Optimal control for a class of nonlinear systems

This paper utilizes Pontryagin´s maximum principle and the Hamiltonian-Jacobi-Bellman equation to generate and demonstrate the time optimal control solution for a class of nonlinear systems. The control is bounded in magnitude by a convex function. It is shown that if the properties of a system are consistant with the bounded control surface, the time optimal control takes a simple form. Examples are discussed for a rigid body spacecraft and a restricted nonlinear system. The latter is shown to be a special case of the optimal control solution given here