This paper investigates an control problem for a class of nonlinear stochastic systems with state- and disturbance-dependent noise. This problem is discussed in both the finite and infinite horizon cases. In this regard, an approach involving Hamilton-Jacobi equations is used in order to develop infinite and finite horizon nonlinear stochastic control designs.
In the main, the authors generalize some results on nonlinear control for deterministic systems to a stochastic setting. In order to treat the infinite horizon nonlinear stochastic control problem, they introduce definitions for the concepts of “zero-state observability” and “zero-state detectability.” Another tool to solve the aforementioned problem is the stochastic LaSalle invariance principle.
Reviewer’s remark: The paper is well-written and of interest to experts in both control as well as nonlinear stochastic systems.