Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion. (English) Zbl 0924.93046

Pan, Zigang; Basar, Tamer

SIAM J. Control Optimization 37, No. 3, 957-995 (1999).

This paper develops a methodology for recursive construction of optimal and near-optimal controllers for strict-feedback stochastic nonlinear systems, given by stochastic differential equations, under a risk-sensitive cost function criterion. The authors investigated cost-level satisfaction problems and obtained the design procedure, using the integrator backstepping procedure. They also extended these results to nonlinear systems with zero dynamics. The theoretical results are applied to a second-order system as a numerical example.

Reviewer: M.Nisio (Osaka)

MSC:

93E20	Optimal stochastic control
93C10	Nonlinear systems in control theory
91A23	Differential games (aspects of game theory)

Keywords:

stochastic stability; stochastic nonlinear systems; risk-sensitive cost function; integrator backstepping procedure; zero dynamics