Stochastic H2/H ∞ Control: A Nash Game Approach
A Nash Game Approach

The H? control has been one of the important robust control approaches since the 1980s. This book extends the area to nonlinear stochastic H2/H? control, and studies more complex and practically useful mixed H2/H? controller synthesis rather than the pure H? control. Different from the commonly used convex optimization method, this book applies the Nash game approach to give necessary and sufficient conditions for the existence and uniqueness of the mixed H2/H? control. Researchers will benefit from our detailed exposition of the stochastic mixed H2/H? control theory, while practitioners can apply our efficient algorithms to address their practical problems.

Mathematical Preliminaries. Linear Continuous-Time Stochastic H2 ∞ H1 Control. Linear Discrete-Time Stochastic H2 ∞ H1 Control. H2 ∞ H1 Control for Linear Discrete Time-Varying Stochastic Systems. Linear Markovian Jump Systems with Multiplicative Noise. Nonlinear Continuous-Time Stochastic H1 and H2 ∞ H1 Controls. Nonlinear Stochastic H1 and H2 ∞ H1 Filtering. Some Further Research Topics in Stochastic H2 ∞ H1 Control. Index.

Weihai Zhang, Lihau Xie, Bor-Sen Chen