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Zbl 1117.93067
Liu, Yun-Gang; Zhang, Ji-Feng
Practical output-feedback risk-sensitive control for stochastic nonlinear systems with stable zero-dynamics. (English)
[J] SIAM J. Control Optim. 45, No. 3, 885-926 (2006). ISSN 0363-0129; ISSN 1095-7138/e

Summary: This paper addresses the design problem of practical (or satisfaction) output-feedback controls for stochastic strict-feedback nonlinear systems in observer canonical form with stable zero-dynamics under long-term average tracking risk-sensitive cost criteria. The cost function adopted here is of the quadratic-integral type usually encountered in practice, rather than the quartic-integral one used to avoid difficulty in control design and performance analysis of the closed-loop system. A sequence of coordinate diffeomorphisms is introduced to separate the zero-dynamics from the entire system, so that the transformed system has an appropriate form suitable for integrator backstepping design. For any given risk-sensitivity parameter and desired cost value, by using the integrator backstepping methodology, an output-feedback control is constructively designed such that (a) the closed-loop system is bounded in probability and (b) the long-term average risk-sensitive cost is upper bounded by the desired value. In addition, this paper does not require the uniform boundedness of the gain functions of the system noise. Furthermore, an example is given to show the effectiveness of the theory.

MSC 2000:: *93E03 General theory of stochastic systems
93D25 Input-output approaches to stability of control systems
93E15 Stochastic stability
93E20 Optimal stochastic control (systems)

Keywords: nonlinear system; stochastic system; integrator backstepping methodology; risk-sensitive control; output-feedback control; zero dynamics

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