PENALTY-FUNCTION SOLUTIONS TO OPTIMAL-CONTROL PROBLEMS WITH GENERAL CONSTRAINTS VIA A DYNAMIC OPTIMIZATION METHOD

The optimal control problem with general constraints is considered. This involves the calculation of the open loop control input as a function of time such that an objective function is minimised and the constraints are satisfied. The approach taken in this paper is to discretise the control input by representing it by a sequence of piecewise constant vectors over equally spaced intervals spanning a finite time horizon. A penalty function approach is then used to reformulate the original constrained problem as an unconstrained minimisation problem which is solved by using a dynamic minimisation algorithm. This algorithm is particularly suitable for penalty functions. The approximate solution obtained minimises the objective function whilst satisfying the original constraints at the discretisation points.