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.