Certainty Equivalent Quadratic Control for Markov Jump Systems

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.

arXiv comment17 pages, 8 figures

References in corpus (4)

• Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification
• Naive Exploration is Optimal for Online LQR
• Efficient Optimistic Exploration in Linear-Quadratic Regulators via Lagrangian Relaxation
• Policy Optimization for Markovian Jump Linear Quadratic Control: Gradient-Based Methods and Global Convergence

Cited by in corpus (1)

• Identification and Adaptive Control of Markov Jump Systems: Sample Complexity and Regret Bounds