Sampled-data in space nonlinear control of scalar semilinear parabolic and hyperbolic systems

Abstract

The paper describes a novel method of sampled-data in space (spatial variable) nonlinear control of scalar semilinear parabolic and hyperbolic systems with unknown parameters, distributed disturbances and finite number of measurements along the spatial variable. Differently from recent results based on piecewise constant control laws, the proposed one is used piecewise nonlinear functions choosing by designer for providing some properties in the closed-loop system. In particular, we propose several types of functions providing reduced control. The gain design in the control law is found as a solution of linear matrix inequalities with minimum ultimate bound guarantee. The simulations confirm theoretical results and show the efficiency of the proposed control scheme compared with some existing ones.