Multi-criterial problems of optimal control: cooperative game solution of Nash–Harsanyi

This paper presents a new method for solving multicriterion control problems based on concepts borrowed from game theory. The present method consists in first suitably allocating the control resources to the different criteria and then reformulating the problem as a cooperative $N$-person differential game without side payments. Utilizing the Nash– Harsanyi solution for such a game, a noninferior control law is singled out as the optimal solution to the problem. A bicriterion control problem, involving the minimization of time and fuel and in which the control variables permit a natural allocation to the criterion, is completely solved. This example brings out several interesting features of this technique.