Nonlinear MPC design for incrementally ISS systems with application to GRU networks

TL;DR

This paper introduces a novel nonlinear MPC approach for incrementally ISS systems, particularly suited for controlling GRU neural networks, avoiding complex terminal conditions and ensuring stability through a minimum prediction horizon.

Contribution

It proposes a new NMPC formulation for incrementally ISS systems that simplifies stability guarantees and applies it to control and observe GRU networks.

Findings

Effective control of GRU networks demonstrated

No need for terminal ingredients in stability design

Good control performance on benchmark system

Abstract

This brief addresses the design of a Nonlinear Model Predictive Control (NMPC) strategy for exponentially incremental Input-to-State Stable (ISS) systems. In particular, a novel formulation is devised, which does not necessitate the onerous computation of terminal ingredients, but rather relies on the explicit definition of a minimum prediction horizon ensuring closed-loop stability. The designed methodology is particularly suited for the control of systems learned by Recurrent Neural Networks (RNNs), which are known for their enhanced modeling capabilities and for which the incremental ISS properties can be studied thanks to simple algebraic conditions. The approach is applied to Gated Recurrent Unit (GRU) networks, providing also a method for the design of a tailored state observer with convergence guarantees. The resulting control architecture is tested on a benchmark system, demonstrating its good control performances and efficient applicability.