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Title:Robust Control of Stochastic Nonlinear Systems
Author(s):Tang, Cheng
Subject(s):Stochastic nonlinear system
Singularly perturbed system
Strict-feedback form
Risk-sensitive stochastic control
Stochastic backstepping design
Abstract:This thesis investigates several topics involving robust control of stochastic nonlinear systems. First, we study the problem of stochastic stabilizability and introduce the concept of stochastic input-to-state stability. It is then applied to singularly perturbed system and shown to be useful in establishing a result of the "total stability" type. To the problem of stochastic optimization, we study a class of nonlinear system in strict-feedback form, where the cost function is risk-sensitive type. Through a constructive stochastic backstepping technique, we derive a state-feedback policy that is both locally optimal and globally inverse optimal, which further leads to closed-loop system trajectories that are bounded in probability. Subsequently, we study the constrained minimax optimization problem, where in addition to the standard Wiener process there is a norm-bounded unknown disturbance driving the system. The bound on the disturbance is a stochastic integral quadratic constraint, and it is also related to the constraint on the relative entropy between the uncertainty probability measure and the reference probability measure. By converting into an unconstrained stochastic differential game and making use of a duality relationship, we obtain a minimax state-feedback control law that is both locally optimal and globally inverse optimal. Furthermore, the closed-loop system is absolutely stable in the presence of stochastic uncertainty disturbances.
Issue Date:2003-06
Publisher:Coordinated Science Laboratory, University of Illinois at Urbana-Champaign
Series/Report:Coordinated Science Laboratory Report no. UILU-ENG-03-2212, DC-208
Sponsor:National Science Foundation / NSF CCR 00-85917 ITR and NSF ECS 02-25481
Date Available in IDEALS:2019-05-16

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