On achievability of consensus in multi-agent control systems with a leader

The paper proposes a distributed control algorithm for multi-agent systems with a leader. The main objective is to ensure the asymptotic convergence of the states of all follower agents to the state of the leader, under the condition that each agent uses only local information obtained from neighboring nodes. The dynamics of the agents are modeled by a second-order system – a double integrator, which allows to take into account both the position and velocity of the agents. This description more accurately reflects the properties of real systems compared to the commonly used simplified first-order models. Graph theory is employed to formalize the topology of communication links between agents. The developed algorithm is based on the idea of pinning control and uses local information about the states of neighboring agents and the leader. The Lyapunov method and eigenvalue analysis were used to study the stability of the system and to obtain analytical conditions for the gain factors that guarantee the achievement of consensus. To illustrate the efficiency and effectiveness of the proposed algorithm, numerical simulations are conducted in MATLAB. The leader's trajectory is chosen based on the optimal trajectory obtained in previous studies by the authors. The results confirm that the states of the follower agents asymptotically converge to the state of the leader over time. The proposed algorithm can be applied to solve problems of group control of mobile robots, unmanned vehicles, and other distributed technical systems.

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