sampling-Based Control via Learned Linear Koopman Dynamics

This paper presents an efficient model predictive path integral (MPPI) control framework for systems with complex nonlinear dynamics. To improve the computational efficiency of classic MPPI while preserving control performance, we replace the nonlinear dynamics used for trajectory propagation with a learned linear deep Koopman operator (DKO) model, enabling faster rollout and more efficient trajectory sampling. The DKO dynamics are learned directly from interaction data, eliminating the need for analytical system models. The resulting controller, termed MPPI-DK, is evaluated in simulation on pendulum balancing and surface vehicle navigation tasks, and validated on hardware through reference-tracking experiments on a quadruped robot. Experimental results demonstrate that MPPI-DK achieves control performance close to MPPI with true dynamics while substantially reducing computational cost, enabling efficient real-time control on robotic platforms.

Wenjian Hao, Yuxuan Fang, Zehui Lu +1

independent researcher

Robotic ControlRobot Trajectory TrackingMPPI ControlOptimal Control
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Feb 23, 2026

RAmmStein: Regime Adaptation in Mean-reverting Markets with Stein Thresholds -- Optimal Impulse Control in Concentrated AMMs

Concentrated liquidity provision in decentralized exchanges presents a fundamental Impulse Control problem. Liquidity Providers (LPs) face a non-trivial trade-off between maximizing fee accrual through tight price-range concentration and minimizing the friction costs of rebalancing, including gas fees and swap slippage. Existing methods typically employ heuristic or threshold strategies that fail to account for market dynamics. This paper formulates liquidity management as an optimal control problem and derives the corresponding Hamilton-Jacobi-Bellman quasi-variational inequality (HJB-QVI). We present an approximate solution RAmmStein, a Deep Reinforcement Learning method that incorporates the mean-reversion speed (theta) of an Ornstein-Uhlenbeck process among other features as input to the model. We demonstrate that the agent learns to separate the state space into regions of action and inaction. We further extend the framework with RAmmStein-Width, which jointly optimizes rebalancing timing and position width via a 6-action DDQN. We evaluate the framework using high-frequency 1Hz Coinbase trade data comprising over 6.8M trades on a realistic environment (10M TVL, 1% default width). Experimental results show that RAmmStein achieves a net ROI of 1.60%, the highest among all realistic (non-omniscient) strategies, while greedy strategies lose up to -8.4% to gas costs. Notably, the agent reduces rebalancing frequency by 85% compared to greedy rebalancing. RAmmStein-Width discovers extreme parsimony on its own, executing only 9 rebalances and $40 in gas, and degrades more slowly than all active strategies at elevated gas costs. Our results demonstrate that regime-aware laziness can significantly improve capital efficiency by preserving the returns that would otherwise be eroded by the operational costs.

Pranay Anchuri

Offchain Labs

HJB EquationsDecentralized FinanceOptimal ControlStochastic Optimal ControlDeep Q-Learning
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Feb 12, 2026

Learning to Control: The iUzawa-Net for Nonsmooth Optimal Control of Linear PDEs

We propose an optimization-informed deep neural network approach, named iUzawa-Net, aiming for the first solver that enables real-time solutions for a class of nonsmooth optimal control problems of linear partial differential equations (PDEs). The iUzawa-Net unrolls an inexact Uzawa method for saddle point problems, replacing classical preconditioners and PDE solvers with specifically designed learnable neural networks. We prove universal approximation properties and establish the asymptotic ε\varepsilon-optimality for the iUzawa-Net, and validate its promising numerical efficiency through nonsmooth elliptic and parabolic optimal control problems. Our techniques offer a versatile framework for designing and analyzing various optimization-informed deep learning approaches to optimal control and other PDE-constrained optimization problems. The proposed learning-to-control approach synergizes model-based optimization algorithms and data-driven deep learning techniques, inheriting the merits of both methodologies.

Yongcun Song, Xiaoming Yuan, Hangrui Yue +1

Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371, Singapore. · Department of Mathematics, The University of Hong Kong, Pok Fu Lam, Hong Kong SAR, China. · School of Mathematical Sciences, Nankai University, Tianjin 300071, China.

Optimal ControlConstrained OptimizationNeural Network OptimizationAlgorithm Unrolling
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Feb 3, 2026

Soft Swing-up: Benchmarking Model-Based Optimal Control for Rigid-Soft Underactuated Systems

Continuum soft robots are inherently underactuated and subject to intrinsic input constraints, making dynamic control particularly challenging, especially in hybrid rigid-soft robots. While most existing methods focus on quasi-static behaviors, dynamic tasks such as swing-up require accurate exploitation of continuum dynamics. This has led to studies on simple low-order template systems that often fail to capture the complexity of real continuum deformations. Model-based optimal control offers a systematic solution; however, its application to rigid-soft robots is often limited by the computational cost and inaccuracy of numerical differentiation for high-dimensional models. Building on recent advances in the Geometric Variable Strain model that enable analytical derivatives, this work investigates three optimal control strategies for underactuated soft systems -- Direct Collocation, Differential Dynamic Programming, and Nonlinear Model Predictive Control -- to perform dynamic swing-up tasks. To address stiff continuum dynamics and constrained actuation, implicit integration schemes and warm-start strategies are employed to improve numerical robustness and computational efficiency. The methods are evaluated in simulation on three Rigid-Soft and high-order soft benchmark systems -- the Soft Cart-Pole, the Soft Pendubot, and the Soft Furuta Pendulum -- highlighting their performance and computational trade-offs.

Daniele Caradonna, Nikhil Nair, Anup Teejo Mathew +5

The BioRobotics Institute, Scuola Superiore Sant’Anna, Pisa, Italy · Department of Excellence in Robotics and AI, Scuola Superiore Sant’Anna, Pisa, Italy · Department of Cognitive Robotics, Delft University of Technology, 2628 CN Delft, The Netherlands +3

Robotic ControlModel Predictive ControlContinuum Robot ControlOptimal ControlSoft Robotics
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Jan 30, 2026

Emergence of Physical Intelligence via Controllable Information Production

Intrinsic Motivation (IM) aims to train agents without external rewards, enabling useful behavior to emerge from the agent's interaction with its environment alone. However, the dominant IM approaches rely on information-theoretic quantities with designer-chosen variables, introducing bias and lacking a principled connection to dynamics or optimal control (OC). We introduce Controllable Information Production (CIP), a novel IM method explicitly grounded in dynamical systems and OC. CIP measures the rate at which an agent produces information, capturing controllable complexity without external knowledge or bias. CIP unifies IM and OC into a single framework, formalizing physical intelligence as the control of information production. It further reveals connections between the structure of the value function and Kolmogorov-Sinai entropy. CIP consistently outperforms prior IM methods on standard benchmarks in robot learning and solves tasks they fail on, including humanoid self-righting. These results support an organizing principle: that physical intelligence emerges from driving systems toward the edge of controllable chaos.

Tristan Shah, Stas Tiomkin

Department of Computer Science, Texas Tech University

Robotic RLReinforcement LearningOptimal Control
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Dec 30, 2025

Soft Fitted Q-Iteration without Bellman Completeness: Occupancy Reweighting and Temperature Annealing

Fitted QQ-iteration (FQI) is a standard regression-based method for optimal control in offline reinforcement learning, but its stability under function approximation often relies on Bellman completeness, which requires Bellman images of the fitted class to remain in the class. We study Kullback--Leibler (KL)-regularized, or soft, FQI relative to a fixed reference policy without this assumption. Our key insight is that soft control locally inherits the contraction of policy evaluation in a discounted-occupancy norm. At the soft-optimal fixed point, the linearization of the soft Bellman operator is exactly the Bellman operator for the soft-optimal policy, which contracts in its discounted-occupancy norm; projection in the same norm preserves this contraction. Standard soft FQI instead projects under the offline state-action distribution and need not preserve this property. Motivated by this observation, we propose occupancy-reweighted soft FQI, which retains standard Bellman targets and least-squares updates while reweighting regressions by discounted-occupancy ratios induced by the current soft policy. Under QQ-function realizability and local regularity, we establish local contraction and finite-sample convergence with estimated ratios, without Bellman completeness. We then use temperature annealing to convert the local result into global convergence from arbitrary initialization: sufficiently high temperature provides a globally contractive starting regime, while gradual cooling connects successive local contraction regions to any prescribed positive target temperature. Under an action-gap margin condition, switching at a fixed positive temperature to hard FQI with refreshed occupancy weights also yields population and finite-sample convergence to the unregularized optimum.

Lars van der Laan, Nathan Kallus

Department of Statistics, University of Washington · Netflix · Cornell University

Reinforcement LearningKL-Regularized RLQ-LearningOffline RLMaximum Entropy RLPolicy Learning+1
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Sep 24, 2025

Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control

Data-driven control increasingly relies on deep models for complex systems whose first-principles models are difficult to obtain. For reliable deployment, however, learned dynamics should respect physical structure and lead to tractable optimal control. We introduce sign constraints, namely sign restrictions on Jacobian entries, as a unified description of monotonicity, positivity, and sign-definiteness. For exactly linearizable deep dynamics, we provide structural conditions and neural-network parameterizations that enforce these constraints by construction. The same structure also allows model predictive control to be formulated as a convex quadratic program or as a convex relaxation, yielding a unique optimizer and a Lipschitz continuous control law. Applications to a three-tank system and a hybrid powertrain demonstrate that the proposed approach offers improved extrapolation performance and smoother control inputs compared with competing nonconvex formulations.

Teruki Kato, Ryotaro Shima, Kenji Kashima

Toyota Central R&D Labs., Inc., 41-1 Yokomichi, Nagakute, Aichi, Japan. · Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, Japan

Data-Driven ControlModel Predictive ControlOptimal Control
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Aug 18, 2025

Observed Control - Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons

This work highlights the duality between state estimation and model predictive control. A model predictive controller, observed control, is presented that uses this duality to efficiently compute control actions with linear prediction horizon length scalability. The proposed algorithms provide exceptional computational efficiency, adaptive time horizon lengths, and early optimization termination criteria. The use of Kalman smoothers as the backend optimization framework provides for a familiar implementation supported by strong theoretical guarantees. Additionally, a formulation is presented that separates linear model predictive control into purely reactive and anticipatory components, enabling any-time any-horizon observed control while ensuring controller stability for short time horizons. Finally, the method is extended to nonlinear systems and non-quadratic cost functions to obtain locally-optimal control of complex systems while maintaining linear prediction horizon scalability and adaptive-horizon capabilities.

Eugene T. Hamzezadeh, Andrew J. Petruska

Colorado School of Mines, Golden, CO 80401, USA

Nonlinear MPCModel Predictive ControlOptimal ControlAdaptive MPC
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Jul 10, 2025

A statistical physics framework for optimal learning

Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can dramatically affect performance. Yet, theoretical understanding of optimal learning strategies remains sparse, especially due to the intricate interplay between evolving metaparameters and nonlinear learning dynamics. The search for optimal protocols is further hindered by the high dimensionality of the learning space, often resulting in predominantly heuristic, difficult to interpret, and computationally demanding solutions. Here, we combine statistical physics with control theory in a unified theoretical framework to identify optimal learning protocols in prototypical neural network models. In the high-dimensional limit, we derive closed-form ordinary differential equations that track online stochastic gradient descent through low-dimensional order parameters. We formulate the design of learning protocols as an optimal control problem directly on the dynamics of the order parameters with the goal of minimizing the generalization error. This formulation encompasses a variety of learning scenarios, optimization constraints, and control budgets. We apply it to representative cases, including optimal curricula, adaptive dropout regularization and noise schedules in denoising autoencoders. We find nontrivial yet interpretable strategies highlighting how optimal protocols mediate learning trade-offs. Our results establish a principled foundation for understanding and designing optimal protocols and suggest a path toward a theory of meta-learning grounded in statistical physics.

Francesca Mignacco, Francesco Mori

1Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ 08544, USA · 2Graduate Center, City University of New York, New York, NY 10016, USA · Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA

Statistical Physics of LearningNeural Network Training DynamicsStatistical Learning TheoryOptimal ControlHyperparameter Optimization
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Jun 9, 2025

Continuous Policy and Value Iteration for Stochastic Control Problems and Its Convergence

We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics. This framework applies to both the entropy-regularized relaxed control problems and the classical control problems, with infinite horizon. We establish policy improvement and demonstrate convergence to the optimal control under the monotonicity condition of the Hamiltonian. By utilizing Langevin-type stochastic differential equations for continuous updates along the policy iteration direction, our approach enables the use of distribution sampling and non-convex learning techniques in machine learning to optimize the value function and identify the optimal control simultaneously.

Qi Feng, Gu Wang

Department of Mathematics, Florida State University, Tallahassee, 32306 · Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA 01609

Stochastic Optimal ControlPolicy IterationOptimal Control
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Jun 8, 2025

BR-MPPI: Barrier-Rate Guided MPPI for Enforcing Multiple Inequality Constraints with Learned Signed Distance Fields

Model Predictive Path Integral (MPPI) control provides a sampling-based framework for optimal control, while Control Barrier Functions (CBFs) provide a principled means of enforcing safety constraints. We introduce BR-MPPI, which integrates CBF-like conditions into MPPI's control sampling procedure. CBFs impose inequality constraints that bound the rate of change of barrier functions using a class-K function of the barrier value. We instead impose the CBF condition as an equality constraint using a parametric linear class-K function and augment the system state with its parameter. The parameter's time derivative serves as an additional control input optimized by MPPI. We further design a cost function that promotes parameter values consistent with Nagumo's condition at the safe-set boundary, thereby encouraging safety. The resulting multiple state- and control-dependent equality constraints pose a challenge for random control sampling. We address this through state transformations and control projections inspired by manifold path planning that map sampled controls onto the constraint manifold. We also incorporate learned signed distance fields to represent robot geometry and reduce computation time. Simulations demonstrate improved sample efficiency over vanilla MPPI and higher navigation success rates across five robot models compared with safety-oriented MPPI variants. Hardware experiments on a quadrotor further demonstrate the method's ability to navigate constrained environments near safe-set boundaries.

Hardik Parwana, Taekyung Kim, Kehan Long +4

Robotics Department, University of Michigan, Ann Arbor, MI 48109, USA · Contextual Robotics Institute, University of California San Diego, La Jolla, CA 92093, USA. · Toyota Motor North America, Research & Development, Ann Arbor, MI 48105, USA.

Constrained Motion PlanningControl Barrier FunctionsSafe Robot NavigationMPPI ControlOptimal Control
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Feb 10, 2025

Rough Stochastic Pontryagin Maximum Principle and an Indirect Shooting Method

We derive first-order Pontryagin optimality conditions for stochastic optimal control with deterministic controls for systems modeled by rough differential equations (RDE) driven by Gaussian rough paths. This Pontryagin Maximum Principle (PMP) applies to systems following stochastic differential equations (SDE) driven by Brownian motion, yet it does not rely on forward-backward SDEs and involves the same Hamiltonian as the deterministic PMP. The proof consists of first deriving various integrable error bounds for solutions to nonlinear and linear RDEs by leveraging recent results on Gaussian rough paths. The PMP then follows using standard techniques based on needle-like variations. As an application, we propose the first indirect shooting method for nonlinear stochastic optimal control and show that it converges 10x faster than a direct method on a stabilization task.

Thomas Lew

Toyota Research Institute

Stochastic Differential EquationsStochastic Optimal ControlOptimal Control
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Jan 26, 2025

Safe Learning Control with Optimality and Stability Guarantees

Merely pursuing performance may adversely affect safety, while a conservative policy for safe exploration will degrade the performance. How to guarantee both safety and performance in learning-based control problems is an interesting yet challenging issue. This paper aims to enhance system performance with a safety guarantee by solving reinforcement learning (RL)-based optimal control problems for nonlinear systems subject to high-relative-degree state constraints and unknown time-varying disturbance/actuator faults. A new type of control barrier functions (CBFs), termed high-order reciprocal-based control barrier function, is proposed to handle high-relative-degree constraints, which extends the design of CBFs to enforce robust safety without knowing the disturbance bound. The concept of gradient similarity is proposed to quantify the relationship between safety and performance. Finally, gradient manipulation and adaptive mechanisms are introduced in the model-based safe RL framework to enhance the performance with a safety guarantee. Two simulation examples illustrate the efficacy of the proposed algorithms.

Xinyang Wang, Hongwei Zhang, Shimin Wang +2

Shenzhen Key Lab for Advanced Motion Control and Modern Automation Equipments, School of Intelligence Science and Engineering, Harbin Institute of Technology, Shenzhen, Guangdong 518055, China · School of Data Science, Lingnan University, Hong Kong · School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, with M3S, SMART, and with MIT CSAIL +1

Control Barrier FunctionsRobust ControlSafe RLOptimal ControlModel-Based RL
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Oct 19, 2023

Entropic perspective on AI resilience, data-minimal learning and optimal control

Behind the general terms like adversarial attacks and generative adversarial networks (GANs), such criteria as AI resilience and AI robustness gained a crucial importance, in trying to make the emergent AI tools reliable, energy-efficient and safe. From mathematical perspective, these problems boil down to finding a mathematically-sound quantification of the smallest-sufficient amounts of the perturbations of function arguments that lead to the largest possible perturbations of the approximated function values. Here, the entropy-optimising perspective on adversarial algorithms from Artificial Intelligence (AI) is proposed to attack this problem. It is shown that adopting this perspective helps proving computational conditions for the global optimality and uniqueness of adversarial attacks based on cheaply-verifiable mathematical criteria. Further, it is shown how this perspective can be used for developing self-attacking learning algorithms, that generate optimal new data points for training, replacing one of the trained agents with this mathematical criterium. On a broad selection of various synthetic and real-life problems from hydrodynamics and biomedicine, it is shown that such self-attacking learning algorithms allow training orders-of-magnitude simpler and cheaper models with superior performance - and can be used to directly train the optimal controls in complex systems, requiring only a small fraction of the training data and outperforming the as-comprehensive-as-the-author-was-able-to-find set of contemporary AI tools (like boosted Random Forests, deep neural networks, foundational models based on transformer architectures, etc.) in complexity (measured as the model descriptor length) and predictive performance.}

Illia Horenko

Chair for Mathematics of AI, Faculty of Mathematics, RPTU Kaiserslautern-Landau, Gottlieb-Daimler-Str. 48, Kaiserslautern, 67663, Germany.

Data-Efficient LearningAdversarial RobustnessAdversarial AttacksOptimal Control
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