Fixed-time cooperative output regulation for second-order nonlinear multiagent systems with an unknown exosystem

This paper investigates the fixed -time cooperative output regulation (FTCOR) problem with unknown exosystem of second -order nonlinear multiagent systems. To solve this problem, it is necessary to ensure that each agent can obtain the reference trajectory originating from an unknown exosystem and reconstruct the solution of the regulator equation containing the exogenous signal and unknown parameter vectors within a fixed time, and the unknown exosystem makes it difficult to solve these two problems with existing tools. By using auxiliary filtering variables, we propose a fixed -time adaptive distributed observer (FTADO) and design a fixed -time distributed internal model (FTDIM) based on this FTADO. These two new tools ensure the solvability of the two problems just mentioned. Then, based on these two tools, we transform the problem into a fixed -time stabilization problem of a so-called augmented system. Through the backstepping technique, we propose a distributed controller that solves this fixedtime stabilization problem while relaxing the assumptions of similar references.