Optimizing Multi-Agent Systems With Uncertain Dynamics: A Finite-Time Adaptive Distributed Approach

The topic of this study is adaptive distributed finite-time (FT) optimization of uncertain nonlinear high-order multi-agent systems (MASs) with disturbances. The proposed two-stage framework consists of an optimal FT estimator and an adaptive FT tracking controller. First, the estimator drives the optimization variables towards the optimal solution. In contrast to existing optimization control studies, high-order MASs subject to unknown dynamics are studied in this case. Second, by using the output of the estimator as a reference signal, the tracking controller allows all agents to approach the optimal point. The use of a command filter avoids the problem of discontinuous gradient functions, while it is possible to handle unknown nonlinear functions using fuzzy logic systems (FLSs). We prove, based on the FT stability criterion and convex optimization theory, that the proposed strategy minimizes the total objective function and results in a closed-loop system with bounded signals and FT convergence to the optimal solution. Finally, through a simulation example, the developed approach is verified.