Constrained Performance Boosting Control for Nonlinear Systems

Abstract

We present the Alternating Direction Method of Multipliers (ADMM) for Performance Boosting (PB), an approach for designing neural controllers for stable nonlinear systems subject to state and input constraints. The method builds on an internal model control formulation of PB. In this setting, the controller is parametrized as a stable neural operator, so closed-loop stability is guaranteed by construction, and its weights are trained offline to improve performance. To provide a systematic procedure for promoting constraint satisfaction during training, we reformulate the finite-horizon problem of the PB formulation by introducing auxiliary state and input trajectories. This augmentation allows us to cast an ADMM-based algorithm that alternates between two steps: a gradient-descent-based update of the controller parameters, having the same structure as the PB training problem without explicit constraints, and a projection step that promotes the trajectory feasibility. As a result, this procedure handles constraints during training without altering the controller architecture or compromising its stability-by-design guarantees. Indeed, the stability guarantee follows from the chosen stable controller parametrization, which is not changed in our framework with respect to the foundational PB formulation, and is independent of ADMM convergence. At the same time, this closed-loop stability guarantee does not imply performance optimality or closed-loop constraint satisfaction, which depend on the convergence of ADMM-PB, which is not yet guaranteed in this work. Our numerical results show that, compared with a baseline based on barrier-inspired soft penalties in the loss, ADMM-PB achieves lower constraint violations, at the price of more conservative closed-loop behavior.

Accepted for publication in Engineering Applications of Artificial Intelligence - Special issue:'TC2.4 Optimal Control'