TY - GEN

T1 - A simplified SDRE technique for regulation in optimal control systems

AU - Naidu, D. Subbaram

AU - Paul, Sudipta

AU - Rieger, Craig R.

PY - 2019/5

Y1 - 2019/5

N2 - 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.

AB - 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.

KW - Differential Lyapunov equation

KW - Finite horizon optimal regulation

KW - Nonlinear optimal control

KW - State dependent Riccati equation

KW - Wind energy conversion system

UR - http://www.scopus.com/inward/record.url?scp=85072830640&partnerID=8YFLogxK

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U2 - 10.1109/EIT.2019.8834201

DO - 10.1109/EIT.2019.8834201

M3 - Conference contribution

AN - SCOPUS:85072830640

T3 - IEEE International Conference on Electro Information Technology

SP - 327

EP - 332

BT - 2019 IEEE International Conference on Electro Information Technology, EIT 2019

PB - IEEE Computer Society

T2 - 2019 IEEE International Conference on Electro Information Technology, EIT 2019

Y2 - 20 May 2019 through 22 May 2019

ER -