Relationship Between Nash Equilibrium Strategies and H/H Control of Stochastic Markov Jump Systems With Multiplicative Noise

• Published in: IEEE transactions on automatic control Vol. 59; no. 9; pp. 2592 - 2597
• Main Authors: Sheng, Li, Zhang, Weihai, Gao, Ming
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.09.2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control systems; Horizon; Markov processes; Mathematical analysis; Nash equilibrium; Noise; Riccati equations; Stochastic systems; Stochasticity; Strategy; Symmetric matrices; Nash equilibrium strategies; stochastic H_{2}/H_{\infty} control; stochastic Markov jump systems; Coupled Riccati equations
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2014.2309274

This technical note is concerned with discussing the relationship between Nash equilibrium strategies and the finite horizon H 2 /H ∞ control of time-varying stochastic systems subject to Markov jump parameters and multiplicative noise. It is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term. Furthermore, necessary and sufficient conditions for the finite horizon H 2 /H ∞ control of stochastic Markov jump systems are presented via coupled matrix-valued equations.