A filled function method for minimizing control variation in constrained discrete-time optimal control problems

This paper considers a discrete-time optimal control problem subject to terminal state constraints and all-time-step inequality constraints, where the cost function involves a terminal cost, a summation cost and a penalty on the change of the control action. The variation of the control signal and the all-time-step constraints are non-smooth functions. Thus, this optimal control problem is formulated as a non-smooth constrained optimization problem. However, it is nonconvex and hence it may have many local minimum points. Thus, a filled function method is introduced in conjunction with local optimization techniques to solve this non-smooth and nonconvex constrained optimization problem. For illustration, two numerical examples are presented and solved using the proposed approach.