A closed-loop symplectic regularized algorithm for constrained time-varying optimal control

TY - JOUR

T1 - A closed-loop symplectic regularized algorithm for constrained time-varying optimal control

AU - Lu, Kebing

AU - Sun, Jian

AU - Li, Zhuo

AU - Chen, Wei

N1 - Publisher Copyright: © 2025

PY - 2026/3/1

Y1 - 2026/3/1

N2 - This article proposes a closed-loop symplectic regularized algorithm for constrained time-varying optimal control problems. Due to the limitations of symplectic methods in constrained time-varying systems, the optimal control problem is transformed and discretized into a discretized symplectic Runge–Kutta form by using variational integrator. Moreover, we derive first-order necessary conditions for the discrete optimal control problem and obtain a set of Euler–Lagrange (EL) equations. To solve the EL equations, we provide a forward–backward sweep iteration algorithm and analyze its error estimation along with regularization terms. Based on this iteration algorithm, a closed-loop symplectic regularized algorithm is proposed consisting of symplectic update and regularized iteration. To be specific, a sequence of quadratic programmings are leveraged in the forward stage of symplectic update to provide good initial values for the regularized iteration. Furthermore, an interior-point barrier function is applied to handle the constraints in the regularized iteration. The convergence analysis of the proposed algorithm is provided, and simulations are conducted to verify its effectiveness.

AB - This article proposes a closed-loop symplectic regularized algorithm for constrained time-varying optimal control problems. Due to the limitations of symplectic methods in constrained time-varying systems, the optimal control problem is transformed and discretized into a discretized symplectic Runge–Kutta form by using variational integrator. Moreover, we derive first-order necessary conditions for the discrete optimal control problem and obtain a set of Euler–Lagrange (EL) equations. To solve the EL equations, we provide a forward–backward sweep iteration algorithm and analyze its error estimation along with regularization terms. Based on this iteration algorithm, a closed-loop symplectic regularized algorithm is proposed consisting of symplectic update and regularized iteration. To be specific, a sequence of quadratic programmings are leveraged in the forward stage of symplectic update to provide good initial values for the regularized iteration. Furthermore, an interior-point barrier function is applied to handle the constraints in the regularized iteration. The convergence analysis of the proposed algorithm is provided, and simulations are conducted to verify its effectiveness.

KW - Closed-loop algorithm

KW - Euler–Lagrange equation

KW - Regularization term

KW - Symplectic method

UR - https://www.scopus.com/pages/publications/105012983894

U2 - 10.1016/j.cam.2025.116985

DO - 10.1016/j.cam.2025.116985

M3 - Article

AN - SCOPUS:105012983894

SN - 0377-0427

VL - 474

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 116985

ER -