Stochastic Stability via Robustness of Linear Systems

Authors: Benjamin Gravell, Tyler Summers

Published: 2021 (Conference Paper)

Source: IEEE Conference on Decision and Control (CDC)

DOI: 10.1109/CDC45484.2021.9683784

Summary

Algorithms for synthesizing mean-square stabilizing controllers for linear systems with multiplicative noise using robustness to static system parameter errors as a design-time device. Leverages theoretical results on the equivalence of robustness to structured determinstic and stochastic uncertainties.

Abstract

Robust stability and stochastic stability have separately seen intense study in control theory since its inception. In this work we establish relations between these properties for discrete-time systems. Specifically, we examine a robustness framework which models the inherent uncertainty and variation in the system dynamics which arise in model-based learning control methods such as adaptive control and reinforcement learning. We provide results which guarantee mean-square stability margins in terms of multiplicative noises which affect the nominal dynamics, as well as connections to prior work which together imply that robust stability and mean-square stability are, in a certain sense, equivalent.

Links

Primary

Paper personal.utdallas.edu

Standard

DOI 10.1109/CDC45484.2021.9683784

Alternate

ieeexplore.ieee.org ieeexplore.ieee.org

Tags

• Linear systems

• Stochastic stability

• Robust stability

• Adaptive control

• Optimal control

• Control theory

• Model-based

• Multiplicative noise

• Stability margin

• Problem Instances

• Linear matrix inequalities

• Semidefinite programming

• Lyapunov equation

• Generalized eigenvalue problem

• Linear time-invariant

• Perturbation

• Convex

• Polytope