A Simplified SDRE Technique for Regulation in Optimal Control Systems

Optimal control of linear systems is a well-established area of research, whereas the closed-loop, optimal control of nonlinear systems has been a challenging research area and there has been recent work in this area using state-dependent Riccati equation (SDRE). The SDRE technique for finite-horizon optimal regulator problem basically involves first representing any given dynamical system in the state-dependent coefficient (SDC) form and then solving the SDRE at small intervals of time during the given finite horizon period of initial time to final time. The process then is to assume that during the small intervals the Riccati coefficient is constant and hence use the algebraic Riccati equation (ARE) to obtain the steady-state Riccati coefficient resulting in an approximate and suboptimal control. In this paper, without the assumption of SDRE coefficient being constant during the small intervals of the finite-horizon period, a simplified SDRE technique is presented by employing the analytic solution for the matrix differential Riccati equation and the associated MATLAB program developed by the authors of this paper, thereby avoiding the approximate nature and eliminating the several steps associated with the existing SDRE technique. The validity of the proposed simplified SDRE technique is illustrated with finite time optimal regulation of a nonlinear, sixth order model of a variable speed, variable pitch (VSVP) wind energy conversion system.