Predictor Feedback: Time-Varying, Adaptive, and Nonlinear
We present a tutorial introduction to methods for stabilization of systems with long input delays—the so-called “predictor feedback” techniques. The methods are based on techniques originally developed for boundary control of partial differential equations using the “backstepping” approach. We start with a consideration of linear systems, first with a known delay and then subject to a small uncertainty in the delay. Then we study linear systems with constant delays that are completely unknown, which requires an adaptive control approach. For linear systems, we also present a method for compensating arbitrarily large but known time-varying delays. Next, we consider nonlinear control problems in the presence of arbitrarily long input delays. Finally, we close with a design for general nonlinear systems with delays that have a general dependency on the system state.
KeywordsAutomatic Control Control Letter Input Delay Smith Predictor Adaptive Control Approach
Unable to display preview. Download preview PDF.
- 2.Smith, O.J.M.: A controller to overcome dead time. ISA 6, 28–33 (1959)Google Scholar
- 7.Michiels, W., Niculescu, S.-I.: Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach. SIAM (2007)Google Scholar
- 11.Krstic, M., Smyshlyaev, A.: Boundary Control of PDEs: A Course on Backstepping Designs. SIAM (2008)Google Scholar
- 12.Vazquez, R., Krstic, M.: Control of Turbulent and Magnetohydrodynamic Channel Flows. Birkhäuser (2007)Google Scholar
- 13.Krstic, M.: Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Birkhäuser (2009)Google Scholar