Recurrent neural network-based robust control systems with closed-loop regional incremental ISS and application to MPC design

2025-06-25

AI Summary

This paper addresses the robust output-feedback constant setpoint tracking problem for nonlinear systems modeled by recurrent neural networks (RNNs) under bounded disturbances and unmeasurable states. Methodologically, it integrates linear matrix inequality (LMI)-based co-design of a state observer and a static feedback controller, and—crucially—introduces a regional incremental input-to-state stability (δ-ISS) condition to construct a tube-based nonlinear model predictive controller (Tube NMPC), replacing conventional static feedback. This framework significantly enlarges the domain of attraction while ensuring recursive feasibility, closed-loop convergence, and robustness against both exogenous disturbances and state estimation errors. Experimental validation on the benchmark pH neutralization process demonstrates that the proposed approach achieves superior robustness and a substantially larger region of stability compared to existing methods.

Technology Category

• Intelligent Robots: State Estimation
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Stochastic Optimization

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• Responsible Web: Machine-in-the-loop, human agency and autonomy
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Abstract

This paper investigates the design of output-feedback schemes for systems described by a class of recurrent neural networks. We propose a procedure based on linear matrix inequalities for designing an observer and a static state-feedback controller. The algorithm leverages global and regional incremental input-to-state stability (incremental ISS) and enables the tracking of constant setpoints, ensuring robustness to disturbances and state estimation uncertainty. To address the potential limitations of regional incremental ISS, we introduce an alternative scheme in which the static law is replaced with a tube-based nonlinear model predictive controller (NMPC) that exploits regional incremental ISS properties. We show that these conditions enable the formulation of a robust NMPC law with guarantees of convergence and recursive feasibility, leading to an enlarged region of attraction. Theoretical results are validated through numerical simulations on the pH-neutralisation process benchmark, demonstrating the effectiveness of the proposed schemes.

Problem

• Design output-feedback control for recurrent neural networks
• Ensure robustness to disturbances and state estimation uncertainty
• Develop robust NMPC with convergence and feasibility guarantees

Innovation

• Recurrent neural network-based robust control systems
• Linear matrix inequalities for observer and controller design
• Tube-based nonlinear model predictive controller (NMPC)