Jean-François Lafay

Decoupling without prediction of linear systems with delays: a structural approach

We exhibit, using a new structural approach specific for linear systems with delays, a necessary and sufficient condition for static row-by-row decoupling without prediction. Moreover, the decoupling problem is analyzed through two different concepts: the total one (without any time assumption), and the partial one (in a temporal mean), which can be considered if the total one has no solution.

Memory Resilient Gain-scheduled State-Feedback Control of Uncertain LTI/LPV Systems with Time-Varying Delays

The stabilization of uncertain LTI/LPV time-delay systems with time-varying delays by state-feedback controllers is addressed. Compared to other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow us to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the H∞ performance measure is considered. The interest of the approach is finally illustrated through several examples.

Design of LPV observers for LPV time-delay systems: an algebraic approach

The design of reduced order observer for linear parameter varying (LPV) time-delay systems is addressed. Necessary conditions guaranteeing critical structural properties for the observation error dynamics are first provided through nonlinear algebraic matrix equalities. An explicit parametrisation of the family of observers fulfilling these necessary conditions is then derived. Finally, an approach based on linear matrix inequalities is provided and used to select a suitable observer within this family, according to some criterion; e.g. maximisation of the delay margin or guaranteed suboptimal ℒ2-gain. Examples from the literature illustrate the efficiency of the approach.

Delay-scheduled state-feedback design for time-delay systems with time-varying delays—A LPV approach

Abstract This paper is concerned with the synthesis of delay-scheduled state-feedback controllers which stabilize linear systems with time-varying delays. In this framework, it is assumed that the delay is approximately known in real-time and used in the controller in a scheduling fashion. First, a new model transformation turning a time-delay system into an uncertain LPV system is introduced. Using this transformation, a new delay-dependent stability test based on the so-called full block S -procedure is developed and from this result, a new delay-dependent stabilization result is derived. Since the resulting LMI conditions depend polynomially on the parameters, a relaxation result is then applied in order to obtain a tractable finite set of finite-dimensional LMIs. The interest of the approach resides in (1) the synthesis of a new type of controller scheduled by the delay value which has a lower memory consumption than controllers with memory (since it is not necessary to store past values of the state), and (2) an easy consideration of uncertainties on the delay knowledge.

Modeling the Visual and Motor Control of Steering With an Eye to Shared-Control Automation

This paper describes a newly developed driver model that focuses on the control of car steering. The model represents visual anticipation of road curvature and compensation of lateral positioning error. It also incorporates a neuromuscular system, inspired by Hoult and Cole (2008), including an internal model of the steering system compliance, muscle co-activation by α and γ signals and the stretch reflex. Preliminary driving simulator experiments with five participants showed that the identification of model parameters yielded consistent results. Moreover, the model was able to steer the driving simulator by itself and showed a behavior similar to that of the human driver who provided the data for parameter identification. This model may be used for the design of automation for shared control of steering.

Delay-Scheduled State-Feedback Design for Time-Delay Systems with Time-Varying Delays

Abstract This paper is concerned in the synthesis of delay-scheduled state-feedback stabilizing linear systems with time-varying delay when the delay can be approximatively known in real-time. First we introduce a new model transformation turning the time-delay system into an uncertain LPV system. Using this reformulation we elaborate delay-dependent stability test based on the so-called full block S-procedure and derive from it a delay-dependent stabilization lemma. Our results are then relaxed using a new relaxation lemma which is shown to have good properties and provide then LMI based theorems, well-known for their tractability. Our results tackle error measurement on the delay. We show the efficiency of the method through an example.

Applied Interval Computation: A New Approach for Time-Delays Systems Analysis

This paper deals with interval analysis applied to linear time-delays systems. With basic examples, we describe some applications to solve various control problems, and to show that interval computation is an effective tool for time-delays systems analysis.

Optimal Control with Preview for Lateral Steering of a Passenger Car: Design and Test on a Driving Simulator

This paper is dedicated to studying the characteristics of the optimal preview control for lateral steering of a passenger vehicle. Such control is known to guarantee improved performance when the near future of the exogenous signal, here the road curvature, is known. The synthesis is performed in continuous time and leads to a two-degrees of freedom feedback and feedforward controller, whose feedforward part is a finite impulse response filter. The controller has been implemented on the SCANeRTMDriving Simulator available at IRCCyN, whose steering column is electrically powered. A methodology for choosing the weighting matrices in the quadratic index and the preview time are finally proposed. The obtained experimental results are discussed as well.

A full-block S-procedure application to delay-dependent H∞ state-feedback control of uncertain time-delay systems

Abstract This paper deals about the robust stabilization of uncertain systems with time-varying state delays in the delay dependent framework. The system is represented using LFR and stability is deduced from Lyapunov-Krasovskii theorem and full-block S-procedure. We derive sufficient conditions to the existence of a robust H infin; state-feedback control law. As this sufficient condition is expressed in terms of NMI we propose a relaxation based on the cone-complementary algorithm which is known to lead to good results for such problems. We show the efficiency of our method trough an example.

Disturbance attenuation by dynamic output feedback for input-delay systems

This paper addresses the disturbance attenuation problem by output feedback for multivariable linear systems with delayed inputs. To solve this problem, a feedback compensator is used, which is decomposed into an observer part, a state predictive part, and a static feedback part. Then, the analysis of the closed loop system is made on an equivalent linear system without delay. Based on the geometric approach, we solve two different disturbance attenuation problems, providing necessary and sufficient conditions for their solvability.