Nonlinear robust control and minimax team problems

The problem of robust stabilization of a linear system leads to the classical H _∞ control problem. The same analysis applied to a nonlinear system leads to the problem of ensuring via output feedback that a nonlinear operator be Lipshitz continuous, with a prescribed Lipshitz modulus. We show that, in the same way as the H _∞ control problem is equivalent to a minimax control problem, the Lipshitz modulus control problem can be approached via a minimax team decision problem. This motivates us to re-visit a class of the so-called `static' team decision problems for nonlinear dynamical control systems. Because of the `static' character, signaling plays no role in that case, which is important for the equivalence with the Lipshitz modulus control problem. We show that under some conditions, a certainty equivalence principle applies that yields a practical solution to the team problem at hand. To reach that conclusion we must first investigate a `partial team' problem where one of the team members has all the information.