Robust Control of Nonlinear Jump Parameter Systems Governed by Uncertain Chains

• Published in: IEEE transactions on automatic control Vol. 53; no. 6; pp. 1520 - 1526
• Main Authors: Ford, J.J., Ugrinovskii, V.A.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Approximation; Australia; Computer science; control theory; systems; Construction costs; Control system synthesis; Control systems; Control theory. Systems; Exact sciences and technology; Filtering theory; Markov chain approximations; Markov jump parameter systems; Mathematical analysis; Mathematical models; Minimax technique; Minimax techniques; Nonlinear control systems; Optimal control; Optimization; Riccati equations; Robust control; stochastic control; Stochastic systems; Uncertain systems; Markov process; Non linear control; Control synthesis; Continuous time; Cost control; Markov chain; Robust control; Markov chain approximations; Uncertain system; Optimal control; Minimax problem; Minimax method; Discrete time; Stochastic control; Markov jump parameter systems; Jump process; Infinite horizon
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2008.928911

We consider an infinite-horizon minimax optimal control problem for stochastic uncertain systems governed by a discrete-state uncertain continuous-time chain. Using existing risk-sensitive control results, a robust suboptimal absolutely stabilizing guaranteed cost controller is constructed. Conditions are presented under which this suboptimal controller is minimax optimal. We then present a numeric algorithm for calculating a robust (sub)optimal controller using a Markov chain approximation technique.