The research in this Master’s thesis presents the theory and application of the existing and simplified version of the Finite-Horizon State-Dependent Riccati Equation (SDRE) nonlinear optimal control techniques. SDRE technique for closed-loop optimal control of nonlinear systems has been an active research area during the last decade. Although SDRE provides great advantages to the control systems designers by providing design flexibility on the state matrices, the existing technique for finite-horizon control is approximate and involves several steps which makes it computationally complex. The SDRE technique for finite-horizon optimal problem involves first representing any given dynamical system in the state-dependent coefficient (SDC) form and then solving the SDRE at each small time interval during the givenfinite-horizon period. The process then is to assume that during the small intervals the Riccati coefficient and vector coefficient are constant and hence use the algebraic Riccati equation and algebraic vector equation. This assumption makes the solution suboptimal. In this research, without the assumption of SDRE coefficients being constant during each small interval, a simplified SDRE technique is presented by employing the analytic solution for the matrix differential Riccati equation and vector differential equation, hence avoiding the suboptimality and eliminating the
several steps associated with the existing SDRE technique. The validity of the proposed simplified SDRE method is illustrated and compared with the existing SDRE for both regulation and tracking problems by implementing them in a nonlinear, sixth-order model of a permanent magnet synchronous generator-based wind energy system. The research conducted in this thesis resulted in the publication of three international conferences and one journal article (under preparation).
University of Minnesota M.S. thesis. June 2021. Major: Electrical Engineering. Advisor: Desineni Subbaram Naidu. 1 computer file (PDF); vi, 62 pages.
Advanced Optimal Control Strategies for Nonlinear Systems with Application to Wind Energy.
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