An alternate approach to the fixed terminal point regulator problem

The conventional calculus of variations solution of the fixed terminal point regulator problem implies the use of time-varying feedback in the controller. In systems with linear plants such a controller calls for gains that approach infinity as the time approaches the terminal time. An alternate, mathematically equivalent, solution is proposed in this paper. This solution expresses the optimum controller in terms of a sum of time-variant feedback (control law) and a forcing term (control function). Since the feedback gains remain constant and the control function is finite for all positive time, such a solution is physically realizable. The control law also guarantees asymptotic stability even after the terminal time has been reached.