Abstract
In this paper, an optimal control problem is considered, in which the constraint of the control variables is a parameter vector to be optimized. A practical example of this problem is an optimal system synthesis problem where the minimization of the sum of the driving cost and the equipping cost of the system is considered. The existence of the solution is shown for the problem with a nonlinear dynamics and a nonlinear cost function. The directional derivative of the cost function with respect to the constraint parameter vector is derived. Under some additional assumption such as a linear dynamics and a convex cost function, the subgradient and the gradient of the cost function are obtained. The numerical algorithm using the gradient is given.
