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Mana Donganont | Applied Mathematics, University of Waterloo
Consensus Problems in Hybrid Multi-Agent Systems
A multi-agent system (MAS) is a dynamic system that consists of a group of interacting agents distributed over a network. In the past decades, the study of distributed coordination of multi-agent systems has been widely attracted by many groups of researchers such as mathematicians, engineers, physicists, and others. This is partly due to various applications in many areas, including spacecraft formation flying, multiple robot coordination, flocking, consensus or synchronization, cooperative control of vehicle formations, etc. As one of the most important problems in distributed coordination, consensus means that a group of agents achieves an agreement on a common value by designing the control law which is based on the information received by interacting with neighbors. There are many consensus methods that have been studied in recent years. Some problems focused on seeking the consensus of continuous-time (CT) multi-agent systems or discrete-time (DT) multi-agent systems, the others considered consensus problems on hybrid systems which are dynamical systems involving the interaction of continuous and discrete dynamics. Most consensus algorithms have been proposed for the multi-agent systems, but most results of consensus analysis are on the situation that all agents are continuous-time or discrete-time dynamic behavior. There are, however, some practical problems that the discrete-time and continuous-time dynamic agents coexist and interact with each other at the same time. Thus, it is reasonable to study consensus problems in such hybrid multi-agent systems (HMASs). Generally, the consensus protocols are designed to ensure that the states of all agents converge to a common value. However, up to date, in many practical problems, the states of agents may converge to prescribed ratios rather than a common value, such as compartmental mass-action systems, water distribution systems, and multiscale coordination control between spacecrafts and their simulating vehicles on ground. To deal with this problem, the scaled consensus problem has been introduced, where all agents will converge to the assigned proportions. Different from the standard consensus, where a group of agents seek to agree on a common quantity depending on the states of agents, scaled consensus implies that the state of each agent will approach prescribed ratios in the asymptote.
So, this work aims to study the (scaled) consensus problems in hybrid multi-agent systems under fixed and switching topologies including linear and nonlinear dynamics. Furthermore, we study consensus problems with communication delays, external perturbations, finite-time (scaled) consensus problems and also apply to the random networks.