OBSERVABILITY AND OBSERVERS FOR A CLASS OF TWO-DIMENSIONAL HYPERBOLIC PDE CHAOTIC SYSTEMS

This paper is concerned with both observability and observers for a class of systems described by the two-dimensional hyperbolic PDEs with superlinear boundary conditions which can exhibit chaos. The exact observability and approximate observability are shown by the method of characteristic and boundary reflection relations. Based on the observability, two Luenberger types of PDE observers are designed by making use of the boundary velocity and boundary displacement measurement, respectively. Some sufficient conditions are then developed to obtain the global exponential stability and global asymptotic stability of the observer error systems. Some numerical simulations are performed to validate the theoretical results.

Automated summary

This paper investigates the observability and observer design for a class of systems described by two-dimensional hyperbolic PDEs with superlinear boundary conditions that can exhibit chaos. The exact and approximate observability are proven using the method of characteristic and boundary reflection relations. Based on observability, two types of Luenberger PDE observers are designed, using boundary velocity and boundary displacement measurements respectively. Sufficient conditions are developed to guarantee the global exponential stability and global asymptotic stability of the observer error systems. Numerical simulations are conducted to validate the theoretical findings.