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To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

This article discusses the issue of robust adaptive neural network (NN) consensus tracking control for nonlinear strict-feedback multi-agent systems with quantised input. By combining the neural network approach with robust techniques, a novel switching function is introduced to guarantee the tracking performance of this system. To estimate the unmeasured state, an NN-based adaptive state observer is developed. Based on backstepping dynamic surface control algorithms, a robust output feedback controller is constructed to guarantee that all signals in the closed-loop system remain globally uniformly ultimately bounded. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]