Sliding control of nonlinear distributed parameter systems based on iterative approximation

The paper studies the sliding mode control of nonlinear, distributed parameter system described by partial differential equations. The nonlinear system is approximated by a sequence of linear, time-varying system which, under very mild conditions, globally converges in the limit to the nonlinear systems considered. This reduces the nonlinear control problem to linear, time-varying control problems. For each iterative approximation, an infinite-dimensional time-varying sliding surface and the corresponding control input is designed. The converged control input could exponentially stabilizes the nonlinear system. Here we give an example of nonlinear wave equation to illustrate the theory.