ODEs with Heat PDE Actuator Dynamics

Part of the Systems & Control: Foundations & Applications book series (SCFA)


In this chapter we use the backstepping approach from Chapter 2 to expand the scope of predictor feedback and build a much broader paradigm for the design of control laws for systems with infinite-dimensional actuator dynamics, as well as for observer design for systems with infinite-dimensional sensor dynamics.

In this chapter we address the problems of compensating for the actuator and sensor dynamics dominated by diffusion, i.e., modeled by the heat equation. Purely convective/first-order hyperbolic PDE dynamics (i.e., transport equation or, simply, delay) and diffusive/parabolic PDE dynamics (i.e., heat equation) introduce different problems with respect to controllability and stabilization. On the elementary level, the convective dynamics have a constant-magnitude response at all frequencies but are limited by a finite speed of propagation. The diffusive dynamics, when control enters through one boundary of a 1D domain and exits (to feed the ODE) through the other, are not limited in the speed of propagation but introduce an infinite relative degree, with the associated significant roll-off of the magnitude response at high frequencies.


Heat Equation Exponential Stability Input Delay Actuator Dynamics Sensor Dynamic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston 2009

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of CaliforniaSan Diego, La JollaUSA

Personalised recommendations