A Sequential Linear Quadratic Approach for Constrained Nonlinear Optimal Control

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state-only constraints. The proposed algorithm formulates linear quadratic optimal control subproblems with a solution that provides a descent direction for a non-differentiable exact penalty function. A set of conditions is given under which the minimization of the merit function produces a sequence of controls with limit points that satisfy the first order necessary conditions of the optimal control problem. The subproblems solved at each step of the algorithm inherit the structure of the nonlinear optimal control problem and can be solved efficiently via Riccati methods.