PDE-based modeling and control of multi-agent systems

Abstract

This study focuses on the modeling and control of multi-agent systems. Such systems arise in several application domains such as smart grid networks, UAV swarms, and so on. Modeling and/or control of such systems is challenging due to the large number of agents involved in these systems. The common approach of modeling such systems using Ordinary Differential Equations leads to models with large numbers of equations, and this makes the analysis of such systems time-consuming. We therefore investigate the use of Partial Differential Equation (PDE) models for such systems. In these PDE models, the number of agents enters the model as a parameter, and because of this, the number of equations in the model does not increase with an increase in the number of agents. In this dissertation, we consider the problems of demand-side energy management, traffic cybersecurity modeling, UAV swarm control and wind farm power generation control. In demand-side energy management, this study present a control scheme for a system of aggregated thermostatically controlled loads that are represented by two coupled PDEs, namely, the Fokker-Planck Equations. The objective of the controller is to ensure that the cumulative power consumption of the system tracks any desired power consumption trend. In the traffic cybersecurity problem, this study develops PDE models of vehicular cyber-attacks. We consider scenarios wherein a group of vehicles perform a coordinated attack to create undesirable wave effects among other vehicles on the highway. In the UAV swarm problem, this study develops guidance laws that enable a swarm of UAVs track the spatio-temporal evolution of a contaminant in 3-Dimensional space. The contaminant spread and the UAV swarm, are both modeled by PDE equations. Finally, this study presents a new PDE-based modeling paradigm for wind farms to model power generated by the wind farms over the range of operating pitch and yaw angles. This PDE model is embedded into a hierarchical control structure which ensures that the cumulative power generated by the wind farm tracks any desired power generation trajectory