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

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.