COORDINATION OF LEADER-FOLLOWER MULTI-AGENT SYSTEM WITH TIME-VARYING OBJECTIVE FUNCTION

This thesis aims to introduce a new framework for the distributed control of multi-agent systems with adjustable swarm control objectives. Our goal is twofold: 1) to provide an overview to how time-varying objectives in the control of autonomous systems may be applied to the distributed control of multi-agent systems with variable autonomy level, and 2) to introduce a framework to incorporate the proposed concept to fundamental swarm behaviors such as aggregation and leader tracking. Leader-follower multi-agent systems are considered in this study, and a general form of time-dependent artificial potential function is proposed to describe the varying objectives of the system in the case of complete information exchange. Using Lyapunov methods, the stability and boundedness of the agents\u27 trajectories under single order and higher order dynamics are analyzed. Illustrative numerical simulations are presented to demonstrate the validity of our results. Then, we extend these results for multi-agent systems with limited information exchange and switching communication topology. The first steps of the realization of an experimental framework have been made with the ultimate goal of verifying the simulation results in practice

Coordination of multi-agent systems: stability via nonlinear Perron-Frobenius theory and consensus for desynchronization and dynamic estimation.

This thesis addresses a variety of problems that arise in the study of complex networks composed by multiple interacting agents, usually called multi-agent systems (MASs). Each agent is modeled as a dynamical system whose dynamics is fully described by a state-space representation. In the first part the focus is on the application to MASs of recent results that deal with the extensions of Perron-Frobenius theory to nonlinear maps. In the shift from the linear to the nonlinear framework, Perron-Frobenius theory considers maps being order-preserving instead of matrices being nonnegative. The main contribution is threefold. First of all, a convergence analysis of the iterative behavior of two novel classes of order-preserving nonlinear maps is carried out, thus establishing sufficient conditions which guarantee convergence toward a fixed point of the map: nonnegative row-stochastic matrices turns out to be a special case. Secondly, these results are applied to MASs, both in discrete and continuous-time: local properties of the agents' dynamics have been identified so that the global interconnected system falls into one of the above mentioned classes, thus guaranteeing its global stability. Lastly, a sufficient condition on the connectivity of the communication network is provided to restrict the set of equilibrium points of the system to the consensus points, thus ensuring the agents to achieve consensus. These results do not rely on standard tools (e.g., Lyapunov theory) and thus they constitute a novel approach to the analysis and control of multi-agent dynamical systems. In the second part the focus is on the design of dynamic estimation algorithms in large networks which enable to solve specific problems. The first problem consists in breaking synchronization in networks of diffusively coupled harmonic oscillators. The design of a local state feedback that achieves desynchronization in connected networks with arbitrary undirected interactions is provided. The proposed control law is obtained via a novel protocol for the distributed estimation of the Fiedler vector of the Laplacian matrix. The second problem consists in the estimation of the number of active agents in networks wherein agents are allowed to join or leave. The adopted strategy consists in the distributed and dynamic estimation of the maximum among numbers locally generated by the active agents and the subsequent inference of the number of the agents that took part in the experiment. Two protocols are proposed and characterized to solve the consensus problem on the time-varying max value. The third problem consists in the average state estimation of a large network of agents where only a few agents' states are accessible to a centralized observer. The proposed strategy projects the dynamics of the original system into a lower dimensional state space, which is useful when dealing with large-scale systems. Necessary and sufficient conditions for the existence of a linear and a sliding mode observers are derived, along with a characterization of their design and convergence properties

Precise Dynamic Consensus under Event-Triggered Communication

This work addresses the problem of dynamic consensus, which consists of estimating the dynamic average of a set of time-varying signals distributed across a communication network of multiple agents. This problem has many applications in robotics, with formation control and target tracking being some of the most prominent ones. In this work, we propose a consensus algorithm to estimate the dynamic average in a distributed fashion, where discrete sampling and event-triggered communication are adopted to reduce the communication burden. Compared to other linear methods in the state of the art, our proposal can obtain exact convergence under continuous communication even when the dynamic average signal is persistently varying. Contrary to other sliding-mode approaches, our method reduces chattering in the discrete-time setting. The proposal is based on the discretization of established exact dynamic consensus results that use high-order sliding modes. The convergence of the protocol is verified through formal analysis, based on homogeneity properties, as well as through several numerical experiments. Concretely, we numerically show that an advantageous trade-off exists between the maximum steady-state consensus error and the communication rate. As a result, our proposal can outperform other state-of-the-art approaches, even when event-triggered communication is used in our protocol