Analytical computation of differential equations involved in dynamical nonlinear optimal problems

Abstract

We present two programs, written in Reduce, for non-constrained free endpoint nonlinear dynamical optimal problems, in fixed time, in closed loop and in open loop, which compute analytically the optimal feedback laws in terms of differential equations. The open loop case leads to ordinary differential equations (ODEs) and the closed loop leads to partial differential equations (PDEs). In the case of closed loop problems the program uses nonstandard Reduce programming for the declarations of dependencies of u and its partial derivatives. Algorithms are presented for the open loop and closed loop cases and the same example is computed in both these cases.