Regulation of Continuous-Time Stochastic Systems under State and Control Constraints

In this paper the regulation problem for continuous-time stochastic systems by linear state-feedback under state and/orcontrol constraints is investigated. Nonlinear dynamical systems affected by stochastic disturbances modelled asq-dimensional Wiener processes with independent components are considered. Linear inequalities on the mean values of the state and the control are considered as control constraints. The analysis is based on the use of monotone comparison systems for Ito type stochastic differential equations and the positive invariance of polyhedral sets. This enables one to derive stability properties in terms of the convergence of the state vector mean values, thus avoiding complicated computations faced when stability properties are obtained by studying the behavior of higher order moments. For the class of linear systems a design approach based on linear programming is proposed. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.