Regularity Properties of Optimization-Based Controllers

TL;DR

This paper investigates the regularity properties of optimization-based controllers, analyzing their solution characteristics and implications for system stability and invariance under various assumptions.

Contribution

It provides comprehensive results on the regularity, existence, and uniqueness of solutions for optimization-based controllers, enhancing understanding of their stability and invariance properties.

Findings

Results on regularity conditions for controllers

Implications for solution existence and uniqueness

Guarantees for forward invariance in closed-loop systems

Abstract

This paper studies regularity properties of optimization-based controllers, which are obtained by solving optimization problems where the parameter is the system state and the optimization variable is the input to the system. Under a wide range of assumptions on the optimization problem data, we provide an exhaustive collection of results about their regularity, and examine their implications on the existence and uniqueness of solutions and the forward invariance guarantees for the resulting closed-loop systems. We discuss the broad relevance of the results in different areas of systems and controls.