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The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms...
This work concerns an enlarged analysis of the problem of asymptotic compensation for a
class of discrete linear distributed systems. We study the possibility of asymptotic
compensation of a disturbance by bringing asymptotically the observation in a given
tolerance zone 𝒞. Under convenient hypothesis, we show the existence and the
unicity of the optimal control ensuring this compensation and we give its
characterization
In this work, we examine, through the observation of a class of linear distributed systems, the possibility of reducing the effect of disturbances (pollution, etc.), by making observations within a given margin of tolerance using a control term. This problem is called enlarged exact remediability. We show that with a convenient choice of input and output operators (actuators and sensors, respectively), the considered control problem has a unique optimal solution, which will be given. We also study...
The exact boundary controllability of linear and nonlinear Korteweg-de
Vries equation on bounded domains with various boundary conditions is
studied. When boundary conditions bear on spatial derivatives up to
order 2, the exact controllability result by Russell-Zhang is directly
proved by means of Hilbert Uniqueness Method. When only the first
spatial derivative at the right endpoint is assumed to be controlled,
a quite different analysis shows that exact controllability holds too.
From...
We prove the exact boundary controllability of the 3-D Euler equation
of incompressible inviscid fluids on a regular connected bounded open set when the
control operates on an open part of the boundary that
meets any of the connected components of the boundary.
We consider the exact controllability of a hybrid system consisting of an elastic beam, clamped at one end and attached at the other end to a rigid antenna. Such a system is governed by one partial differential equation and two ordinary differential equations. Using the HUM method, we prove that the hybrid system is exactly controllable in an arbitrarily short time in the usual energy space.
We consider the exact controllability of a hybrid
system consisting of an elastic beam, clamped at one end and attached
at the other end to a
rigid antenna. Such a system is governed by one partial
differential equation and two ordinary differential equations. Using the
HUM method, we prove that the hybrid system is exactly
controllable in an arbitrarily short time in the usual energy space.
We study the boundary controllability of a nonlinear Korteweg–de Vries equation with the Dirichlet boundary condition on an interval with a critical length for which it has been shown by Rosier that the linearized control system around the origin is not controllable. We prove that the nonlinear term gives the local controllability around the origin.
We study the exact boundary controllability of two coupled one dimensional wave equations with a control acting only in one equation. The problem is transformed into a moment problem. This framework has been used in control theory of distributed parameter systems since the classical works of A.G. Butkovsky, H.O. Fattorini and D.L. Russell in the late 1960s to the early 1970s. We use recent results on the Riesz basis property of exponential divided differences.
By means of a direct and constructive method based on the theory of
semi-global C1 solution, the local exact boundary
observability is established for one-dimensional first order
quasilinear hyperbolic systems with general nonlinear boundary conditions. An implicit duality between the
exact boundary controllability and the exact boundary observability is then shown in the quasilinear case.
A model representing the vibrations of a fluid-solid coupled structure is
considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we
establish exact controllability results for this model with an internal control
in the fluid part and there is no control in the solid part. Novel features
which arise because of the coupling are pointed out. It is a source of
difficulty in the proof of observability inequalities, definition of weak
solutions and the proof of controllability...
A model representing the vibrations of a fluid-solid coupled structure is considered. Following Hilbert Uniqueness Method (HUM) introduced by Lions, we establish exact controllability results for this model with an internal control in the fluid part and there is no control in the solid part. Novel features which arise because of the coupling are pointed out. It is a source of difficulty in the proof of observability inequalities, definition of weak solutions and the proof of controllability results....
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