Model reference adaptive control of abstract nonlinear distributed parameter systems

We briefly describe and discuss an abstract theory for the model reference adaptive control (MRAC) of abstract nonlinear distributed parameter systems. We consider a general class of abstract nonlinear systems in Hilbert space, and we assume that the entire state is available for measurement. We assume that the reference model is an abstract parabolic system, and that the control objective is to find a feedback controller which forces the unknown plant to track the state trajectory of the reference model while all signals in the closed loop remain bounded. We are also interested in obtaining convergence of the estimates for the unknown plant parameters. The class of distributed parameter systems that we are particularly interested in applying our abstract theory to include ones involving linear and nonlinear diffusion and damped wave/beam equations, fluid flow, thermoelasticity, and hereditary systems or delay equations.