Jump LQR Systems With Unknown Transition Probabilities

• Published in: IEEE transactions on automatic control Vol. 66; no. 6; pp. 2693 - 2708
• Main Authors: Tzortzis, Ioannis, Charalambous, Charalambos D., Hadjicostis, Christoforos N.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Codification; Control systems; Dynamic programming; Linear quadratic regulator; Linear systems; Markov processes; Mathematical analysis; Measurement; minimax optimization; Minimax technique; nonhomogeneous Markov jump linear systems; Optimal control; Optimization; Probability distribution; Robust control; robust linear quadratic regulator; Robustness; Stochastic processes; Transition probabilities; uncertain/ambiguous transition probabilities; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.3013844

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.