Adaptive state feedback stabilization of n + 1 coupled linear hyperbolic PDEs

Abstract

We design an adaptive control law for a set of n +1 linear partial differential equations (PDEs) of the hyperbolic type. The control law is based on swapping design, where filters are used to express the system states as linear, static combinations of the filters and the unknown parameters, facilitating for estimating the parameters using any standard adaptive law. The estimates generated by the adaptive law combined with the filters can then be used to generate estimates of system states for which an adaptive controller is designed. Boundedness and square integrability in L2 for all signals in the closed loop is proved, and the theory is demonstrated in a simulation.