A general approach to nonlinear multiple control problems with perturbation consideration

In this paper, we consider a general nonlinear optimal control problem involving multiple criteria. We show that the problem can be transformed into a standard optimal control problem, and hence, is solvable by conventional techniques. However, the optimal control so obtained is of open loop nature and is rather sensitive to perturbations. Based on the first-order approximation, neighboring extremal approach is used to obtain a local linear feedback correction control law, leading to a combined controller. Two numerical examples are solved using the proposed method to demonstrate the effectiveness of the combined control.