Showing papers by "Jamal Daafouz published in 2016"

Stabilization of Nonlinear Systems Using Event-Triggered Output Feedback Controllers

Abstract: The objective is to design output feedback event-triggered controllers to stabilize a class of nonlinear systems. One of the main difficulties of the problem is to ensure the existence of a minimum amount of time between two consecutive transmissions, which is essential in practice. We solve this issue by combining techniques from event-triggered and time-triggered control. The idea is to turn on the event-triggering mechanism only after a fixed amount of time has elapsed since the last transmission. This time is computed based on results on the stabilization of time-driven sampled-data systems. The overall strategy ensures an asymptotic stability property for the closed-loop system. The results are proved to be applicable to linear time-invariant (LTI) systems as a particular case.

Synchronization in networks of linear singularly perturbed systems

Abstract: This work is motivated by the fact that many real systems are characterized by two features. The first one is that they are obtained by interconnecting a bunch of simpler subsystems that have to synchronize in order to reach a global goal. The second one is that each subsystem presents dynamics that evolves on different time-scales. Taking into account the two features leads to the problem of synchronization in networks of singularly perturbed systems. In this work we are providing a preliminary study that considers the problem where each subsystem is linear and the network topology is represented by a connected undirected graph that is fixed in time. We show that we can proceed to a time-scale separation of the overall network dynamics and design the controls that synchronize the slow dynamics and the fast ones. Applying the joint control actions to the network of singularly perturbed systems we obtain an approximation of the synchronization behavior imposed for each scale. The methodology requires a variable transformation to overcome the fact that we are dealing with non-standard singularly perturbed systems. One example illustrates the synchronization behavior of linear singularly perturbed systems.

Near-Optimal Strategies for Nonlinear and Uncertain Networked Control Systems

Abstract: We consider problems where a controller communicates with a general nonlinear plant via a network, and must optimize a performance index. The system is modeled in discrete time and may be affected by a class of stochastic uncertainties that can take finitely many values. Admissible inputs are constrained to belong to a finite set. Exploiting some optimistic planning algorithms from the artificial intelligence field, we propose two control strategies that take into account the communication constraints induced by the use of the network. Both strategies send in a single packet long-horizon solutions, such as sequences of inputs. Our analysis characterizes the relationship between computation, near-optimality, and transmission intervals. In particular, the first strategy imposes at each transmission a desired near-optimality, which we show is related to an imposed transmission period; for this setting, we analyze the required computation. The second strategy has a fixed computation budget, and within this constraint it adapts the next transmission instant to the last state measurement, leading to a self-triggered policy. For this case, we guarantee long transmission intervals. Examples and simulation experiments are provided throughout the paper.

Delays and Networked Control Systems

Abstract: This edited monograph includes state-of-the-art contributions on continuous time dynamical networks with delays. The book is divided into four parts. The first part presents tools and methods for the analysis of time-delay systems with a particular attention on control problems of large scale or infinite-dimensional systems with delays. The second part of the book is dedicated to the use of time-delay models for the analysis and design of Networked Control Systems. The third part of the book focuses on the analysis and design of systems with asynchronous sampling intervals which occur in Networked Control Systems. The last part of the book exposes several contributions dealing with the design of cooperative control and observation laws for networked control systems. The target audience primarily comprises researchers and experts in the field of control theory, but the book may also be beneficial for graduate students.

Trajectory planning for energy-efficient vehicles with communications constraints

Abstract: A new problem of optimizing a wireless mobile terminal trajectory under a given communication constraint is introduced. The mobile or vehicle has to move from a given starting point to a target point while uploading/downloading a given amount of data; this contrasts with the classical mobile communications paradigm where the communication and motion aspects are assumed to be independent. To reach the two aforementioned objectives, the mobile has to move sufficiently close to the wireless base station, while accounting for the energy cost due to motion. This setup is formalized here and leads us to determining non-trivial trajectories for the mobile. Remarkably, a counterpart of the Snell-Descartes law for the light propagation is exhibited (see Prop. 2) for the optimal trajectory of the mobile when the latter crosses zones in which the available data rates are different.

Output feedback event-triggered control

Abstract: Event-triggered control has been proposed as an alternative implementation to conventional time-triggered approach in order to reduce the amount of transmissions. The idea is to adapt transmissions to the state of the plant such that the loop is closed only when it is needed according to the stability or/and the performance requirements. Most of the existing event-triggered control strategies assume that the full state measurement is available. Unfortunately, this assumption is often not satisfied in practice. There is therefore a strong need for appropriate tools in the context of output feedback control. Most existing works on this topic focus on linear systems. The objective of this chapter is to first summarize our recent results on the case where the plant dynamics is nonlinear. The approach we follow is emulation as we first design a stabilizing output feedback law in the absence of sampling; then we consider the network and we synthesize the event-triggering condition. The latter combines techniques from event-triggered and time-triggered control. The results are then proved to be applicable to linear time-invariant (LTI) systems as a particular case. We then use these results as a starting point to elaborate a co-design method, which allows us to jointly construct the feedback law and the triggering condition for LTI systems where the problem is formulated in terms of linear matrix inequalities (LMI). We then exploit the flexibility of the method to maximize the guaranteed minimum amount of time between two transmissions. The results are illustrated on physical and numerical examples.

Stratégies événementielles de réinitialisation pour un consensus dans les systémes multi-agents

Abstract: Cet article porte sur le probleme du consensus dans un reseau partitionne en plusieurs clusters. Au sein de chaque cluster, les agents interagissent de maniere continue. En plus chaque cluster contient un agent specifique appele leader ayant la capacite de communiquer avec d'autres leaders en vue de s'accorder avec eux. Ces interactions s'averent couteuses puisqu'elles requierent des echanges sur des distances longues ou mal protegees. Neanmoins, ces interactions sont necessaires pour accomplir l'objectif global du reseau. Nous traitons dans cet article differentes strategies d'interconnections entre les leaders en vue d'optimiser le cout et la consommation d'energie et nous essayons de mettre l'accent sur l'apport de la technique evenementielle par rapport aux approches quasi-periodiques classiques.

Stability analysis of singularly perturbed switched and impulsive linear systems

Abstract: This paper proposes a new methodology for stability analysis of singularly perturbed linear systems whose dynamics is affected by switches and state jumps. The overall problem is formulated in the framework of hybrid singularly perturbed systems and we use Lyapunov-based techniques to investigate its stability. We emphasize that, beside the stability of slow and fast dynamics, we need a dwell-time condition to guarantee the overall singularly perturbed system is globally asymptotically stable. Furthermore, we characterize this dwell-time as the sum of one term related to the stabilization of systems evolving on one time-scale (slow dynamics) and one term of the order of the parameter defining the ratio between the time-scales. As highlighted in the paper the second term is required to compensate the effect of the jumps introduced in the state of the boundary layer system by the switches and impulses affecting the overall dynamics. Some numerical examples illustrates our results.

Design and Analysis of Reset Strategy for Consensus in Networks with Cluster Pattern

Abstract: This chapter addresses the problem of consensus in networks partitioned in several disconnected clusters. Each cluster is represented by a fixed, directed, and strongly connected graphs. In order to enforce the consensus, we assume that each cluster poses a leader that can reset its state by taking into account other leaders state. First, we characterize the consensus value of this model. Second, we provide sufficient condition in LMI form for the stability of the consensus. Finally, we perform a decay rate analysis and design the interaction network of the leaders which allows to reach a prescribed consensus value.