Non-linear estimation is easy

Non-linear state estimation and some related topics, like parametric estimation, fault diagnosis, and perturbation attenuation, are tackled here via a new methodology in numerical differentiation. The corresponding basic system theoretic definitions and properties are presented within the framework of differential algebra, which permits to handle system variables and their derivatives of any order. Several academic examples and their computer simulations, with on-line estimations, are illustrating our viewpoint

An algebraic state estimation approach for the recovery of chaotically encrypted messages

In this article we use a variant of recently introduced algebraic state estimation method obtained from a fast output signal time derivatives computation process. The fast time derivatives calculations are entirely based on the consequences of using the "algebraic approach" in linear system description. Here we demonstrate, through computer simulations, the effectiveness of the proposed algebraic approach in the accurate and fast (i.e. non asymptotic) estimation of the chaotic states in some of the most popular chaotic systems. The propsed state estimation method can then be used in a coding-decoding process of a secret message transmission using the message modulated chaotic system states and the reliable transmission of the chaotic system output. Simulation examples, using Chen's chaotic system output and the Rossler system, demonstrate the importance of the proposed fast state estimation method in the accurate extraction of a chaotically encrypted message. In our simulation results, the proposed approach is shown to be quite robust with respect to (computer generated) transmission noise perturbations. We also propose a way to evade computational singularities associated with the local lack of observability of certain chaotic system outputs and still carry out the encrypting and decoding of secret messages in a reliable manner

Control via state estimations of some nonlinear systems

This semiplenary talk at the IFAC Symposium on Nonlinear Control Systems (NOLCOS, Stuttgart, September 2004) is proposing state reconstructors for nonlinear systems. Our techniques extend a previous work on state reconstructors for linear systems by the same authors (Reconstructeurs d'état, C.R. Acad. Sci. Paris, série I, 338, 2004, pp. 91-96), which bypasses some of the classic difficulties related to asymptotic observers and Kalman filtering (lack of robustness and knowledge of the statistics). Our viewpoint which avoids the integration of differential equations and therefore any asymptotic estimation yields fast implementable algebraic formulae. Two concrete case studies are presented, which are (differentially) flat. Our state estimation permits a state-feedback around the flatness-based reference trajectory. Convincing computer simulations are provided, which demonstrate the robustness of our control strategy with respect to noises with unknown statistical properties

ADAPTIVE DYNAMICAL FEEDBACK REGULATION STRATEGIES FOR LINEARIZABLE UNCERTAIN SYSTEMS

In this paper we address the design of adaptive dynamical feedback strategies of the continuous and discontinuous, types for the output stabilization of nonlinear systems. The class of systems considered corresponds to nonlinear controlled systems exhibiting linear parametric uncertainty. Dynamical feedback controllers, ideally achieving output stabilization via exact linearization, are obtained by means of repeated output differentiation and, either, pole placement, or, sliding mode control techniques. The adaptive versions of the dynamical stabilizing controllers are then obtainable through standard, direct, overparamemzed adaptive control strategies available for linearizable systems. Illustrative examples are provided which deal with the regulation of electromechanical systems

Pulse Width Modulated Control of Robotic Manipulators

In this paper we propose a practical discontinuous feedback control scheme for the regulation of joint positions of robotic manipulators. A robust on-off switching control strategy based on a pulse-width-modulation (PWM) feedback scheme is proposed for the joint torques. The discontinuous PWM controller design is carried out on the basis of a suitable controller designed for an average model which is of continuous nature. Simulations of the closed loop performance of the proposed control scheme are presented for a two-link robotic manipulato

Vers une commande multivariable sans modèle

A control strategy without any precise mathematical model is derived for linear or nonlinear systems which are assumed to be finite-dimensional. Two convincing numerical simulations are provided

A Linear Active Disturbance Rejection Control for a Ball and Rigid Triangle System

This paper proposes an application of linear flatness control along with active disturbance rejection control (ADRC) for the local stabilization and trajectory tracking problems in the underactuated ball and rigid triangle system. To this end, an observer-based linear controller of the ADRC type is designed based on the flat tangent linearization of the system around its corresponding unstable equilibrium rest position. It was accomplished through two decoupled linear extended observers and a single linear output feedback controller, with disturbance cancelation features. The controller guarantees locally exponentially asymptotic stability for the stabilization problem and practical local stability in the solution of the tracking error. An advantage of combining the flatness and the ADRC methods is that it possible to perform online estimates and cancels the undesirable effects of the higher-order nonlinearities discarded by the linearization approximation. Simulation indicates that the proposed controller behaves remarkably well, having an acceptable domain of attraction

Discrete-time linear parametric identification: An algebraic approach

An improved and extended version is available at http://hal.inria.fr/inria-00188435/en/An algebraic framework for continuous-time linear systems identification introduced in the literature some years ago has revealed as an interesting alternative way for on-line parameter identification. The present contribution aims at conveying those ideas to linear time-invariant discrete-time systems, with particular emphasis attached to application issues. To this end, an on-line linear identifier for n-th order systems is evolved, re-sorting to the operational representation of the dynamics. Being discussed on the basis of a fifth-ordermodel of a drive-train, the numerical condition of the obtained setting of the identifier is found to suffer significantly with decreasing sampling times. A setting not experiencing these numerical problems is finally introduced by means of a re-parametrization of the identifier via application of the bilinear Tustin transform. The already implemented computer programs, where computer algebra plays an important role, are available. Note added on November 17th, 2007.- An improved and extended version is available at http://hal.inria.fr/inria-00188435/fr

Questioning some paradigms of signal processing via concrete examples

This paper was presented in November 2003 in Mexico City. It gives an overview of recent on-line and non-asymptotic estimation techniques in signal processing, which do not necessitate any precise statistical knowledge of the noises. Several concrete examples with their computer simulations are discussed