Error-Feedback Output Regulation of Linear Stochastic Systems: a Hybrid Nonlinear Approach

The problem of output regulation for linear stochastic systems is addressed. We first define and solve the ideal problem of output regulation via error feedback. We note that its solution is not implementable in practice because the Brownian motion is not available for measure. Therefore, we define an approximate problem for which we provide a practical solution. The implemented controller is hybrid, in that a continuous-time, deterministic control law is supplemented by a discrete-time, stochastic correction. This correction is performed using an a-posteriori approximation of the variations of the Brownian motion provided by a nonlinear estimator. The resulting hybrid closed-loop system is nonlinear, as the scalars approximating the increments of the Brownian motion depend nonlinearly on the states and the inputs. The error between the solution of the approximate problem and the solution of the ideal problem is characterised. We show that the ideal solution is retrieved as the sampling time tends to zero. We illustrate the results by means of a numerical example. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.