Computational aspects of discrete-time optimal control

摘要

Our opinion is that a little-known technique called “differential dynamicprogramming” offers the potential of enormously expanding the scale of discrete-time optimal- control problems which are subject to numerical solution. Among the attractive features of this method are that no discretization of control or state space is used; the memory requirements grow as m2 and the computational requirements as m3, with m being the dimension of the control variable; the successive approximations converge globally under lenient smoothness assumptions; and the convergence is quadratic if certain convexity assumptions hold. The contribution of the present paper is to demonstrate the practical merit of differential dynamic programming by reporting computational solutions to problems having as many as forty control variables and no particularly convenient structure. Additionally, we give a more algorithmically oriented presentation of the method than hitherto available, extend the basic methodto the nonconvex case, and give a proof of global convergence.