Article ID Journal Published Year Pages File Type
4623835 Journal of Mathematical Analysis and Applications 2006 14 Pages PDF
Abstract

We consider the differential game formulation of the nonlinear state feedback H∞ control problem, in which the control term enters linearly in the dynamics and quadratically in the cost. Under well-known conditions on the linearisation of this problem around the equilibrium point at the origin, there exists a stable Lagrangian manifold Λ. This manifold has a generating function S quadratic at infinity. A Lusternick–Schnirelman minimax construction produces from S a Lipschitz function W over state space. We show that, for problems in general position, −W is the lower value function for the H∞ problem, and prove existence of a weak globally optimal set valued feedback solution in terms of ∂W, the generalised gradient of W. This feedback generalises, to a maximal region over which Λ is simply connected, the classical smooth feedback defined on the neighbourhood of the origin over which Λ has a well-defined projection onto state space.

Related Topics
Physical Sciences and Engineering Mathematics Analysis