ABSTRACT
This chapter generalizes the linear stochastic H2/H∞ control to nonlinear stochastic Ito's systems. Nonlinear H∞ control of deterministic continuous-time systems was a popular research topic in the 1990s. It discusses the differential geometric approach was employed to study the strict relation between the Hamilton–Jacobi equation (HJE) and invariant manifolds of Hamiltonian vector fields, and the existence of local solution to the primal nonlinear H∞ control. However, the differential geometric approach has seldom been applied to stochastic control systems. The chapter uses the method of completion of squares together with stochastic dissipative theory to discuss global solutions to nonlinear stochastic H∞ and mixed H2/H∞ control problems.
