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- W308187645 abstract "Many systems modeling physical, mechanical, biological or economical phenomena are governed by partial differential equations. Such systems are called distributed parameter systems. The theory of distributed parameter systems is becoming a more and more complete theory, containing all the topics that are well known from finite-dimensional systems theory or lumped parameter systems described by ordinary differential equations. One direction of research in the theory of distributed parameter systems consists of studying their stability or stabilization, that is, the design of feedback controls to stabilize or to enhance stability. In this talk, we intend to investigate the stabilization of some distributed parameter systems, namely, (i) A one dimensional diffusive-wave equation commonly used in hydraulic engineering to describe dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important. In order to stabilize and regulate the system, we propose a proportional and integral boundary controller. Contrary to many physical systems, we end up with a non-dissipative closed-loop system with non-collocated actuators and sensors. We show that the closed-loop system is a Riesz spectral system and generates an analytic semigroup. Then, we shall be able to assign the spectrum of the closed-loop system in the open left-half plane to ensure its exponential stability as well as the output regulation independently of any known or unknown constant perturbation. These results are illustrated by several numerical examples. (ii) An n-dimensional wave equation with Neumann boundary conditions but without the presence of any displacement term. To stabilize the system, we propose a boundary feedback control involving only a damping term. Then using a new energy function, we show that the solutions of the system asymptotically converge to a stationary position, which depends on the initial data. Both linear and nonlinear controls are considered." @default.
- W308187645 created "2016-06-24" @default.
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- W308187645 date "2011-12-10" @default.
- W308187645 modified "2023-10-18" @default.
- W308187645 title "Plenary lecture 1: contributions to the stabilization of some distributed parameter systems" @default.
- W308187645 hasPublicationYear "2011" @default.
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