Adaptive Control of a Linear, Scalar Hyperbolic PDE with Time-Varying Coefficients

Abstract

We extend a previous result regarding adaptive control of a linear hyperbolic partial differential equation (PDE) with time-varying in-domain source coefficient in two ways. Firstly, we introduce a parametrization of the uncertain time-varying in-domain source coefficient that allows for a broader class of systems compared to previous result. Secondly, and more importantly, we introduce an uncertain scaling factor in the input boundary condition which is present in most applications, but wasn't handled in the previous result. All system parameters except the transport speed are uncertain and time-varying, although parametrizable as a linear combination of uncertain constants and certain time-variance. Closed-loop convergence of the state to the origin is proven, and performance is demonstrated for a numerical example.