Lotfi Belkoura

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.

Parameters estimation of systems with delayed and structured entries

This paper deals with on-line identification of continuous-time systems with structured entries. Such entries, which may consist of inputs, perturbations or piecewise polynomial (time varying) parameters, can be defined as signals that can be easily annihilated. The proposed cancellation method allows to obtain non asymptotic estimators for the unknown coefficients. Application to delayed and switching hybrid systems are proposed. Numerical simulations with noisy data but also experimental results on a delay process are provided.

On identifiability of linear time-delay systems

Identifiability analysis is developed for linear time-delay systems with delayed states, control inputs, and measured outputs, all with a finite number of lumped delays. These systems are governed by linear functional differential equations with uncertain time-invariant parameters and delays. It is shown that the transfer function of such a system admits the online identification if a sufficiently nonsmooth input signal is applied to the system. Sufficiently nonsmooth signals are constructively defined by imposing different smoothness properties on the control input and the state of the system. The required nonsmoothness property is verified independently of any underlying time-delay system.

Identifiabilty of systems described by convolution equations

Parameter identifiability is studied for a class of finite- and infinite-dimensional systems described by convolution equations. The notion of sufficiently rich input which enforces identifiability is also addressed and the results are obtained assuming knowledge of solutions on a bounded time interval.

Identifiability analysis of linear time-delay systems

Identifiability analysis is developed for linear time-delay systems with delayed states, control inputs and measured outputs, all with a finite number of lumped delays. These systems are governed by linear functional differential equations with uncertain time-invariant parameters and delays. It is shown that the transfer function of such a system admits the online identification if a sufficiently nonsmooth input signal is applied to the system. Sufficiently nonsmooth signals are constructively defined by imposing different smoothness properties on the control input and the state of the system. This definition is verified independently of any underlying time-delay system. By applying the theory developed to linear time-delay systems whose states are available to measurements with an a priori known sensor delay, the system parameters and delays are proven to be, in principle, identifiable if and only if the system is weakly controllable. Just in case, the parameter identifiability is also enforced by a sufficiently nonsmooth control input.

A convolution approach for delay systems identification

Abstract This paper deals with on-line identification of delay systems. Based on non-asymptotic techniques, the estimation approach reduces to solving polynomials or eigenvalue problems. Numerical simulations with noisy data but also with slowly time varying parameters and delay are provided.

A DISTRIBUTION FRAMEWORK FOR THE FAST IDENTIFICATION OF LINEAR SYSTEMS WITH DELAYS

Abstract This paper deals with on line identification of delay systems. The work is based on the approach initiated in (Fliess M., 2003) and extended to delays identification.

A fast identification algorithm for systems with delayed inputs

A fast identification algorithm is proposed for systems with delayed inputs. It is based on a non-asymptotic distributional estimation technique initiated in the framework of systems without delay. Such a technique leads to simple realisation schemes, involving integrators, multipliers and piecewise polynomial or exponential time functions. Thus, it allows for a real-time implementation. In order to introduce a generalisation to systems with input delay, three simple examples are presented here. The first illustration is a first-order model with delayed input and noise. Then, a second-order system driven through a transmission line is considered. A third example shows a possible link between simultaneous identification and generalised eigenvalue problems.

Identifiability and algebraic identification of time delay systems

Identifiability and algebraic identification of time delay systems are investigated in this paper. Identifiability results are first presented for linear delay systems described by convolution equations. On-line algorithms are next proposed for both parameters and delay estimation. Based on a distributional technique, these algorithms enable an algebraic and simultaneous estimation by solving a generalized eigenvalue problem. Simulation studies with noisy data and experimental results show the performance of the proposed approach.

Algebraic switching time identification for a class of linear hybrid systems

Abstract In this paper, a method for the finite time estimation of the switching times in linear switched systems is proposed. The approach is based on distribution theory. Switching time estimates are given by explicit algebraic formulae that can be implemented in a straightforward manner using standard tools from computational mathematics. Simulations illustrate the proposed techniques.