This paper studies an optimal consensus problem for a group of heterogeneous high-order agents with unknown control directions. Compared with existing consensus results, the consensus point is further required to an optimal solution to some distributed optimization problem. To solve this problem, we first augment each agent with an optimal signal generator to reproduce the global optimal point of the given distributed optimization problem, and then complete the global optimal consensus design by developing some adaptive tracking controllers for these augmented agents. Moreover, we present an extension when only real-time gradients are available. The trajectories of all agents in both cases are shown to be well-defined and achieve the expected consensus on the optimal point. Two numerical examples are given to verify the efficacy of our algorithms.

中文翻译：

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未知控制方向的多智能体最优共识

本文研究了一组具有未知控制方向的异构高阶智能体的最优共识问题。与现有的共识结果相比，对于一些分布式优化问题的最优解，进一步需要共识点。为了解决这个问题，我们首先用一个最优信号发生器来增强每个智能体以重现给定分布式优化问题的全局最优点，然后通过为这些增强的智能体开发一些自适应跟踪控制器来完成全局最优一致性设计。此外，当只有实时梯度可用时，我们提出了一个扩展。在这两种情况下，所有代理的轨迹都被证明是明确定义的，并且在最佳点上达到了预期的共识。给出了两个数值例子来验证我们算法的有效性。