Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling

Mihaela-Larisa Clement; Mónika Farsang; Agnes Poks; Johannes Edelmann; Manfred Plöchl; Radu Grosu; Ezio Bartocci

cs.LGMar 25, 2026

Towards Safe Learning-Based Non-Linear Model Predictive Control through Recurrent Neural Network Modeling

Authors: Mihaela-Larisa Clement, Mónika Farsang, Agnes Poks, Johannes Edelmann, Manfred Plöchl, Radu Grosu, Ezio Bartocci

Organizations: Institute of Computer Engineering, TU Wien, Vienna, Austria · AIT Austrian Institute of Technology, Vienna, Austria · Institute of Mechanics and Mechatronics, TU Wien, Vienna, Austria

Abstract

The practical deployment of nonlinear model predictive control (NMPC) is often limited by online computation: solving a nonlinear program at high control rates can be expensive on embedded hardware, especially when models are complex or horizons are long. Learning-based NMPC approximations shift this computation offline but typically demand large expert datasets and costly training. We propose Sequential-AMPC, a sequential neural policy that generates MPC candidate control sequences by sharing parameters across the prediction horizon. For deployment, we wrap the policy in a safety-augmented online evaluation and fallback mechanism, yielding Safe Sequential-AMPC. Compared to a naive feedforward policy baseline across several benchmarks, Sequential-AMPC requires substantially fewer expert MPC rollouts and yields candidate sequences with higher feasibility rates and improved closed-loop safety. On high-dimensional systems, it also exhibits better learning dynamics and performance in fewer epochs while maintaining stable validation improvement where the feedforward baseline can stagnate.

Figures & tables

Fig. 1: Proposed Sequential Approximate MPC (Seq-AMPC) generates the horizon recursively with a shared simple RNN cell (hidden size 256) and output head, preserving the same final output format

\hat{U}_{t}\in\mathbb{R}^{N\times n_{u}}

. Seq-AMPC replaces

\Pi_{\text{AMPC}}

of [ 5 ] , resulting in a better-aligned controller, particularly in producing feasible horizon proposals. For deployment, Seq-AMPC is embedded in a safety-augmented online evaluation and fallback wrapper: candidate sequences are checked for feasibility and cost, and, if necessary, a safe fallback candidate and terminal controller are applied. We refer to the overall wrapped controller as Safe Seq-AMPC.

	AMPC		Seq-AMPC
	Epochs	Feas.	Epochs	Feas.
Task	[ $10^{3}$ ]	[%]	[ $10^{3}$ ]	[%]
Quadcopter	$100$	72	2.75	83.6
ST-Vehicle Kinematic	$7.9$	35.3	4.1	36.4
ST-Vehicle Dynamic	3.7	35.6	$7.9$	39.5

TABLE I: Open-loop comparison of naive AMPC (MLP) and naive Seq-AMPC (RNN) using 1,000 uniformly sampled points from a disjoint test dataset. Epochs denote the number of epochs until early stopping (patience =1,000) or termination

	AMPC		Seq-AMPC
Task	Safe [%]	Interv. [%]	Safe [%]	Interv. [%]
Quadcopter	84.8	8.2	89.1	78.8
ST-Vehicle Kinematic	92.2	90.6	92.9	90.0
ST-Vehicle Dynamic	54.1	94.4	58.7	95.6

TABLE II: Closed-loop comparison of Safe AMPC (MLP) and Safe Seq-AMPC (RNN) from 1,000 random feasible initial states. We report the percentage of safe rollouts (Safe) given by the naive NN and the percentage of rollouts where the safe candidate was applied (Interv.).

Panel of Figure 4 — Fig. 2: Learning curves of AMPC (MLP) and Seq-AMPC (RNN) on the single-track vehicle model tasks, for the kinematic model on the left and the dynamic model on the right. Seq-AMPCs converged to lower validation losses. Early stopping was used to avoid overfitting to the training datasets.

	Training		Closed-loop
Samples	Epochs [ $10^{3}$ ]	Feas. [%]	Safe [%]	Interv. [%]
1x	2.75	83.6	89.1	78.8
1/4x	$4.92$	83.5	87.5	78.4
1/10x	$6.59$	79.9	82.8	78.2

TABLE III: Quadcopter Seq-AMPC (RNN) scaling with decreasing training sample sizes. We report training compute (epochs), open-loop feasibility rate (Feas.), and closed-loop metrics (Safe, Interv.).

	AMPC			Seq-AMPC
Task	State	Term.	Cost	State	Term.	Cost
Quadcopter	72.5	2.6	40.6	9.2	98.5	44.5
ST-Vehicle Kinematic	0.0	90.5	57.7	0.0	89.5	64.0
ST-Vehicle Dynamic	0.0	90.0	79.6	0.0	90.0	71.6

TABLE IV: Reasons for applying the safe candidate on the vehicle benchmarks (multiple reasons may apply). Percentages are computed over rollouts where the safe candidate is applied.

Panel of Figure 7 — Fig. 3: Examples of a naive and a safe trajectory are shown. Two blue-colored blocks are the obstacles that the vehicle needs to avoid. The non-safe trajectory collides at the red cross while the safe trajectory is able to reach and stop at the target point without collision.

Nonlinear MPC

Nonlinear model predictive control (NMPC) repeatedly optimizes future actions using nonlinear system models and constraints.

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Jun 4, 2026J/K move · Enter open · S save

Amortized Nonlinear Model Predictive Control

Francesco Pillitteri, Alberto Bemporad

IMT School for Advanced Studies, Lucca, Italy

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

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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.

Abstract

Nonlinear MPC

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