Adaptive distributed optimization of high-order nonlinear multi-agent systems with predefined accuracy under state observer

This paper discusses adaptive distributed optimization with predefined accuracy for high-order nonlinear multi-agent systems (MASs) that are subject to disturbances and nonlinear uncertainties. To estimate the global optimal solution in real-time, a distributed proportional-integral optimization technique is used to generate a virtual system for each agent. For the unknown control gain of the controller, the Nussbaum function is employed. Then, a fuzzy adaptive observer is designed to estimate the unmeasured state by leveraging the general approximation capabilities of fuzzy logic systems. Using the Lyapunov stability method and backstepping technique, we develop the adaptive law and a new distributed controller. This ensures that the outputs of multi-agent systems converge to optimal values. Finally, a simulation example is used to confirm the viability of the presented control mechanism.