Robust output feedback stabilization and nonlinear observer design

2004 ◽  
Author(s):  
l. Karafyllis ◽  
C. Kravaris
Keyword(s):  
Output Feedback ◽  
Feedback Stabilization ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Output Feedback Stabilization

Nonlinear Control of the Viscous Burgers Equation: Trajectory Generation, Tracking, and Observer Design

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Miroslav Krstic ◽  
Lionel Magnis ◽  
Rafael Vazquez
Keyword(s):  
Output Feedback ◽  
Burgers Equation ◽  
Nonlinear Partial Differential Equation ◽  
Trajectory Generation ◽  
Output Feedback Control ◽  
Companion Paper ◽  
Feedback Stabilization ◽  
Observer Design ◽  
Nonlinear Observer ◽  
Equilibrium Profiles

In a companion paper we have solved the basic problem of full-state stabilization of unstable “shock-like” equilibrium profiles of the viscous Burgers equation with actuation at the boundaries. In this paper we consider several advanced problems for this nonlinear partial differential equation (PDE) system. We start with the problems of trajectory generation and tracking. Our algorithm is applicable to a large class of functions of time as reference trajectories of the boundary output, though we focus in more detail on the special case of sinusoidal references. Since the Burgers equation is not globally controllable, the reference amplitudes cannot be arbitrarily large. We provide a sufficient condition that characterizes the allowable amplitudes and frequencies, under which the state trajectory is bounded and tracking is achieved. We then consider the problem of output feedback stabilization. We design a nonlinear observer for the Burgers equation that employs only boundary sensing. We employ its state estimates in an output feedback control law, which we prove to be locally stabilizing. The output feedback law is illustrated with numerical simulations of the closed-loop system.

scholarly journals Stability of Sampled-Data PDE-ODE Systems and Application to Observer Design and Output-Feedback Stabilization

2017 ◽  
Vol 50 (1) ◽  
pp. 13289-13294
Author(s):  
Iasson Karafyllis ◽  
Tarek Ahmed-Ali ◽  
Fouad Giri ◽  
Miroslav Krstic ◽  
Françoise Lamnabhi-Lagarrigue
Keyword(s):  
Output Feedback ◽  
Feedback Stabilization ◽  
Observer Design ◽  
Sampled Data ◽  
Output Feedback Stabilization ◽  
Ode Systems
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