Multiagent systems with hybrid interacting dynamics

Multiagent systems with hybrid interacting dynamics are groups of systems whose individual components have hybrid dynamics that affect each other's behavior at both the continuous and discrete levels. These systems are found in a wide range of applications including multivehicle systems, networks of sensors, actuators and embedded control systems, and communication networks. In this dissertation we study the modeling and control of these systems from various different perspectives. Motivated by a control problem in the design of future communication networks, we study a multiagent system whose agents move across a network of discrete locations competing for resources they obtain from such locations. The resources they compete for are continuous while the movements of agents in the network are discrete due to the discrete nature of their environment. The ultimate objective is to be able to control agents and nodes such that their interacting dynamics converge to a point that optimizes the usage of the network's resources. This motivates the formulation of a hybrid dynamical model for agents and nodes to be able to capture the continuous dynamics of the resource allocation, and the discrete dynamics of moving agents and changing network conditions. Additionally we apply resource allocation theory on the design of the continuous dynamics of agents and nodes. We then explore dynamical properties of Interconnected Hybrid Systems (IHS), which is a framework we propose to model general multiagent systems with hybrid interacting dynamics. In particular we obtain conditions for the existence and uniqueness of the executions of IHS and apply these conditions in the design of the general structure of the discrete dynamics of the agents in the resource allocation problem. Then we explore the application of randomized optimization algorithms to the optimal control of individual and multiagent hybrid systems. In the case of individual hybrid systems we compare the randomized approach to existing gradient based techniques obtaining comparable performance to this model-based technique. In the multiagent case we apply the same algorithm to the resource allocation problem, achieving the initial design objective of controlling the movements of agents towards a configuration that optimizes the usage of resources in the network. Finally, we explore the use of abstractions for the model simplification of individual hybrid systems, and discuss its applicability to the resource allocation problem. The abstraction we propose substitutes the continuous dynamics of a hybrid system for docks, creating a timed automaton that is simpler than the original system but retains the reachability and stability properties of the original system, and keeps track of the time that takes the original system to converge to an equilibrium set.