ODEs with wave PDE actuator dynamics

Abstract

In Chapter 15 we provided a first extension of the predictor feedback concept to systems whose actuator dynamics are infinite-dimensional and more complex than a simple pure delay. We provided a design for actuator dynamics governed by the heat PDE. In this chapter we consider actuator dynamics governed by the wave PDE, a rather more challenging problem than that in Chapter 15. To imagine the physical meaning of having a wave PDE in the actuation path, one can think of having to stabilize a system to whose input one has access through a string. The challenges of overcoming string/wave dynamics in the actuation path include their infinite dimension, the finite (limited) propagation speed of the control signal (large control doesn“t help), and the fact that all of their (infinitely many) eigenvalues are on the imaginary axis.