Ph.D. Tezi Görüntüleme | |||||||||||||||||||||
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| Summary: In many applications such as search and rescue, mapping, target tracking, transportation, a multi-agent system must maintain a formation when accomplishing the planned task(s). Therefore, formation control is one of the fundamental problems in motion control of multi-agent systems. The formation control objective is to design a controller that drives all individuals to the desired formation in the state space. To maintain a formation, mobile agents need to exchange information such as relative positions and velocities. In this dissertation, the differential game approach to the leaderless formation control problem of a linear dynamical multi-agent system with the directed graph topology is considered. Under the framework of the linear-quadratic differential game, the game model of the multi-agent formation control is constituted, and for the non-cooperative mode of play the finite horizon Nash equilibrium solution is investigated. In this study, three different subproblems are constituted. First, the formation control problem is modeled as a linear-quadratic differential game. In this model, for every agent, an individual quadratic cost function is defined. As a result, with a leaderless approach, novel linear-quadratic modeling for the formation control is introduced. The solution has to be obtained numerically. In order to obtain an analytic formation control law as another subproblem in this study, each agent has been evaluated under a new cost function. As a result, a differential game formulation to formation control ensuring the existence of the formation control for every finite horizon time is proposed. As the third subproblem, the formation control problem is formulated a discrete-time dynamic game. As a result, the conditions for the existence of the discrete-time coupled Riccati difference equations are determined, and an analytical approximate solution of these equations is obtained. Throughout the dissertation, illustrative simulations approving the models and solutions are given.
Key Words: Formation control, Game theory, Differential game, Nash equilibrium; Coupled Riccati differential equations, Distributed control. | |||||||||||||||||||||