Output regulation for a class of linear boundary controlled first-order hyperbolic PIDE systems

This manuscript addresses the output regulation problem for a class of scalar boundary controlled first-order hyperbolic partial integro-differential equation (PIDE) systems with Fredholm integrals. In particular, with the advantage of the backstepping approach, simple structure systems can be obtained such that regulator equations for the state feedback regulator design are analyzed and solved in backstepping coordinates. Moreover, the finite time output regulation is achieved. In the observer-based output feedback regulator design, it is not necessary that the outputs to be controlled belong to the available output measurements and these outputs can be distributed, point-wise and/or boundary in nature, while the boundary placed measurements are used for regulator design. For the observer gains design, a transformation of the ODE-PDE system into an ODE-PDE cascade is considered. It is also shown that the separation principle holds for the output feedback regulator design and the exponential output regulation is realized for the resulting stable closed-loop system. Finally, the output regulation results are illustrated with two numerical simulations: a Korteweg-de Vries-like equation and a PDE-ODE interconnected system.