Nonlinear finite-dimensional control of a class of nonlinear distributed parameter systems using residual mode filters: A proof of local exponential stability

AbstractIn any attempt to control an infinite-dimensional distributed parameter system (DPS) with a finite-dimensional controller, some compensation for deleterious controller interaction with unmodeled modes is needed. We introduce the concepts of both a finite-dimensional nonlinear controller based on any reasonable, nonlinear reduced-order model of the DPS and stability compensation by a finite-dimensional, nonlinear residual mode filter. Under appropriate Lipschitz continuity conditions on the nonlinearities, this new pair of interconnected finite-dimensional systems will produce closed-loop (exponentially) stable control of the nonlinear DPS