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Distributed Optimization in Multi-Agent Systems: Game Theory Based Sensor Coverage and Continuous-Time Convex Optimization


A multi-agent system is defined as a collection of autonomous agents which are able to interact with each other or with their environments to accomplish a task. The distributed control of MSNs is the main focus of recent research in this area. Examples of cooperative tasks include mobile sensor networks, distributed optimization, automated parallel delivery of payloads, region following formation control and coordinated path planning. One of the most important and well known task in multi-agent system is optimizing a cost function ( utility function) in a distributed manner. In this task, the action of each agent affects the team cost function, which is unknown to individual agents. Here our goal is to design a control algorithm for individual selfish agents to optimize the team cost function. In this dissertation, two optimization problems are investigated, where two different methods of game theory and convex optimization are employed to solve these problems.

In our first problem, the coverage problem in an unknown environment by a Mobile Sensor Network (MSN) is studied. An algorithm based on game theory is proposed, where a collection of distributed agents communicate with local neighbors and use their local information to make decisions.

In our second problem, a time-varying distributed convex optimization problem is studied for continuous-time multi-agent systems.

The objective is to minimize the sum of local time-varying cost functions, each of which is known to only an individual agent, through local interaction. Here the optimal point is time varying and creates an optimal trajectory.

In last part of this dissertation, the distributed average tracking problem is addressed for a group of heterogeneous physical agents consisting of single-integrator, double-integrator and Euler-Lagrange dynamics. Here, the goal is that each agent uses local information and local interaction to calculate the average of individual time-varying reference inputs, one per agent. Dynamic average tracking is the main challenge in many other distributed algorithms, such as distributed optimization, and distributed Kalman filtering.

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