An Efficient Model Based Control Algorithm for the Determination of an Optimal Control Policy for a Constrained Stochastic Linear System

Abstract

In this paper, the authors have proposed an ensemble Kalman filter based stochastic model predictive control algorithm to determine an optimal control policy at every sampling time instant for a constrained stochastic linear system. To determine an optimal control policy for the constrained linear system affected by random disturbances and measurements corrupted by random noise, the authors have minimized the uncertain objective function, subject to uncertain state & output constraints and deterministic input constraints using the quantile based scenario analysis approach. In this work, ensemble Kalman filter is being employed, to generate a recursive estimate of states of the constrained stochastic linear system. The number of scenarios is considered to be equivalent to that of number of sample points used in the ensemble Kalman filter. Each scenario is viewed as one realization of the process noise, measurement noise over the prediction horizon as well as the ith sample point of the state estimate at the beginning of the prediction horizon generated by the ensemble Kalman filter. Simulation studies have been carried out to assess the efficacy of the proposed control scheme on the simulated model of the constrained single-input and single-output linear stochastic system.