Practical Finite‐Time and Fixed‐Time Guaranteed Cost Consensus for Second‐Order Nonlinear Multi‐Agent Systems With Switching Topology and Actuator Faults

ABSTRACT This paper investigates finite‐time and fixed‐time the guaranteed cost consensus problem for nonlinear second‐order systems, respectively, accompanied by unknown nonlinear functions approximated by a fuzzy logic system (FLS). Considering the possibility of actuator failures and topology switching, finite‐time and fixed‐time controllers are proposed to enable the system to eventually achieve finite‐time and fixed‐time guaranteed cost consensus, respectively. Furthermore, upper bounds on the guaranteed cost are obtained based on the Lyapunov functions designed for finite‐time and fixed‐time proofs, respectively. Finally, two examples are provided corresponding to the feasibility of proving the theorem using finite‐time and fixed‐time controllers, respectively.