J-p Barbot | ENSEA - Academia.edu (original) (raw)
Papers by J-p Barbot
Proceedings of the International Conference on Control Applications
This paper proposes a new nonlinear sliding mode observer for induction motors. It points out the... more This paper proposes a new nonlinear sliding mode observer for induction motors. It points out the significance of higher order sliding modes to estimate in finite time the process variables. Some good simulation results have been obtained, that also exhibits the robustness properties of such a method.
SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483)
ABSTRACT In this paper we illustrate how to use the advantage of the differential flatness and th... more ABSTRACT In this paper we illustrate how to use the advantage of the differential flatness and the high order sliding mode control to deal with the problem of the trajectory planning and robust tracking of a car like robot.
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
This paper deals with nonholonomic perturbed systems. A necessary and sufficient condition on the... more This paper deals with nonholonomic perturbed systems. A necessary and sufficient condition on the perturbation vector field is given in order to put the system into a perturbed one-chained form. Then a sliding mode control strategy (with time-varying manifolds) to stabilize the system despite the perturbation is presented. Finally, simulations on the cart-like mobile robot are given
2007 46th IEEE Conference on Decision and Control, 2007
This paper deals with observability conditions and state observer design for a class of hybrid sy... more This paper deals with observability conditions and state observer design for a class of hybrid systems combining continuous and discrete dynamics. The main contribution of the work lies in the performed observability conditions for this class of systems and a design of hybrid observer to reconstruct both continuous and discrete states starting only from the knowledge of a continuous output. An illustrative example is presented showing the efficiency of the proposed observer.
2009 American Control Conference, 2009
This paper deals with necessary and sufficient conditions to transform a class of switched system... more This paper deals with necessary and sufficient conditions to transform a class of switched systems to a particular form dedicated to observer design with and without zeno phenomena. Meanwhile, sufficient observability conditions for switched system with or without zeno phenomena are given. In the last section, some observer structures are proposed upon two academical examples.
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
In this paper, the fundamental problem of residual generation is studied. The solution of this pr... more In this paper, the fundamental problem of residual generation is studied. The solution of this problem is the first step for the solution of the fault detection problem. Here, a class of nonlinear perturbed input-affine system is considered. The technique proposed is based on two steps: the first one consists of decoupling the perturbation with respect to the fault by using the technique of output injection; and the second one consists of fault detection by logic decision. A nonlinear observer with linearizable estimated error dynamics decoupled from the input and the disturbance is used as a residual generator. An illustrative example is presented
Proceedings of International Conference on Control Applications, 1995
ABSTRACT
Proceedings of IEEE Systems Man and Cybernetics Conference - SMC
This paper deals with the control under sampling of nonlinear singularly perturbed systems. Discr... more This paper deals with the control under sampling of nonlinear singularly perturbed systems. Discretization schemes for such systems are proposed, on the basis of a two time scale control law. The control under sampling of synchronous motors in a (α-β) representation is considered as a case study. This allows us to underline some pathology due to the discretization and reduction of this kind of nonlinear systems
Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
ABSTRACT
Chaos Theory, 2011
The paper belongs to the field of chaotic based cryptography. It relies on some ideas from classi... more The paper belongs to the field of chaotic based cryptography. It relies on some ideas from classical fundamentals as mixing functions suggested by C.E. Shannon for secrecy systems, and on the known publication of M.S. Baptista, a paper essentially implying the ergodicity assumption of the chaotic signal in cipher design. In this paper, the first step was to choose a chaotic system of a higher dimension than Baptista used, aiming to obtain a more complex system having a hyperchaotic behavior. The proposed algorithm is based on Generalized Hénon Map (3D), stated in literature as hyperchaotic for a number of bifurcation parameters. The paper advances a new mixing enciphering scheme based on the Generalized Hénon Map (GHM), which may be used as an inner element in a cipher, providing a good practical diffusion and confusion. A random variable transform is applied on the state of the chaotic system at each iteration in order to obtain a new random variable of a quasi uniform law. This new random variable is further transformed, through a series of other functions containing elements of the secret key, into a discrete random variable. The discrete values-which are ASCII numbers-are combined by a simple relation with the plain message, also in ASCII format. It is obtained a first mask of the original message, involving the GHM. On this result (in its binary representation form) other simple transformations that depend on the state of the GHM are applied. That finally allows getting a transformed version of the message that can be included in one of the states of the GHM without disturbing its chaotic behavior. The results, including a perception of the diffusion and the confusion involved, are illustrated on natural text and jpeg image.
International Symposium on Signals, Circuits and Systems ISSCS2013, 2013
Nonlinear Analysis: Hybrid Systems, 2010
In this paper, a mathematical analysis of a possible way to chaos for bounded piecewise smooth sy... more In this paper, a mathematical analysis of a possible way to chaos for bounded piecewise smooth systems of dimension 3 submitted to one of it's specific bifurcations, namely the sliding ones, is proposed. This study is based on period doubling method applied to the relied Poincaré maps.
Mathematics of Control, Signals, and Systems, 2009
This paper deals with quadratic equivalence, normal forms of observability, characteristic matric... more This paper deals with quadratic equivalence, normal forms of observability, characteristic matrices and normal quadratic numbers for nonlinear Single-Input Single-Output (SISO) systems. We investigated both cases; nonlinear systems linearly observable and nonlinear systems with one linear unobservable mode. Particularly, the e¤ect of the normal quadratic numbers on the observer design is pointed out. Finally, a faster observability analysis is proposed using characteristic matrices and normal quadratic numbers. Throughout the paper, academic examples as well as bio-reactor example highlight our purpose.
International Journal of Control, 2006
In this paper is given a constructive algorithm that transforms a linear system with unknown inpu... more In this paper is given a constructive algorithm that transforms a linear system with unknown inputs into a novel observability form. This form is useful to derive finite time observers even if the system does not satisfy some matching conditions usually required for the design of unknown input observers. The practical example of an aircraft subject to actuator faults is provided to show the efficiency of the approach.
International Journal of Control, 1999
ABSTRACT
International Journal of Bifurcation and Chaos, 2005
In this article, the secure transmission of data is being realized on the basis of the synchroniz... more In this article, the secure transmission of data is being realized on the basis of the synchronization of two chaotic systems. The transmitted signal is only the sign of a projection of the state. This has the advantage of making the transmission not very sensitive to the noises of transmission and the attenuation of the transmitted signal without using a VCO (Voltage Control Oscillatory) into the transmitter and the receiver. It should be noted that for the considered type of chaotic system, the traditional conditions of observability and linearization by injection of outputs are not checked. Here, we can only carry out an estimator.
IEEE Transactions on Automatic Control, 2013
The design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both... more The design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both state and input, still constitutes an open problem. In this paper, we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a Lyapunov-Krasovskii functional suitable choice. Sufficient conditions are provided to prove the practical stability of the observer. It is shown that the observation error is bounded and depends on the size of two parameters: the known upper bound delay of the unknown time-varying function delay and the instantaneous state dynamic variation. Furthermore, for the particular case of constant known time delay, the convergence of the proposed observer becomes exponential. The feasibility of the proposed strategy is illustrated by a numerical example.
IEEE Transactions on Automatic Control, 2011
This paper deals with the observability of a class of switched systems with Zeno phenomenon or hi... more This paper deals with the observability of a class of switched systems with Zeno phenomenon or high switching frequency. Particularly, three observability forms are proposed and the observability for each form with knowledge of filtered switching signal is analyzed. Meanwhile, sufficient and necessary conditions for the existence of a diffeomorphism to transform a class of switched systems into one of such forms are presented. Examples and simulations are given at the end to highlight the theoretical results.
IEEE Signal Processing Letters, 2010
Compressive sensing is a new methodology to capture signals at sub-Nyquist rate. To guarantee exa... more Compressive sensing is a new methodology to capture signals at sub-Nyquist rate. To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. In this letter, we propose to construct the sensing matrix with chaotic sequence following a trivial method and prove that with overwhelming probability, the RIP of this kind of matrix is guaranteed. Meanwhile, its experimental comparisons with Gaussian random matrix, Bernoulli random matrix and sparse matrix are carried out and show that the performances among these sensing matrix are almost equal.
Automatica, 2009
This paper provides some new developments in the design of unknown input observers for nonlinear ... more This paper provides some new developments in the design of unknown input observers for nonlinear systems. An algorithm which states if the state and the unknown input of the system can be recovered in finite time is introduced. This algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers. The proposed method is useful to relax some restrictive conditions of existing nonlinear unknown input observer design procedures.
Proceedings of the International Conference on Control Applications
This paper proposes a new nonlinear sliding mode observer for induction motors. It points out the... more This paper proposes a new nonlinear sliding mode observer for induction motors. It points out the significance of higher order sliding modes to estimate in finite time the process variables. Some good simulation results have been obtained, that also exhibits the robustness properties of such a method.
SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483)
ABSTRACT In this paper we illustrate how to use the advantage of the differential flatness and th... more ABSTRACT In this paper we illustrate how to use the advantage of the differential flatness and the high order sliding mode control to deal with the problem of the trajectory planning and robust tracking of a car like robot.
Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000
This paper deals with nonholonomic perturbed systems. A necessary and sufficient condition on the... more This paper deals with nonholonomic perturbed systems. A necessary and sufficient condition on the perturbation vector field is given in order to put the system into a perturbed one-chained form. Then a sliding mode control strategy (with time-varying manifolds) to stabilize the system despite the perturbation is presented. Finally, simulations on the cart-like mobile robot are given
2007 46th IEEE Conference on Decision and Control, 2007
This paper deals with observability conditions and state observer design for a class of hybrid sy... more This paper deals with observability conditions and state observer design for a class of hybrid systems combining continuous and discrete dynamics. The main contribution of the work lies in the performed observability conditions for this class of systems and a design of hybrid observer to reconstruct both continuous and discrete states starting only from the knowledge of a continuous output. An illustrative example is presented showing the efficiency of the proposed observer.
2009 American Control Conference, 2009
This paper deals with necessary and sufficient conditions to transform a class of switched system... more This paper deals with necessary and sufficient conditions to transform a class of switched systems to a particular form dedicated to observer design with and without zeno phenomena. Meanwhile, sufficient observability conditions for switched system with or without zeno phenomena are given. In the last section, some observer structures are proposed upon two academical examples.
Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187)
In this paper, the fundamental problem of residual generation is studied. The solution of this pr... more In this paper, the fundamental problem of residual generation is studied. The solution of this problem is the first step for the solution of the fault detection problem. Here, a class of nonlinear perturbed input-affine system is considered. The technique proposed is based on two steps: the first one consists of decoupling the perturbation with respect to the fault by using the technique of output injection; and the second one consists of fault detection by logic decision. A nonlinear observer with linearizable estimated error dynamics decoupled from the input and the disturbance is used as a residual generator. An illustrative example is presented
Proceedings of International Conference on Control Applications, 1995
ABSTRACT
Proceedings of IEEE Systems Man and Cybernetics Conference - SMC
This paper deals with the control under sampling of nonlinear singularly perturbed systems. Discr... more This paper deals with the control under sampling of nonlinear singularly perturbed systems. Discretization schemes for such systems are proposed, on the basis of a two time scale control law. The control under sampling of synchronous motors in a (α-β) representation is considered as a case study. This allows us to underline some pathology due to the discretization and reduction of this kind of nonlinear systems
Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
ABSTRACT
Chaos Theory, 2011
The paper belongs to the field of chaotic based cryptography. It relies on some ideas from classi... more The paper belongs to the field of chaotic based cryptography. It relies on some ideas from classical fundamentals as mixing functions suggested by C.E. Shannon for secrecy systems, and on the known publication of M.S. Baptista, a paper essentially implying the ergodicity assumption of the chaotic signal in cipher design. In this paper, the first step was to choose a chaotic system of a higher dimension than Baptista used, aiming to obtain a more complex system having a hyperchaotic behavior. The proposed algorithm is based on Generalized Hénon Map (3D), stated in literature as hyperchaotic for a number of bifurcation parameters. The paper advances a new mixing enciphering scheme based on the Generalized Hénon Map (GHM), which may be used as an inner element in a cipher, providing a good practical diffusion and confusion. A random variable transform is applied on the state of the chaotic system at each iteration in order to obtain a new random variable of a quasi uniform law. This new random variable is further transformed, through a series of other functions containing elements of the secret key, into a discrete random variable. The discrete values-which are ASCII numbers-are combined by a simple relation with the plain message, also in ASCII format. It is obtained a first mask of the original message, involving the GHM. On this result (in its binary representation form) other simple transformations that depend on the state of the GHM are applied. That finally allows getting a transformed version of the message that can be included in one of the states of the GHM without disturbing its chaotic behavior. The results, including a perception of the diffusion and the confusion involved, are illustrated on natural text and jpeg image.
International Symposium on Signals, Circuits and Systems ISSCS2013, 2013
Nonlinear Analysis: Hybrid Systems, 2010
In this paper, a mathematical analysis of a possible way to chaos for bounded piecewise smooth sy... more In this paper, a mathematical analysis of a possible way to chaos for bounded piecewise smooth systems of dimension 3 submitted to one of it's specific bifurcations, namely the sliding ones, is proposed. This study is based on period doubling method applied to the relied Poincaré maps.
Mathematics of Control, Signals, and Systems, 2009
This paper deals with quadratic equivalence, normal forms of observability, characteristic matric... more This paper deals with quadratic equivalence, normal forms of observability, characteristic matrices and normal quadratic numbers for nonlinear Single-Input Single-Output (SISO) systems. We investigated both cases; nonlinear systems linearly observable and nonlinear systems with one linear unobservable mode. Particularly, the e¤ect of the normal quadratic numbers on the observer design is pointed out. Finally, a faster observability analysis is proposed using characteristic matrices and normal quadratic numbers. Throughout the paper, academic examples as well as bio-reactor example highlight our purpose.
International Journal of Control, 2006
In this paper is given a constructive algorithm that transforms a linear system with unknown inpu... more In this paper is given a constructive algorithm that transforms a linear system with unknown inputs into a novel observability form. This form is useful to derive finite time observers even if the system does not satisfy some matching conditions usually required for the design of unknown input observers. The practical example of an aircraft subject to actuator faults is provided to show the efficiency of the approach.
International Journal of Control, 1999
ABSTRACT
International Journal of Bifurcation and Chaos, 2005
In this article, the secure transmission of data is being realized on the basis of the synchroniz... more In this article, the secure transmission of data is being realized on the basis of the synchronization of two chaotic systems. The transmitted signal is only the sign of a projection of the state. This has the advantage of making the transmission not very sensitive to the noises of transmission and the attenuation of the transmitted signal without using a VCO (Voltage Control Oscillatory) into the transmitter and the receiver. It should be noted that for the considered type of chaotic system, the traditional conditions of observability and linearization by injection of outputs are not checked. Here, we can only carry out an estimator.
IEEE Transactions on Automatic Control, 2013
The design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both... more The design of observers for nonlinear systems with unknown, time-varying, bounded delays, on both state and input, still constitutes an open problem. In this paper, we show how to solve it for a class of nonlinear systems by combining the high gain observer approach with a Lyapunov-Krasovskii functional suitable choice. Sufficient conditions are provided to prove the practical stability of the observer. It is shown that the observation error is bounded and depends on the size of two parameters: the known upper bound delay of the unknown time-varying function delay and the instantaneous state dynamic variation. Furthermore, for the particular case of constant known time delay, the convergence of the proposed observer becomes exponential. The feasibility of the proposed strategy is illustrated by a numerical example.
IEEE Transactions on Automatic Control, 2011
This paper deals with the observability of a class of switched systems with Zeno phenomenon or hi... more This paper deals with the observability of a class of switched systems with Zeno phenomenon or high switching frequency. Particularly, three observability forms are proposed and the observability for each form with knowledge of filtered switching signal is analyzed. Meanwhile, sufficient and necessary conditions for the existence of a diffeomorphism to transform a class of switched systems into one of such forms are presented. Examples and simulations are given at the end to highlight the theoretical results.
IEEE Signal Processing Letters, 2010
Compressive sensing is a new methodology to capture signals at sub-Nyquist rate. To guarantee exa... more Compressive sensing is a new methodology to capture signals at sub-Nyquist rate. To guarantee exact recovery from compressed measurements, one should choose specific matrix, which satisfies the Restricted Isometry Property (RIP), to implement the sensing procedure. In this letter, we propose to construct the sensing matrix with chaotic sequence following a trivial method and prove that with overwhelming probability, the RIP of this kind of matrix is guaranteed. Meanwhile, its experimental comparisons with Gaussian random matrix, Bernoulli random matrix and sparse matrix are carried out and show that the performances among these sensing matrix are almost equal.
Automatica, 2009
This paper provides some new developments in the design of unknown input observers for nonlinear ... more This paper provides some new developments in the design of unknown input observers for nonlinear systems. An algorithm which states if the state and the unknown input of the system can be recovered in finite time is introduced. This algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers. The proposed method is useful to relax some restrictive conditions of existing nonlinear unknown input observer design procedures.