Stochastic H2/H ∞ Control: a Nash Game Approach

Stochastic H2/H Control: A Nash Game Approach presents the latest results in stochastic H2=H1 control and filtering based on the Nash game approach. After providing some basics of stochastic differential equations, stochastic stability, stochastic observability and detectability, the book solves the H2=H1 control for linear lto systems and establishes a relationship between the H2=H1 control and two-person non-zero sum Nash game. It then discusses the H2=H1 control for linear discrete time-invariant systems with multiplicative noise, then focuses on linear discrete time-varying systems. After a discussion of mixed H2=H1 control for linear Markov jump systems with multiplicative noise, it establishes the equivalence between stochastic dissipativity and the solvability of nonlinear Lure. The next chapter can be viewed as an extension of deterministic nonlinear HM control. The penultimate chapter is concerned with nonlinear H and H2= H1 filters of ltd systems, which have potential applications in communication and signal processing. Finally, the authors present some further research topics in stochastic H2= H1 control, including the H2=H1 control of the following systems: (i) stochastic ltd systems with random coefficients; (ii) nonlinear discrete-time stochastic systems with multiplicative noise; (iii) singular stochastic Ito systems and singular discrete-time systems with multiplicative noise; and (iv) mean-field stochastic system. At the end of each chapter there is a brief review of related background knowledge and further research topics. Book jacket.