针对群系统编队形成问题，提出了一种满足LQR（Linear Quadratic Regulator）指标的优化控制方法。首先，建立编队形成问题的数学描述和设计编队形成控制协议。其次，给出群系统实现时变编队的充要条件，借助李雅普诺夫方法分析系统的稳定性。然后，设计了编队协议增益矩阵，给出了控制协议满足LQR指标的最优性条件。最后，仿真实验验证了控制方法的有效性。
For the problem of formation achievement for swarm systems， an optimal control method with LQR performance index is put forward. Firstly， a mathematical description of the formation achievement problem is established， and a formation achievement control protocol is developed. Secondly， necessary and sufficient conditions for the swarm system with time-varying formation are obtained， and the stability of the system is analyzed using the Lyapunov approach. Then， the gain matrices of the formation protocol are designed， and the optimal conditions for the control protocol with LQR performance index are given. Finally， a numerical simulation is conducted to illustrate the effectiveness of the control method proposed.
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