Constrained Performance Boosting Control for Nonlinear Systems via ADMM

TL;DR

This paper introduces ADMM-PB, a novel control design method for nonlinear systems that guarantees stability and constraint satisfaction, improving performance over traditional barrier-based approaches.

Contribution

It integrates neural-network controller design with ADMM to explicitly handle input and state constraints without altering the controller structure.

Findings

Lower constraint violations compared to barrier-based methods.

Slightly more cautious closed-loop behaviors achieved.

Demonstrated effectiveness through numerical simulations.

Abstract

We present the Alternating Direction Method of Multipliers for Performance Boosting (ADMM-PB), an approach to design performance boosting controllers for stable or pre-stabilized nonlinear systems, while explicitly seeking input and state constraint satisfaction. Rooted on a recently proposed approach for designing neural-network controllers that guarantees closed-loop stability by design while minimizing generic cost functions, our strategy integrates it within an alternating direction method of multipliers routine to seek constraint handling without modifying the controller structure of the aforementioned seminal strategy. Our numerical results showcase the advantages of the proposed approach over a baseline penalizing constraint violation through barrier-like terms in the cost, indicating that ADMM-PB can lead to considerably lower constraint violations at the price of inducing slightly more cautious closed-loop behaviors.