A Simplified SDRE Technique for Finite Horizon Tracking Problem in Optimal Control Systems

Abstract

Closed loop optimal control of nonlinear systems using state dependent Riccati equation (SDRE) technique has been an active research area during the last decade. The existing SDRE technique for continuous time, finite horizon, optimal tracking problem is approximate and involves several steps which makes it computationally complex. In this paper, a simplified SDRE technique is proposed for a nonlinear closed loop finite horizon optimal tracking problem. For tracking, one is faced with not only solving the nonlinear matrix differential Riccati equation (DRE) but also solving the nonhomogeneous vector differential equation (VDE). The proposed simplified SDRE method for optimal tracking, without the assumption of the Riccati coefficient and vector coefficient being constant during the small intervals of the finite-horizon period, employs the analytic solution of matrix DRE and VDE and the associated MATLAB program developed by the authors of this paper at each small intervals, thereby avoiding the approximate nature and eliminating the several steps associated with the existing SDRE technique. The proposed simplified finite horizon SDRE tracking technique is illustrated with a permanent magnet synchronous generator (PMSG) based wind energy conversion system (WECS).