Closed-Loop Finite-Time Analysis of Suboptimal Online Control

TL;DR

This paper develops finite-time performance guarantees for suboptimal control methods in nonlinear, time-varying systems, enabling better control design under computational constraints.

Contribution

It provides a novel finite-time analysis framework for suboptimal control, linking stability properties to performance bounds without requiring global smoothness.

Findings

Finite-time performance bounds are established for suboptimal control methods.

Exponential incremental input-to-state stability implies exponential stability for nonlinear systems.

The approach is demonstrated on a suboptimal model predictive control example.

Abstract

Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. Although these methods are ubiquitous, their transient performance remains relatively unstudied. We consider the control of discrete-time, nonlinear time-varying dynamical systems and establish sufficient conditions to analyze the finite-time closed-loop performance of such methods in terms of the additional cost incurred due to suboptimality. Finite-time guarantees allow the control design to distribute a limited computational budget over a time horizon and estimate the on-the-go loss in performance due to suboptimality. We study exponential incremental input-to-state stabilizing policies and show that for nonlinear systems, under some mild conditions, this property is directly implied by exponential stability without further assumptions on global smoothness. The analysis is showcased on a suboptimal model predictive control use case.