This paper considers the containment control problem for the discrete-time nonlinear multi-agent systems with unknown parameters and completely unknown control gains. In this paper, the dynamics of each agent are nonlinearly coupled with the neighbors’ states. To deal with the unknown parameters and control gains, a projection-type estimation algorithm is designed with the singular value avoided in the estimated control gains. The bounded estimation errors of parameters and control gains are guaranteed by the convergence analysis based on the Lyapunov approach. Then, using the estimated parameters and control gains, a distributed adaptive control protocol with only local information is designed for multi-agent systems. Under the proposed control protocol, the containment of multi-agent systems is guaranteed from a novel viewpoint of the absorbing Markov chain. Furthermore, simulations are carried out to illustrate the effectiveness of the proposed containment control protocol.

本文考虑了参数未知，控制增益完全未知的离散非线性多智能体系统的控制问题。在本文中，每个代理的动力学与邻居状态非线性耦合。为了处理未知参数和控制增益，设计了一种投影类型的估计算法，在估计的控制增益中避免了奇异值。基于Lyapunov方法的收敛性分析保证了参数和控制增益的有界估计误差。然后，使用估计的参数和控制增益，为多主体系统设计仅具有本地信息的分布式自适应控制协议。根据建议的控制协议，从吸收马尔可夫链的新颖观点出发，保证了多主体系统的包容性。此外，进行仿真以说明所提出的安全壳控制协议的有效性。