This article investigates a penalty-based distributed optimization algorithm of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints. The proposed method addresses the distributed optimization problem by designing a penalty function in the form of a quadratic function, which is the sum of the global objective function and the consensus constraint. Moreover, the observer is presented to address the unmeasurable state of each agent. Radial basis function neural networks (RBFNN) are employed to approximate the unknown nonlinear functions. Then, by integrating RBFNN and dynamic surface control (DSC) techniques, an adaptive backstepping controller based on the barrier Lyapunov function (BLF) is proposed. Finally, the effectiveness of the suggested control strategy is verified under the condition that the state constraints are not broken. Simulation results indicate that the output trajectories of all agents remain within the upper and lower boundaries, converging asymptotically to the global optimal signal.

中文翻译：

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具有状态约束的高阶非线性不确定多智能体系统二分遏制控制的分布式凸优化。

本文研究了具有状态约束的高阶非线性不确定多智能体系统的基于惩罚的分布式二分遏制控制优化算法。该方法通过设计二次函数形式的罚函数来解决分布式优化问题，该罚函数是全局目标函数与一致约束的总和。此外，观察者被提出来解决每个代理的不可测量的状态。采用径向基函数神经网络（RBFNN）来逼近未知的非线性函数。然后，通过集成RBFNN和动态表面控制（DSC）技术，提出了一种基于势垒Lyapunov函数（BLF）的自适应反步控制器。最后在不打破状态约束的情况下验证了所提出控制策略的有效性。仿真结果表明，所有智能体的输出轨迹均保持在上下边界内，渐近收敛于全局最优信号。