An Evolutionary Approach to Nonlinear Discrete-Time Optimal Control with Terminal Constraints

The nonlinear discrete-time optimal control problem with terminal constraints is treated using a new evolutionary approach which combines a genetic search for finding the control sequence with a solution of the initial value problem for the state variables. The main advantage of the method is that it does not require to obtain the solution of the adjoint problem which usually leads to a two-point boundary value problem combined with an optimality condition for finding the control sequence. The method is verified by solving the problem of discrete velocity direction programming with the effects of gravity and thrust and a terminal constraint on the final vertical position. The solution compared favorably with the results of gradient methods.