Nonlinear robust control and minimax team problems

The problem of robust stabilization of a linear system leads to the classic al H-infinity control problem. The same analysis applied to a nonlinear sys tem leads to the problem of ensuring via output feedback that a nonlinear o perator be Lipshitz continuous, with a prescribed Lipshitz modulus. We show that, in the same way as the H-infinity control problem is equivalent to a minimax control problem, the Lipshitz modulus control problem can be appro ached via a minimax team decision problem. This motivates us to re-visit a class of the so-called 'static' team decision problems for nonlinear dynami cal 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 e quivalence principle applies that yields a practical solution to the team p roblem at hand. To reach that conclusion we must first investigate a 'parti al team' problem where one of the team members has all the information. Cop yright (C) 1999 John Wiley & Sons, Ltd.