No abstract

The backstepping approach is adapted to the problem of globally uniformly asymptotically stabilizing nonlinear systems in feedback form with a delay arbitrarily large in the input. The strategy of design relies on the construction of a Lyapunov-Krasovskii functional. Continuously differentiable control laws are constructed.

No abstract

In this paper, we propose a sex-structured entomological model that serves as a basis for design of control strategies relying on releases of sterile male mosquitoes (Aedes spp) and aiming at elimination of the wild vector population in some target locality. We consider different types of releases (constant and periodic impulsive), providing necessary conditions to reach elimination. However, the main part of the paper is focused on the study of the periodic impulsive control in different situations. When the size of wild mosquito population cannot be assessed in real time, we propose the so-called open-loop control strategy that relies on periodic impulsive releases of sterile males with constant release size. Under this control mode, global convergence towards the mosquito-free equilibrium is proved on the grounds of sufficient condition that relates the size and frequency of releases. If periodic assessments (either synchronized with releases or more sparse) of the wild population size are available in real time, we propose the so-called closed-loop control strategy, which is adjustable in accordance with reliable estimations of the wild population sizes. Under this control mode, global convergence to the mosquitofree equilibrium is proved on the grounds of another sufficient condition that relates not only the size and frequency of periodic releases but also the frequency of sparse measurements taken on wild populations. Finally, we propose a mixed control strategy that combines open-loop and closed-loop strategies. This control mode renders the best result, in terms of overall time needed to reach elimination and the number of releases to be effectively carried out during the whole release campaign, while requiring for a reasonable amount of released sterile insects.

No abstract

The present paper is devoted to the study of average consensus problems for undirected networks of dynamic agents having communication delays. The accent is put here on the study of the time-delays influence: both constant and time-varying delays are considered, as well as uniform and non uniform repartitions of the delays in the network. The main results provide sufficient conditions (also necessary in most cases) for existence of average consensus under bounded, but otherwise unknown, communication delays. Simulations are provided that show adequation with these results. IntroductionIn the last few years, the study of multi-agent systems has received a major attention within the control community. Driving applications include unmanned aerial vehicles, satellite clusters, automated highways and mobile robots. In all cases the aim is to control a group of agents connected through a wireless network. More precisely, rather than stabilizing the movement of each agent around a given set point, the goal is to understand how to make the agents coordinate and self-organize in moving formations. This problem becomes even more challenging under partial communication protocols, i.e. when each agent exchanges information only with few others.Many works in the literature focused on conditions for guaranteeing that the agents asymptotically reach a consensus, i.e. they agree upon a common value of a quantity of interest [11] happens when all vehicles asymptotically move with the same velocity. In the aforementioned papers, consensus problems have been studied under a variety of assumptions on the network topology (fixed/switching), the communication protocol (bidirectional or not), additional performance requirements (e.g. collision avoidance, obstacle avoidance, cohesion), and the control scheme adopted (also termed consensus protocol ). So far, just few works considered consensus problems when communication is affected by time-delays. Some results for discrete-time agent models are given in [5] and [1]. Two different consensus protocols for continuous-time agent dynamics have been investigated in [14] and [16]. More specifically, assuming that agents behave like integrators and that communication delays are constant in time and uniform (i.e. they have the same value in all channels), an analysis of the maximal delay that can be tolerated without compromising consensus has been performed in [14] and [16]. In particular, the protocol adopted in [16] is capable to guarantee average consensus (i.e. the state of each agent converges, asymptotically, to the average of the initial agent states rather than to an arbitrary constant) and the authors provide an explicit formula for the largest transmission delay.In the present work we generalize the results of [16] in various ways. First, we consider uniform and unknown time-varying delays and provide upper bounds to the maximal delay that does not prevent from achieving average consensus. Second, we derive similar conditions for networks affected by non uniform, constant or...

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of individuals carrying the Wolbachia parasite that need to be introduced into the natural population. The introduced mosquitoes are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human.In this study, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then use feedback control techniques to devise an introduction protocol which is proved to guarantee that the population converges to a stable equilibrium where the totality of mosquitoes carry Wolbachia.

The paper presents a result which relates connectedness of the interaction graphs in multi-agent discrete-time systems with the capability for global convergence to a common equilibrium of the system. In particular, we extend previously known results by Bertsekas and Tsitsiklis and by Moreau, by including the possibility of arbitrary bounded time delays in the communication channels and relaxing the convexity of the allowed regions for the state transition map of each agent.