Recurrent neural network-based robust control systems with closed-loop regional incremental ISS and application to MPC design
This work addresses robust control for neural network-based systems, offering incremental improvements in stability guarantees for applications like process control.
The paper tackles the design of robust output-feedback control for recurrent neural network systems, proposing methods based on linear matrix inequalities and nonlinear model predictive control to ensure stability and robustness, validated with simulations on a pH-neutralisation benchmark.
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.