Weighted optimization for multiobjective full-information control problems

We consider a nonlinear multiobjective full-information optimal control problem, where a controller is to be designed such that a number of constraints are to be satisfied for all possible disturbances. We show that, under certain continuity assumptions, such a controller exists if and only if, for every weighted combination of the constraints, there exists a controller satisfying the weighted constraint. Our analysis is based extensively on nonlinear H_∞ dynamic programming methods