A multi-objective dynamic programming approach to constrained discrete-time optimal control

This work presents a multi-objective differential dynamic programming approach to constrained discrete-time optimal control. In the backward sweep of the dynamic programming in the quadratic sub problem, the sub problem input at a stage or time step is solved for in terms of the sub problem state entering that stage so as to minimize the summed immediate and future cost subject to minimizing the summed immediate and future constraint violations, for all such entering states. The method differs from previous dynamic programming methods, which used penalty methods, in that the constraints of the sub problem, which may include terminal constraints and path constraints, are solved exactly if they are solvable; otherwise, their total violation is minimized. Again, the resulting solution of the sub problem is an input history that minimizes the quadratic cost function subject to being a minimizer of the total constraint violation. The expected quadratic convergence of the proposed algorithm is demonstrated on a numerical example.