Dorothée Normand-cyrot | CNRS UMR 8167 (original) (raw)

Papers by Dorothée Normand-cyrot

Research paper thumbnail of Exponential representations of Volterra-like expansions: an explicit computation of the exponent series

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

The paper concerns the exponential form representation of the flow associated with the solution o... more The paper concerns the exponential form representation of the flow associated with the solution of time varying nonlinear differential equations. Starting from the known fact that the exponent is a Lie series, an iterative computation of the successive Lie polynomials which define this exponent is proposed. The result is specified in the case of nonlinear difference equations.

Research paper thumbnail of On the solution of a Hamilton-Jacobi type equation in nonlinear discrete-time H/sub ∞/-control

Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1994

The subject of this paper is to show that there exists a smooth solution to the Hamilton-Jacobi t... more The subject of this paper is to show that there exists a smooth solution to the Hamilton-Jacobi type equation arising in nonlinear discrete-time H∞-control provided that a solution to the Riccati equation associated to the linear approximated problem is available. An approximated solution of the Hamilton-Jacobi type equation can be then iteratively computed making use of algebraic expansions

Research paper thumbnail of Nonlinear decoupling with stability via static state feedback for a class of discrete-time systems

Proceedings of the 36th IEEE Conference on Decision and Control, 1997

The paper deals with noninteracting control with stability via regular static state feedback for ... more The paper deals with noninteracting control with stability via regular static state feedback for a particular class of nonlinear discretetime systems. Discrete-time systems, nonlinear decoupling, stability.

Research paper thumbnail of Quadratic dynamic feedback linearization with observer in discrete time

Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1994

Research paper thumbnail of A Backstepping-like Approach to Adaptive Control in Discrete Time

European Journal of Control, 2000

Nonlinear adaptive control in discrete time is still largely open. The existing results deal with... more Nonlinear adaptive control in discrete time is still largely open. The existing results deal with particular cases and are mainly based upon traditional estimation techniques issued from the linear literature. In this paper, combining a backstepping strategy and "a posteriori" estimation concepts, a novel approach for achieving adaptive stabilization is proposed. It can directly be applied to a class of nonlinear discrete-time systems that, analogous to the continuous-time context, are said to be in a parametric strict-feedback form. Necessary and sufficient geometric conditions guaranteeing the equivalence of a general discrete-time dynamics to the parametric strict-feedback form or to some related classes of dynamics are also proposed.

Research paper thumbnail of Formal power series and input-output linearization of nonlinear discrete-time systems

The 22nd IEEE Conference on Decision and Control, 1983

ABSTRACT

Research paper thumbnail of An approach to nonlinear discrete-time H/sub ∞/-control

Proceedings of 32nd IEEE Conference on Decision and Control, 1993

Following recent works proposed in the continuous-time context concerning the nonlinear equivalen... more Following recent works proposed in the continuous-time context concerning the nonlinear equivalent of the I€,control problem and its connection with game theory and Isaacs equation, the present paper sets and studies the same problem in the discrete-time context. A digital static feedback law achieving closed-loop stability and disturbance attenuation is firstly designed under full information assumption and then by making use of an observer.

Research paper thumbnail of On the sampling of a linear analytic control system

1985 24th IEEE Conference on Decision and Control, 1985

... FA3 = 11 :30 ON THE SAMPLING OF A LINEAR AKALYTIC COI'ITZOL SVSTEM 5. Mo... more ... FA3 = 11 :30 ON THE SAMPLING OF A LINEAR AKALYTIC COI'ITZOL SVSTEM 5. Monaco* and D. Normand-Cyrot** *Department of "Informatica e S istemistica " . ... where ui:t; E E, f and the gi s, i (1, ..., m;, are analytic vector fields on Rn which are assumed to be complete. ...

Research paper thumbnail of A combinatorial approach of the nonlinear sampling problem

Lecture Notes in Control and Information Sciences, 1990

ABSTRACT

Research paper thumbnail of Nonlinear Systems in Discrete Time

Algebraic and Geometric Methods in Nonlinear Control Theory, 1986

Research paper thumbnail of ON THE CONTROL OF SINGULARLY PERTURBED NONLINEAR SYSTEMS

Nonlinear Control Systems Design 1992, 1993

Research paper thumbnail of Zero dynamics of sampled nonlinear systems

Systems & Control Letters, 1988

... 7. A. Isidori and C. Moog , On the nonlinear equivalent of the notion of transmission zeros. ... more ... 7. A. Isidori and C. Moog , On the nonlinear equivalent of the notion of transmission zeros. In:Modelling and Adaptive Control, Proc. IIASA Conf. (1986). ... 9. S. Monaco and D. Normand-Cyrot , Minimum phase non-linear discrete-time systems and feedback stabilisation. In: Proc. ...

Research paper thumbnail of Minimum-phase nonlinear discrete-time systems and feedback stabilization

26th IEEE Conference on Decision and Control, 1987

* Dipartimento di Ingegneria Elettrica, Universitl di L'Aquila, 67100 Montel... more * Dipartimento di Ingegneria Elettrica, Universitl di L'Aquila, 67100 Monteluco, L'Aquila. ** Laboratoire des Signax et SystePmes, CNRS-ESE, Plateau du Moulon, 91190 Gif-sur-Yvette, France. ... Abstract I nthispaper , followingideasrecentl ydeveloped for a class of continuous ...

Research paper thumbnail of Partial realization of a nonlinear discrete-time system from an equilibrium point

The 23rd IEEE Conference on Decision and Control, 1984

ABSTRACT

Research paper thumbnail of Issues on Nonlinear Digital Control

European Journal of Control, 2001

The purpose of this work is to show the real need to motivate theoretical research in nonlinear d... more The purpose of this work is to show the real need to motivate theoretical research in nonlinear digital control not only for solving control problems which are specific to the context, but also for giving the intuition of new control methodologies. Digital control methods can, indeed, be used either for the design of piecewice constant feedback strategies or for the design of discontinuous and hybrid controllers.

Research paper thumbnail of Canonical Representations of Nonlinear Discrete-time Systems

Systems, Models and Feedback: Theory and Applications, 1992

Research paper thumbnail of Adaptive control of discrete-time dynamics in parametric strict-feedback form

Proceedings of 35th IEEE Conference on Decision and Control, 1996

Stabilization under static-state feedback in presence of parametric uncertainties is studied for ... more Stabilization under static-state feedback in presence of parametric uncertainties is studied for a class of feedback linearizable discrete-time nonlinear dynamics. An iterative design procedure is proposed for dynamics which admit the parametric strict-feedback form. Starting from a specific class of discrete-time dynamics, necessary and sufficient geometric conditions for the existence of the parametric strict-feedback form are given.

Research paper thumbnail of Differential representations of driftless discrete-time dynamics

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998

The paper deals with nonlinear driftless discrete-time dynamics. I t is shown that such dynamics ... more The paper deals with nonlinear driftless discrete-time dynamics. I t is shown that such dynamics can always be represented by an exponential form which corresponds to the solution of a suitable differential equation. This enables us t o characterize the associated Lie group structure and to further understand invariance, accessibility and passivity properties. 2 Nonlinear driftless dynamics Let the driftless discrete-time dynamics be where x belongs to M , an analytic n-dimensional manifold, F : M x I R -+ M , is an analytic function of both arguments satisfying F ( . , 0) = 0. For U in a neighbourhood U, of 0, let the expansion of Id + F ( ., U ) be Id + F ( . , u ) = Id + '11 22 1 0-7803-4394-8198 $1 0.00 0 1998 IEEE 4620 Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 23,2010 at 13:38:47 UTC from IEEE Xplore. Restrictions apply.

Research paper thumbnail of On the differential/difference representation of sampled dynamics

Proceedings of the 44th IEEE Conference on Decision and Control, 2005

In this paper, the differential/difference representation (DDR) of an input-affine dynamics under... more In this paper, the differential/difference representation (DDR) of an input-affine dynamics under sampling is characterized. Making use of combinatoric identities and formal calculus techniques, it is shown how to compute the sampled dynamics at any desired degree of approximation.

Research paper thumbnail of An introduction to motion planning under multirate digital control

[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992

... [14] Monaco S. and D. Normand-Cyrot, Invariant Distributions under Sampling, in Theory and Ap... more ... [14] Monaco S. and D. Normand-Cyrot, Invariant Distributions under Sampling, in Theory and Applications of Nonlinear Control Systems, (CI Byrnes and A. Lindquist eds.) Elsevier Science Publishers, North-Holland, 1986, pp. [15] Monaco S. and D. Normand-Cyrot, Multirate ...

Research paper thumbnail of Exponential representations of Volterra-like expansions: an explicit computation of the exponent series

Proceedings of the 41st IEEE Conference on Decision and Control, 2002., 2002

The paper concerns the exponential form representation of the flow associated with the solution o... more The paper concerns the exponential form representation of the flow associated with the solution of time varying nonlinear differential equations. Starting from the known fact that the exponent is a Lie series, an iterative computation of the successive Lie polynomials which define this exponent is proposed. The result is specified in the case of nonlinear difference equations.

Research paper thumbnail of On the solution of a Hamilton-Jacobi type equation in nonlinear discrete-time H/sub ∞/-control

Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1994

The subject of this paper is to show that there exists a smooth solution to the Hamilton-Jacobi t... more The subject of this paper is to show that there exists a smooth solution to the Hamilton-Jacobi type equation arising in nonlinear discrete-time H∞-control provided that a solution to the Riccati equation associated to the linear approximated problem is available. An approximated solution of the Hamilton-Jacobi type equation can be then iteratively computed making use of algebraic expansions

Research paper thumbnail of Nonlinear decoupling with stability via static state feedback for a class of discrete-time systems

Proceedings of the 36th IEEE Conference on Decision and Control, 1997

The paper deals with noninteracting control with stability via regular static state feedback for ... more The paper deals with noninteracting control with stability via regular static state feedback for a particular class of nonlinear discretetime systems. Discrete-time systems, nonlinear decoupling, stability.

Research paper thumbnail of Quadratic dynamic feedback linearization with observer in discrete time

Proceedings of 1994 33rd IEEE Conference on Decision and Control, 1994

Research paper thumbnail of A Backstepping-like Approach to Adaptive Control in Discrete Time

European Journal of Control, 2000

Nonlinear adaptive control in discrete time is still largely open. The existing results deal with... more Nonlinear adaptive control in discrete time is still largely open. The existing results deal with particular cases and are mainly based upon traditional estimation techniques issued from the linear literature. In this paper, combining a backstepping strategy and "a posteriori" estimation concepts, a novel approach for achieving adaptive stabilization is proposed. It can directly be applied to a class of nonlinear discrete-time systems that, analogous to the continuous-time context, are said to be in a parametric strict-feedback form. Necessary and sufficient geometric conditions guaranteeing the equivalence of a general discrete-time dynamics to the parametric strict-feedback form or to some related classes of dynamics are also proposed.

Research paper thumbnail of Formal power series and input-output linearization of nonlinear discrete-time systems

The 22nd IEEE Conference on Decision and Control, 1983

ABSTRACT

Research paper thumbnail of An approach to nonlinear discrete-time H/sub ∞/-control

Proceedings of 32nd IEEE Conference on Decision and Control, 1993

Following recent works proposed in the continuous-time context concerning the nonlinear equivalen... more Following recent works proposed in the continuous-time context concerning the nonlinear equivalent of the I€,control problem and its connection with game theory and Isaacs equation, the present paper sets and studies the same problem in the discrete-time context. A digital static feedback law achieving closed-loop stability and disturbance attenuation is firstly designed under full information assumption and then by making use of an observer.

Research paper thumbnail of On the sampling of a linear analytic control system

1985 24th IEEE Conference on Decision and Control, 1985

... FA3 = 11 :30 ON THE SAMPLING OF A LINEAR AKALYTIC COI'ITZOL SVSTEM 5. Mo... more ... FA3 = 11 :30 ON THE SAMPLING OF A LINEAR AKALYTIC COI'ITZOL SVSTEM 5. Monaco* and D. Normand-Cyrot** *Department of "Informatica e S istemistica " . ... where ui:t; E E, f and the gi s, i (1, ..., m;, are analytic vector fields on Rn which are assumed to be complete. ...

Research paper thumbnail of A combinatorial approach of the nonlinear sampling problem

Lecture Notes in Control and Information Sciences, 1990

ABSTRACT

Research paper thumbnail of Nonlinear Systems in Discrete Time

Algebraic and Geometric Methods in Nonlinear Control Theory, 1986

Research paper thumbnail of ON THE CONTROL OF SINGULARLY PERTURBED NONLINEAR SYSTEMS

Nonlinear Control Systems Design 1992, 1993

Research paper thumbnail of Zero dynamics of sampled nonlinear systems

Systems & Control Letters, 1988

... 7. A. Isidori and C. Moog , On the nonlinear equivalent of the notion of transmission zeros. ... more ... 7. A. Isidori and C. Moog , On the nonlinear equivalent of the notion of transmission zeros. In:Modelling and Adaptive Control, Proc. IIASA Conf. (1986). ... 9. S. Monaco and D. Normand-Cyrot , Minimum phase non-linear discrete-time systems and feedback stabilisation. In: Proc. ...

Research paper thumbnail of Minimum-phase nonlinear discrete-time systems and feedback stabilization

26th IEEE Conference on Decision and Control, 1987

* Dipartimento di Ingegneria Elettrica, Universitl di L'Aquila, 67100 Montel... more * Dipartimento di Ingegneria Elettrica, Universitl di L'Aquila, 67100 Monteluco, L'Aquila. ** Laboratoire des Signax et SystePmes, CNRS-ESE, Plateau du Moulon, 91190 Gif-sur-Yvette, France. ... Abstract I nthispaper , followingideasrecentl ydeveloped for a class of continuous ...

Research paper thumbnail of Partial realization of a nonlinear discrete-time system from an equilibrium point

The 23rd IEEE Conference on Decision and Control, 1984

ABSTRACT

Research paper thumbnail of Issues on Nonlinear Digital Control

European Journal of Control, 2001

The purpose of this work is to show the real need to motivate theoretical research in nonlinear d... more The purpose of this work is to show the real need to motivate theoretical research in nonlinear digital control not only for solving control problems which are specific to the context, but also for giving the intuition of new control methodologies. Digital control methods can, indeed, be used either for the design of piecewice constant feedback strategies or for the design of discontinuous and hybrid controllers.

Research paper thumbnail of Canonical Representations of Nonlinear Discrete-time Systems

Systems, Models and Feedback: Theory and Applications, 1992

Research paper thumbnail of Adaptive control of discrete-time dynamics in parametric strict-feedback form

Proceedings of 35th IEEE Conference on Decision and Control, 1996

Stabilization under static-state feedback in presence of parametric uncertainties is studied for ... more Stabilization under static-state feedback in presence of parametric uncertainties is studied for a class of feedback linearizable discrete-time nonlinear dynamics. An iterative design procedure is proposed for dynamics which admit the parametric strict-feedback form. Starting from a specific class of discrete-time dynamics, necessary and sufficient geometric conditions for the existence of the parametric strict-feedback form are given.

Research paper thumbnail of Differential representations of driftless discrete-time dynamics

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998

The paper deals with nonlinear driftless discrete-time dynamics. I t is shown that such dynamics ... more The paper deals with nonlinear driftless discrete-time dynamics. I t is shown that such dynamics can always be represented by an exponential form which corresponds to the solution of a suitable differential equation. This enables us t o characterize the associated Lie group structure and to further understand invariance, accessibility and passivity properties. 2 Nonlinear driftless dynamics Let the driftless discrete-time dynamics be where x belongs to M , an analytic n-dimensional manifold, F : M x I R -+ M , is an analytic function of both arguments satisfying F ( . , 0) = 0. For U in a neighbourhood U, of 0, let the expansion of Id + F ( ., U ) be Id + F ( . , u ) = Id + '11 22 1 0-7803-4394-8198 $1 0.00 0 1998 IEEE 4620 Authorized licensed use limited to: Universita degli Studi di Roma La Sapienza. Downloaded on April 23,2010 at 13:38:47 UTC from IEEE Xplore. Restrictions apply.

Research paper thumbnail of On the differential/difference representation of sampled dynamics

Proceedings of the 44th IEEE Conference on Decision and Control, 2005

In this paper, the differential/difference representation (DDR) of an input-affine dynamics under... more In this paper, the differential/difference representation (DDR) of an input-affine dynamics under sampling is characterized. Making use of combinatoric identities and formal calculus techniques, it is shown how to compute the sampled dynamics at any desired degree of approximation.

Research paper thumbnail of An introduction to motion planning under multirate digital control

[1992] Proceedings of the 31st IEEE Conference on Decision and Control, 1992

... [14] Monaco S. and D. Normand-Cyrot, Invariant Distributions under Sampling, in Theory and Ap... more ... [14] Monaco S. and D. Normand-Cyrot, Invariant Distributions under Sampling, in Theory and Applications of Nonlinear Control Systems, (CI Byrnes and A. Lindquist eds.) Elsevier Science Publishers, North-Holland, 1986, pp. [15] Monaco S. and D. Normand-Cyrot, Multirate ...