Nonlinear MPC design for incrementally ISS systems with application to GRU networks
This work addresses control design for systems modeled by recurrent neural networks, offering a more efficient method for practitioners, but it is incremental as it builds on existing ISS and NMPC frameworks.
The paper tackles the design of a Nonlinear Model Predictive Control (NMPC) strategy for exponentially incremental Input-to-State Stable (ISS) systems, eliminating the need for terminal ingredients by using a minimum prediction horizon, and applies it to Gated Recurrent Unit (GRU) networks, demonstrating good control performance on a benchmark system.
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.