Vincent Andrieu

Brief paper: High gain observers with updated gain and homogeneous correction terms

Exploiting dynamic scaling and homogeneity in the bi-limit, we develop a new class of high gain observers which incorporate a gain update law and nonlinear output error injection terms. A broader class of systems can be addressed and the observer gain is better fitted to the incremental rate of the nonlinearities. The expected improved performance is illustrated.

Survey paper: A unifying point of view on output feedback designs for global asymptotic stabilization

The design of output feedback for ensuring global asymptotic stability is a difficult task which has attracted the attention of many researchers with very different approaches. We propose a unifying point of view aiming at covering most of these contributions. We start with a necessary condition on the structure of the Lyapunov functions for the closed loop system. This motivates the distinction of two classes of designs: -the direct approach, also called control error model analysis, in which the attention is focused on directly estimating a stabilizer, and -the indirect approach, also called dynamic error model analysis, in which the stabilization task is fulfilled for an estimated model of the system and not directly for the system itself. We show how most available results on this topic can be reinterpreted along these lines.

Uniting two Control Lyapunov Functions for affine systems

We consider the problem of piecing together two control Lyapunov functions (CLFs). The first CLF characterizes a local controllability property toward the origin, whereas the second CLF satisfies a global controllability property with respect to a compact set. We give a sufficient condition to express explicitly a solution to this uniting problem. This sufficient condition is shown to be always satisfied for a simple chain of integrator. In a second part, we show how this uniting CLF problem can be useful to solve the problem of piecing together two stabilizing control laws.

Asymptotic tracking of a reference trajectory by output-feedback for a class of non linear systems

We consider the problem of approximately tracking a reference trajectory by means of output feedback for a class of nonlinear systems with some non-globally Lipschitz nonlinearities. We solve this problem combining dynamic scaling, homogeneity in the bi-limit and new small gain arguments.

Global Asymptotic Stabilization for Nonminimum Phase Nonlinear Systems Admitting a Strict Normal Form

In this paper, we address the problem of global asymptotic stabilization by output feedback for nonminimum phase nonlinear systems which admit a strict normal form. We assume the knowledge of an observer and, depending on its properties, we propose various approaches to design the control law. Each of these approaches needs a different stabilizability assumption on the inverse dynamics. In this way, within a unified framework, we recover and extend some already published results and we establish new ones.

48th IEEE Conference on Decision and Control

This paper presents sufficient conditions for dissipativity on the Duhem hysteresis model. The result of this paper describes the dissipativity property of several standard hysteresis models, including the backlash and Prandtl operator. It also allows the curve in the hysteresis diagram (the phase plot between the input and the output) to have negative gradient.

Synthesis of a global asymptotic stabilizing feedback law for a system satisfying two different sector conditions

Global asymptotic stabilization for a class of nonlinear systems is addressed. The dynamics of these systems are composed of a linear part to which is added some nonlinearities which satisfy two different sector bound conditions depending wether the state is closed or distant from the origin. The approach described here is based on the uniting of control Lyapunov functions as introduced in [2]. The stabilization problem may be recast as an LMI optimization problem for which powerful semidefinite programming softwares exist. This is illustrated by a numerical example.

Homogeneity in the bi-limit as a tool for observer and feedback design

We introduce an extension of the notion of homogeneous approximation to make it valid both at the origin and at infinity (homogeneity in the bi-limit). Exploiting this extension, we give several results concerning stability, robustness and uniform (in the initial condition) finite time convergence for a homogeneous in the bi-limit vector field. We then introduce a homogeneous in the bi-limit observer and state-feedback for a chain of integrators. Combining these two tools we establish a global asymptotic stabilization result by output feedback for feedback and feedforward systems. We obtain also a finite time observer for globally Lipschitz system.

Sufficient conditions for dissipativity on Duhem hysteresis model

This paper presents sufficient conditions for dissipativity on the Duhem hysteresis model. The result of this paper describes the dissipativity property of several standard hysteresis models, including the backlash and Prandtl operator. It also allows the curve in the hysteresis diagram (the phase plot between the input and the output) to have negative gradient.