Wilfrid Perruquetti

Sliding Mode Control in Engineering

Introduction - an overview of classical sliding mode control differential inclusions and sliding mode control high-order sliding modes sliding mode observers dynamic sliding mode control and output feedback sliding modes, passivity, andflatness stability and stabilization discretization issues adaptive and sliding mode control steady modes in relay systems with delay sliding mode control for systems wiht time delay sliding mode control for systems with time delay sliding modecontrol of infinite-dimensional systems.

Finite-Time Observers: Application to Secure Communication

In this paper, control theory is used to formalize finite-time chaos synchronization as a nonlinear finite-time observer design issue. This paper introduces a finite-time observer for nonlinear systems that can be put into a linear canonical form up to an output injection. The finite-time convergence relies on the homogeneity properties of nonlinear systems. The observer is then applied to the problem of secure data transmission based on the finite-time chaos synchronization and the two-channel transmission method.

A novel higher order sliding mode control scheme

A higher order sliding mode control algorithm is proposed for a class of uncertain multi-input multi-output nonlinear systems. This problem can be viewed as the flnite time stabilization of a higher order input-output dynamic system with bounded uncertainties. The developed control scheme is based on geometric homogeneity and sliding mode control. The proposed procedure provides explicit conditions on the controller parameters and guarantees robustness against uncertainties. An illustrative example of a hovercraft vessel control demonstrates the advantages of the strategy.

Finite-time stability and stabilization of time-delay systems

Finite-time stability and stabilization of retarded-type functional differential equations are developed. First, a theoretical result on finite-time stability inspired by the theory of differential equations, using Lyapunov functionals, is given. As it may appear not easily usable in practice, we show how to obtain finite-time stabilization of linear systems with delays in the input by using an extension of Artsteins model reduction to nonlinear feedback. With this approach, we give an explicit finite-time controller for scalar linear systems and for the chain of integrators with delays in the input.

Brief Higher-order sliding mode stabilization for a class of nonholonomic perturbed systems

This paper deals with nonholonomic perturbed systems. Necessary and sufficient geometric conditions on the perturbation vector field are given in order to put the system into a perturbed one-chained form. Two different sliding mode control strategies are then designed to robustly stabilize, under some conditions, this chained system: one providing a practical stabilization, the other performing a finite time convergence. As a way of illustration, simulations on the example of the unicycle-type mobile robot are presented.

On the robust fault detection via a sliding mode disturbance observer

This paper deals with robust fault detection for non-linear systems. This problem is usually solved by designing an observable subsystem which is only affected by the fault and not by the control and disturbance inputs. However, such a subsystem may not exist so that the so-called fundamental problem of residual generation (FPRG) is not solvable. The aim of the present paper is to design a fault detection filter when the conditions for the existence of a solution to the non-linear FPRG are not satisfied. Our approach is made in a geometric context. Under some decoupling assumptions, the design of sliding mode observers allows us to reconstruct the disturbance inputs and then to generate an effective residual. An illustrative example is given throughout the paper.

Finite-time and fixed-time stabilization

Theorems on Implicit Lyapunov Functions (ILF) for finite-time and fixed-time stability analysis of nonlinear systems are presented. Based on these results, new nonlinear control laws are designed for robust stabilization of a chain of integrators. High order sliding mode (HOSM) algorithms are obtained as particular cases. Some aspects of digital implementations of the presented algorithms are studied, it is shown that they possess a chattering reduction ability. Theoretical results are supported by numerical simulations.

Finite time stability conditions for non-autonomous continuous systems

Finite time stability is defined for continuous non-autonomous systems. Starting with a result from Haimo (1986) we then extend this result to n-dimensional non-autonomous systems through the use of smooth and non-smooth Lyapunov functions as in Perruquetti and Drakunov (2000). One obtains two different sufficient conditions and a necessary one for finite time stability of continuous non-autonomous systems.

Brief paperFinite-time and fixed-time stabilization: Implicit Lyapunov function approach☆

Theorems on Implicit Lyapunov Functions (ILF) for finite-time and fixed-time stability analysis of nonlinear systems are presented. Based on these results, new nonlinear control laws are designed for robust stabilization of a chain of integrators. High order sliding mode (HOSM) algorithms are obtained as particular cases. Some aspects of digital implementations of the presented algorithms are studied, it is shown that they possess a chattering reduction ability. Theoretical results are supported by numerical simulations.

Delay identification in time-delay systems using variable structure observers

In this paper we discuss delay estimation in time-delay systems. In the introduction section a short overview is given of some existing estimation techniques as well as identifiability studies. In the following sections we propose several algorithms for the delay identification based on variable structure observers.