Convergence of Trajectories for a Controlled Viscous Burgers’ Equation
In this paper we consider a boundary control problem for Burgers’ equation on a finite interval. The controls enter as gain parameters in the boundary conditions as in [1, 2]. The uncontrolled problem is obtained by equating the control parameters to zero while the zero dynamics system is obtained by equating the control parameters to infinity, or (intuitively) as the “high gain limit” of the system as the gains approach plus infinity. The main result of the paper is a nonlinear enhancement of the classical root locus result which states that the trajectories of the closed loop system converge to the trajectories of the zero dynamics system as the gains are increased to infinity.
1991 Mathematics Subject Classification93B05 93B28 93B52
Key words and phrasesBoundary control nonlinear distributed parameter systems zero dynamics convergence of trajectories
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