Didier Georges

Remote Stabilization Via Communication Networks With a Distributed Control Law

In this note, we investigate the problem of remote stabilization via communication networks involving some time-varying delays of known average dynamics. This problem arises when the control law is remotely implemented and leads to the problem of stabilizing an open-loop unstable system with time-varying delay. We use a time-varying horizon predictor to design a stabilizing control law that sets the poles of the closed-loop system. The computation of the horizon of the predictor is investigated and the proposed control law explicitly takes into account an estimation of the average delay dynamics. The resulting closed loop system robustness with respect to some uncertainties on the delay estimation is also considered. Simulation results are finally presented.

Remote output stabilization under two channels time-varying delays

Abstract In this paper we investigate the problem of remote output stabilization via two channels with time-varying delays. This problem arises when the control law is remotely implemented. The exchange of data between the controller and the system is done via two different transmission channels introducing time-varying delays with known dynamics. Assuming a known model for each of the time-delay dynamics, the work in (Witrant et al ., 2003) is extended to the case of two different delays appearing: (1) in the output measurement channel and, (2) in the transmission of the control law. This result is extended to output stabilisation by introducing a state observer built upon the delayed output of the plant. Simulation results are also presented.

A collocation model for water-hammer dynamics with application to leak detection

This paper presents a new model for so-called water hammer equations based on a collocation method. This model is shown to fairly represent possible leak effects in a pipeline and thus to be useful in the purpose of leak detection. This is illustrated in simulation by an example of observer-based leak detector relying on this model.

On the use of State Predictors in Networked Control Systems

Without pretending to be exhaustive, the aim of this chapter is to give an overview on the use of the state predictor in the context of time-delay systems, and more particularly for the stabilisation of networked control systems. We show that the stabilisation of a system through a deterministic network can be considered as the stabilisation of a time-delayed system with a delay of known dynamics. The predictor approach is proposed, along with some historical background on its application to time-delayed systems, to solve this problem. Some simulation results are also presented.

Input Optimization for Observability of State Affine Systems

In this paper a method for designing the input of a state affine system in order to guarantee a pre-specified degree of observability is proposed. It consists of an off-line algorithm to build an optimal, and so-called regularly persistent, input for the system. Optimality is defined with respect to the minimization of the input energy, and observability through a lower bound for the observability Gramian of the system, which is known to allow for an exponential observer design. The approach is presented for discrete-time systems, and is illustrated in simulation by an application example corresponding to a problem of fault detection in pipelines.

Finite-Difference Modeling Improvement for Fault Detection in Pipelines

This paper comes in continuation of former studies on finite-difference modeling for pipelines dynamics with a purpose of model-based fault detection. The finite-difference model is here revisited, and enhanced with extremal instrumentation modeling. It is then emphasized how such a model can indeed be useful for fault detection, in particular including instrumentation faults in addition to leaks for instance.

Online observability optimization for state affine systems with output injection and observer design

Observability being in general subject to the applied input for a nonlinear system, the aim of the present work is to propose an input selection strategy for a special class of systems, so as to make them observable. The considered systems are those admitting a state-affine structure with output injection. For such systems, an online algorithm is proposed to compute an appropriate input in real time. It guarantees observability by ensuring a lower bound on the related Gramian, and minimizes at the same time the input variations with respect to some reference value required for the system operation. This computation is updated at each time with the new output measurements becoming available. The proposed methodology is illustrated on a piping system example, for which an exponential observer is finally obtained.

Receding horizon boundary control of nonlinear conservation laws with shock avoidance

This paper deals with the boundary control for scalar non-linear hyperbolic systems of conservation laws. One of the issues arising from these systems is the occurrence of singularities (called shocks) in the domain. We will show that to avoid the shock, a set of constraints on both the control and the state at the boundary has to be fulfilled. Then, a proof of the exponential stability of the system is established provided that there is no shock and that the state at the boundary is exponentially stable. These conditions are shown to be achieved by the Receding Horizon Optimal Control approach. A simulation is finally carried out with the freeway traffic model to demonstrate the effectiveness of the here-proposed control.

Input selection in observer design for non-uniformly observable systems

Abstract In this paper the problem of inputs in observer design for systems which are not uniformly observable is considered. It is emphasized how it amounts to a control problem , which can be solved in a general way by some appropriate optimization approach. This is illustrated on the basis of a quite general Kalman-like observer form – possibly with high gain , as well as related simulation results on an application example.

Leak detection and location based on improved pipe model and nonlinear observer

This paper proposes a new contribution to observer-based approaches for detection and location of leaks in pipelines. In previous studies for such approaches, the observer is most of the time designed for a model obtained from hydraulic dynamical equations and finite difference techniques, using pressures at both ends of the pipe as boundary conditions; in the present work, the finite difference model is modified by using other boundary conditions, which are the pressure in the inlet pump and the pressure at the end of the pipe system. This modification provides a better representation of the pipeline dynamics, as illustrated by comparing the behavior simulated in this way with real data. It is then emphasized that this improved model may be used for an observer-based direct estimation of a possible leak flow in the pipe - together with its position, only using two measured variables (instead of four in former studies): one pressure at one end of the pipe, and one flow at the other pipe side. The other two variables, to be known by the observer - related to the boundary conditions, can indeed be taken here as constant values, since they correspond to the inlet pump pressure and the atmospheric pressure respectively. Results obtained with an Extended Kalman observer designed on this basis are finally presented, both in simulation and with real data.