Minimum Time Disturbance Rejection and Tracking Control of n+m Linear Hyperbolic PDEs

Abstract

We extend recent results regarding disturbance rejection control of n+m linear hyperbolic partial differential equations (PDEs) in a number of ways: 1) We allow spatially varying coefficients; 2) The disturbance is allowed to enter in the interior of the domain, and; 3) Rejection is achieved in minimum time. Additionally, we solve a tracking problem, where the tracking objective is achieved in finite, minimum time. We use a recently derived Fredholm transformation technique in addition to infinite-dimensional backstepping in our design.