Fixed-Time Distributed Optimization of High-Order Nonlinear Multiagent Systems Under Switching Topologies: A Two-Layer Control Framework

This paper investigates the fixed-time distributed optimization of nonlinear multi-agent systems (MASs) under switching topologies. In contrast to existing optimization strategies, this paper considers uncertain high-order dynamics and realizes fixed-time stability. To overcome the challenges brought by the coexistence of the switching topologies and high-order uncertain dynamics, a novel distributed optimization control method via two-layer framework is constructed, which consists of a Network Layer-optimization estimator design and a Physical Layer-Agents’ reference-tracking control law design. In Network Layer, the fixed-time optimal signal generator is constructed by using information interaction between agent and real-time feedback value of local gradient information over switching topologies. Then, in Physical Layer, the fixed-time fuzzy adaptive tracking control strategy is designed via backstepping technology to track the virtual signal generated from the Network-Layer. A fast fixed-time filter (FFTF) is introduced to avoid taking the derivation of discontinuous gradient functions in the process of backstepping. Furthermore, fuzzy logic systems (FLSs) are used to handle unknown nonlinear functions. By using the convex optimization theory, Lyapunov stability theory, and the fixed-time stability criterion, we analyze the convergence of the system and fixed-time stability. Finally, a simulation example is given to validate the control strategy.