Distributed optimal consensus via PI regulation for high‐order nonlinear agents over directed networks

This paper studies the optimal consensus problem of high‐order nonlinear agents under digraphs by PI regulation. A new type of adaptive PI variables is proposed for the first time, which is independent of the global information of graphs and complex dynamics. With the proposed variables, a key lemma is derived to transform the optimal consensus problem into a regulation problem, such that classical control techniques are used to regulate the adaptive PI variables for more complex dynamics. We also develop a new kind of distributed control algorithms based on the adaptive PI variables, Nussbaum‐type functions, and neural networks (NN). The proposed algorithms achieve the optimal consensus for high‐order nonlinear agents with nonidentical unknown control directions, bounded disturbances, and input saturation over weight‐unbalanced directed networks. Finally, a simulation example is provided to illustrate the effectiveness of the proposed algorithms.