A Numerical Implementation of an Extended Luenberger Observer for a Class of Semilinear Hyperbolic PIDEs

In this paper, an extended Luenberger observer for a class of semilinear hyperbolic PIDEs is proposed to solve the problem of state estimation. The nonlinear observer error dynamics is linearized and then stabilized locally by applying the backstepping method for time-varying linear hyperbolic PIDEs presented recently. Since the resulting kernel equation is computationally quite expensive, a numerical algorithm is proposed to obtain the solution in an efficient way. Finally, this algorithm is applied to an example with multiple equilibrium points, and the influence of the design parameters on the stability is investigated in more detail.