Jump LQR Systems With Unknown Transition Probabilities

This article develops a robust linear quadratic regulator (LQR) approach applicable to nonhomogeneous Markov jump linear systems with uncertain transition probability distributions. The stochastic control problem is investigated under two equivalent formulations, using i) minimax optimization theory, and ii) a total variation distance metric as a tool for codifying the level of uncertainty of the jump process. By following a dynamic programming approach, a robust optimal controller is derived, which in addition to minimizing the quadratic cost, it also restricts the influence of uncertainty. A solution procedure for the LQR problem is also proposed, and an illustrative example is presented. Numerical results indicate the applicability and effectiveness of the proposed approach.

Automated summary

This article presents a robust LQR approach for nonhomogeneous Markov jump linear systems, deriving a robust optimal controller via dynamic programming and limiting the influence of uncertainty. Numerical results demonstrate the applicability and effectiveness of the proposed method.