Control With State-Dependent Noise

This paper discusses the stochastic control problem with state-dependent noise. By means of the stabilization, exact observability and stochastic detectability of stochastic sys- tems, the infinite horizon stochastic control design is de- veloped. For the finite horizon control problem, our re- sults generalize the corresponding deterministic ones to the sto- chastic models. Finally, the observer-based suboptimal stochastic control is discussed in which the state variables cannot be measured directly, and a feasible design algorithm is proposed. Index Terms—Coupled Riccati equations, exact observability, state-dependent noise, stochastic detectability, stochastic control.

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