Consensus-based control for a network of diffusion PDEs with boundary local interaction

In this paper the problem of driving the state of a network of identical agents, modeled by boundary-controlled heat equations, towards a common steady-state profile is addressed. Decentralized consensus protocols are proposed to address two distinct problems. The first problem is that of steering the states of all agents towards the same constant steady-state profile which corresponds to the spatial average of the agents initial condition. A linear local interaction rule addressing this requirement is given. The second problem deals with the case where the controlled boundaries of the agents dynamics are corrupted by additive persistent disturbances. To achieve synchronization between agents, while completely rejecting the effect of the boundary disturbances, a nonlinear sliding-mode based consensus protocol is proposed. Performance of the proposed local interaction rules are analyzed by applying a Lyapunov-based approach. Simulation results are presented to support the effectiveness of the proposed algorithms

On The Joint Modeling of The Behavior of Social Insects and Their Interaction With Environment by Taking Into Account Physical Phenomena Like Anisotropic Diffusion

International audienceThis work takes place in the framework of GEODIFF project (funded by CNRS) and deals with the general issue of the social behavior modeling of pest insects with a particular focus on Bark Beetles. Bark Beetles are responsible for pine trees devastation in North America since 2005. In order to stem the problem and to apply an adapted strategy, one should be able to predict the evolution of the population of Bark Beetles. More precisely, a model taking into account a given population of insects (a colony) interacting with its environment, the forest ecosystem, would be very helpful. In a previous work, we aimed to model diffusive phenomenons across the environment using a simple reactive Multi-agent System. Bark beetle use pheromones as a support for recruitment of other bark beetles in the neighborhood in order to achieve a mass attack over a tree. They are first attracted by the ethanol or other phytopheromones emitted by a sick, stressed or dead tree and reinforce the presence of other individuals amongst the targeted tree. Both ethanol and semiochemicals are transported through the forest thanks to the wind, thermic effects and this advection phenomenon is modulated by the topology of the environment, tree and other obstacles distribution. In other words, the environment is involved in the process of a bark beetle attack. The first modeling we used to tackle our objective was not spatially explicit as long as free space propagation only was taken into account (isotropic phenomenon) with no constraint imposed by the environment such as wind. This article is intended to take into account such physical phenomenons and push the modeling one step further by providing predictions driven by measures provided by a Geographical Information System

Intracellular mechanochemical waves in an active poroelastic model

Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. We incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as an interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing, and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.Peer ReviewedPostprint (published version

Coverage and Field Estimation on Bounded Domains by Diffusive Swarms

In this paper, we consider stochastic coverage of bounded domains by a diffusing swarm of robots that take local measurements of an underlying scalar field. We introduce three control methodologies with diffusion, advection, and reaction as independent control inputs. We analyze the diffusion-based control strategy using standard operator semigroup-theoretic arguments. We show that the diffusion coefficient can be chosen to be dependent only on the robots' local measurements to ensure that the swarm density converges to a function proportional to the scalar field. The boundedness of the domain precludes the need to impose assumptions on decaying properties of the scalar field at infinity. Moreover, exponential convergence of the swarm density to the equilibrium follows from properties of the spectrum of the semigroup generator. In addition, we use the proposed coverage method to construct a time-inhomogenous diffusion process and apply the observability of the heat equation to reconstruct the scalar field over the entire domain from observations of the robots' random motion over a small subset of the domain. We verify our results through simulations of the coverage scenario on a 2D domain and the field estimation scenario on a 1D domain.Comment: To appear in the proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016

A Multiscale Model of Biofilm as a Senescence-Structured Fluid

We derive a physiologically structured multiscale model for biofilm development. The model has components on two spatial scales, which induce different time scales into the problem. The macroscopic behavior of the system is modeled using growth-induced flow in a domain with a moving boundary. Cell-level processes are incorporated into the model using a so-called physiologically structured variable to represent cell senescence, which in turn affects cell division and mortality. We present computational results for our models which shed light on modeling the combined role senescence and the biofilm state play in the defense strategy of bacteria

Dynamic coordinated control laws in multiple agent models

We present an active control scheme of a kinetic model of swarming. It has been shown previously that the global control scheme for the model, presented in \cite{JK04}, gives rise to spontaneous collective organization of agents into a unified coherent swarm, via a long-range attractive and short-range repulsive potential. We extend these results by presenting control laws whereby a single swarm is broken into independently functioning subswarm clusters. The transition between one coordinated swarm and multiple clustered subswarms is managed simply with a homotopy parameter. Additionally, we present as an alternate formulation, a local control law for the same model, which implements dynamic barrier avoidance behavior, and in which swarm coherence emerges spontaneously.Comment: 20 pages, 6 figure