Certainty Equivalent Quadratic Control for Markov Jump Systems

TL;DR

This paper analyzes the robustness of certainty equivalent quadratic control for Markov jump systems, providing explicit bounds on how parameter uncertainties affect the control solution and optimal cost.

Contribution

It offers new theoretical bounds on the sensitivity of control solutions and costs to parameter uncertainties in Markov jump linear systems.

Findings

Explicit perturbation bounds for Riccati solutions

Bounds decay as uncertainties decrease

Enhanced understanding of robustness in MJS control

Abstract

Real-world control applications often involve complex dynamics subject to abrupt changes or variations. Markov jump linear systems (MJS) provide a rich framework for modeling such dynamics. Despite an extensive history, theoretical understanding of parameter sensitivities of MJS control is somewhat lacking. Motivated by this, we investigate robustness aspects of certainty equivalent model-based optimal control for MJS with quadratic cost function. Given the uncertainty in the system matrices and in the Markov transition matrix is bounded by $\epsilon$ and $\eta$ respectively, robustness results are established for (i) the solution to coupled Riccati equations and (ii) the optimal cost, by providing explicit perturbation bounds which decay as $\mathcal{O}(\epsilon + \eta)$ and $\mathcal{O}((\epsilon + \eta)^2)$ respectively.