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New trends in design of observers for time-delay systems

Olivier Sename (2001)

Kybernetika

This paper presents some recent results about the design of observers for time-delay systems. It is focused on methods that can lead to design some useful observers in practical situations. First the links between observability properties and observers design is emphasized. Then some necessary and sufficient conditions and a method are provided to obtain unknown input observers for time-delay systems. Furthermore some H design using Lyapunov–Krasovskii and Lyapunov–Razumikhin theories are presented...

Non-linear observer design method based on dissipation normal form

Václav Černý, Josef Hrušák (2005)

Kybernetika

Observer design is one of large fields investigated in automatic control theory and a lot of articles have already been dedicated to it in technical literature. Non-linear observer design method based on dissipation normal form proposed in the paper represents a new approach to solving the observer design problem for a certain class of non-linear systems. As the theoretical basis of the approach the well known dissipative system theory has been chosen. The main achievement of the contribution consists...

Nonlinear observers for locally uniformly observable systems

Hassan Hammouri, M. Farza (2003)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4, 5, 6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems....

Nonlinear observers for locally uniformly observable systems

Hassan Hammouri, M. Farza (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the observability analysis and the observer synthesis of a class of nonlinear systems. In the single output case, it is known [4-6] that systems which are observable independently of the inputs, admit an observable canonical form. These systems are called uniformly observable systems. Moreover, a high gain observer for these systems can be designed on the basis of this canonical form. In this paper, we extend the above results to multi-output uniformly observable systems....

Nonlinear observers in reflexive Banach spaces

Jean-François Couchouron, P. Ligarius (2003)

ESAIM: Control, Optimisation and Calculus of Variations

On an arbitrary reflexive Banach space, we build asymptotic observers for an abstract class of nonlinear control systems with possible compact outputs. An important part of this paper is devoted to various examples, where we discuss the existence of persistent inputs which make the system observable. These results make a wide generalization to a nonlinear framework of previous works on the observation problem in infinite dimension (see [11, 18, 22, 26, 27, 38, 40] and other references therein).

Nonlinear observers in reflexive Banach spaces

Jean-François Couchouron, P. Ligarius (2010)

ESAIM: Control, Optimisation and Calculus of Variations

On an arbitrary reflexive Banach space, we build asymptotic observers for an abstract class of nonlinear control systems with possible compact outputs. An important part of this paper is devoted to various examples, where we discuss the existence of persistent inputs which make the system observable. These results make a wide generalization to a nonlinear framework of previous works on the observation problem in infinite dimension (see [11,18,22,26,27,38,40] and other references therein).

Nonlinear state observers and extended Kalman filters for battery systems

Andreas Rauh, Saif S. Butt, Harald Aschemann (2013)

International Journal of Applied Mathematics and Computer Science

The focus of this paper is to develop reliable observer and filtering techniques for finite-dimensional battery models that adequately describe the charging and discharging behaviors. For this purpose, an experimentally validated battery model taken from the literature is extended by a mathematical description that represents parameter variations caused by aging. The corresponding disturbance models account for the fact that neither the state of charge, nor the above-mentioned parameter variations...

Null controllability of a coupled model in population dynamics

Younes Echarroudi (2023)

Mathematica Bohemica

We are concerned with the null controllability of a linear coupled population dynamics system or the so-called prey-predator model with Holling type I functional response of predator wherein both equations are structured in age and space. It is worth mentioning that in our case, the space variable is viewed as the “gene type” of population. The studied system is with two different dispersion coefficients which depend on the gene type variable and degenerate in the boundary. This system will be governed...

Null controllability of a nonlinear diffusion system in reactor dynamics

Kumarasamy Sakthivel, Krishnan Balachandran, Jong-Yeoul Park, Ganeshan Devipriya (2010)

Kybernetika

In this paper, we prove the exact null controllability of certain diffusion system by rewriting it as an equivalent nonlinear parabolic integrodifferential equation with variable coefficients in a bounded interval of with a distributed control acting on a subinterval. We first prove a global null controllability result of an associated linearized integrodifferential equation by establishing a suitable observability estimate for adjoint system with appropriate assumptions on the coefficients. Then...

Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type

Karine Beauchard (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator x 2 + | x | 2 γ y 2 ( γ > 0 ) in the rectangle ( x , y ) ( - 1 , 1 ) × ( 0 , 1 ) or with the Kolmogorov-type operator v γ x f + v 2 f ( γ { 1 , 2 } ) in the rectangle ( x , v ) 𝕋 × ( - 1 , 1 ) , under an additive control supported in an open subset ω of the space domain.We prove that the Grushin-type equation is null controllable in any positive time for γ < 1 and that there is no time for which it is null controllable for γ > 1 ....

Null controllability of Grushin-type operators in dimension two

Karine Beauchard, Piermarco Cannarsa, Roberto Guglielmi (2014)

Journal of the European Mathematical Society

We study the null controllability of the parabolic equation associated with the Grushin-type operator A = x 2 + x 2 γ γ 2 , ( γ > 0 ) , in the rectangle Ω = ( - 1 , 1 ) × ( 0 , 1 ) , under an additive control supported in an open subset ω of Ω . We prove that the equation is null controllable in any positive time for γ < 1 and that there is no time for which it is null controllable for γ > 1 . In the transition regime γ = 1 and when ω is a strip ω = ( a , b ) × ( 0 , 1 ) ( 0 < a , b 1 ) ), a positive minimal time is required for null controllability. Our approach is based on the fact that, thanks to the particular...

Null controllability of the heat equation in unbounded domains by a finite measure control region

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically + or N . Considering an unbounded and disconnected control region of the form ω : = n ω n , we prove two null controllability results: under some technical assumption on the control parts ω n , we prove that every initial datum in some weighted L 2 space can be controlled to zero by usual control functions, and every initial datum in L 2 ( Ω ) can...

Null controllability of the heat equation in unbounded domains by a finite measure control region

Piermarco Cannarsa, Patrick Martinez, Judith Vancostenoble (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Motivated by two recent works of Micu and Zuazua and Cabanillas, De Menezes and Zuazua, we study the null controllability of the heat equation in unbounded domains, typically + or  N . Considering an unbounded and disconnected control region of the form ω : = n ω n , we prove two null controllability results: under some technical assumption on the control parts ω n , we prove that every initial datum in some weighted L2 space can be controlled to zero by usual control functions, and every initial datum in L2(Ω)...

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