Boundary Set-Point Regulation of a Linear 2×2 Hyperbolic PDE with Uncertain Bilinear Boundary Condition

Abstract

We design an adaptive controller for a 2 × 2 linear hyperbolic PDE with uncertain boundary parameters where measurements are taken at both boundaries, while only one boundary is actuated. The uncertainty, which appears in the un-actuated boundary, is in a bilinear form, which allows us to use bilinear adaptive laws for which parameter estimate convergence is guaranteed under a simple, a priori verifiable, persistence of excitation criterion. The control objective is boundary set-point regulation where the set-point is dependent on one of the unknown parameters. Stability is proved in the L 2 -sense and all signals in the closed loop are shown to be bounded.