Complementarity Constraints for Nonlinear Systems

Abstract This paper develops complementarity constraints for nonlinear feedback control systems with additive output disturbances and sensor noise, and for nonlinear filtering in the presence of process noise and additive measurement noise. In the control case, the complementarity constraint is the nonlinear counterpart of the well known fact in linear feedback control theory that the sum of the sensitivity operator, S ( s ), and complementary sensitivity operator, T ( s ), is the identity operator. Performance limitations induced by this nonlinear complementarity constraint in the case of open loop unstable and non-minimum phase plants are explored.