TY - GEN
T1 - Closed-Loop Neighboring Extremal Optimal Control Using HJ Equation
AU - Rai, Ayush
AU - Mou, Shaoshuai
AU - Anderson, Brian D.O.
N1 - Publisher Copyright:
© 2023 IEEE.
PY - 2023
Y1 - 2023
N2 - This study introduces a method to obtain a neighboring extremal optimal control (NEOC) solution for a broad class of nonlinear systems with nonquadratic performance indices by investigating the variation to a known closed-loop optimal control law caused by small, known variations in the system parameters or in the performance index. The NEOC solution can formally be obtained by solving a linear partial differential equation similar to those arising in an iterative solution procedure for a nonlinear Hamilton-Jacobi equation. Motivated by numerical procedures for solving such an equation, we also propose a numerical algorithm based on the Galerkin algorithm that uses basis functions to solve the underlying Hamilton-Jacobi equation. This approach allows the determination of the minimum performance index as a function of both the system state and parameters and extends to allow the determination of the adjustment to an optimal control law given a small adjustment of parameters in the system or the performance index, effectively by computing the derivative of the law with respect to those parameters. The validity of the claims and theory is supported by numerical simulations.
AB - This study introduces a method to obtain a neighboring extremal optimal control (NEOC) solution for a broad class of nonlinear systems with nonquadratic performance indices by investigating the variation to a known closed-loop optimal control law caused by small, known variations in the system parameters or in the performance index. The NEOC solution can formally be obtained by solving a linear partial differential equation similar to those arising in an iterative solution procedure for a nonlinear Hamilton-Jacobi equation. Motivated by numerical procedures for solving such an equation, we also propose a numerical algorithm based on the Galerkin algorithm that uses basis functions to solve the underlying Hamilton-Jacobi equation. This approach allows the determination of the minimum performance index as a function of both the system state and parameters and extends to allow the determination of the adjustment to an optimal control law given a small adjustment of parameters in the system or the performance index, effectively by computing the derivative of the law with respect to those parameters. The validity of the claims and theory is supported by numerical simulations.
UR - http://www.scopus.com/inward/record.url?scp=85184808359&partnerID=8YFLogxK
U2 - 10.1109/CDC49753.2023.10383777
DO - 10.1109/CDC49753.2023.10383777
M3 - Conference contribution
AN - SCOPUS:85184808359
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 3270
EP - 3275
BT - 2023 62nd IEEE Conference on Decision and Control, CDC 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 62nd IEEE Conference on Decision and Control, CDC 2023
Y2 - 13 December 2023 through 15 December 2023
ER -