Certainty Equivalent Quadratic Control for Markov Jump Systems
This work addresses robustness issues in control theory for systems with abrupt changes, providing theoretical guarantees for practitioners, but it appears incremental as it builds on existing MJS frameworks.
The paper tackled the problem of robustness in certainty equivalent model-based optimal control for Markov jump linear systems with quadratic cost, establishing explicit perturbation bounds for the solution to coupled Riccati equations and the optimal cost that decay as O(ε+η) and O((ε+η)^2) respectively.
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 $ε$ and $η$ 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 $\mathcal{O}(ε+ η)$ and $\mathcal{O}((ε+ η)^2)$ respectively.