ε-approximate output regulation of linear stochastic systems: a hybrid approach

The problem of output regulation for linear stochastic systems is addressed. The controlled system belongs to a general class of linear systems, namely the state, the control input and the exogenous input appear in both the drift and diffusion terms of the differential equations. Building upon the solution of the ideal, non-causal, stochastic regulator problem,we define an approximate full-information problem. By means of measurements of the state vector, we provide a way to compute a sequence of scalars approximating a posteriori the variations of the Brownian motion. Then, we propose a hybrid control architecture which solves the approximate problem.The continuous-time part of the controller is deterministic,whereas the discrete-time part has the function of “correcting”the control action by means of the approximate discrete-time Brownian motion. The solution of the ideal stochastic regulator problem is recovered as the sampling time tends to zero. We illustrate the results by means of a numerical example and conclude the paper with some final remarks:the proposed control architecture is the first causal solution of the full-information output regulation problem and is an essential intermediate step for the solution of the error-feedback problem