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Robust Distributed Control of Networked Systems with Linear Programming Objectives /

Abstract

The pervasiveness of networked systems in modern engineering problems has stimulated the recent research activity in distributed control. Under this paradigm, individual agents, having access to partial information and subject to real-world disturbances, locally interact to achieve a common goal. Here, we consider network objectives formulated as a linear program where the individual agents' states correspond to components of the decision vector in the optimization problem. To this end, the first contribution we make is the development of a robust distributed continuous-time dynamics to solve linear programs. We systematically argue that the robustness properties we establish for this dynamics are as strong as can be expected for linear programming algorithms. The next contribution we make is the design of a distributed event-triggered communication protocol for the aforementioned algorithm. We establish various state- based rules for agents to determine when they should broadcast their state, allowing us to relax the need for continual information flow between agents. Turning our attention to a specific network control problem for which our algorithm can be applied, we consider distributed bargaining in exchange networks. In this scenario, agents autonomously form coalitions of size two (called a match) and agree on how to split a payoff between them. We emphasize fair and stable bargaining outcomes, whereby matched agents benefit equally from the collaboration and cannot improve their allocation by unilaterally deviating from the outcome. We synthesize distributed algorithms that converge to such outcomes. Finally, we focus on cooperation-inducing mechanisms to ensure that agents in a bargaining outcome effectively realize the payoff they were promised. As an illustrative example, we study how to allocate the leader role in unmanned aerial vehicle (UAV) formation pairs. We show how agents can strategically decide when to switch from leading to following in the formation to ensure that the other UAV cooperates. Throughout the thesis, we emphasize the development of provably correct algorithms, making use of tools from the controls systems community such as Lyapunov analysis and the Invariance Principle. Simulations in distributed optimal control, multi-agent task assignment, channel access control in wireless communication networks, and UAV formations illustrate our results

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