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In this article, we consider the design of a tracking controller for a class of uncertain nonlinear systems with external disturbances and actuator failures and achieve predesignated performance results on the tracking error. First, since the existing prescribed performance strategies are unable to specify performance bounds in an arbitrary way, we propose a new tool to address the prescribed performance issue by constructing chained first‐order filters and an input switching method. With the aid of the new and flexible prescribed performance tool, any predesignated continuous bounds can be formed by setting the reference coordinate values, sufficiently small coordinate value intervals and the gain parameters of the filters. Second, a full state feedback controller design scheme based on the prescribed performance bounds, which describe the convergence rate and maximum overshoot of the tracking error, is proposed. It is proven that the tracking error always satisfies the prescribed performance bounds. Finally, simulation studies are used to illustrate the effectiveness of the proposed tool and the correctness of the established theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This article considers the distributed finite‐time output consensus tracking problem for a class of high‐order nonlinear multiagent systems with the powers of positive odd rational numbers and output constraints. First, since the finite‐time tracking design method for a single system with the powers of positive odd rational numbers cannot be extended to the finite‐time consensus tracking for multiagent systems, an especial configuration method of the powers is constructed. Second, a new exponential brake function (EBF) that purely depends on the outputs is proposed to address the asymmetric output constraints directly. By adjusting a related parameter, the large converted value can be avoided when the output approaches the constrained boundaries, which may reduce the control input over a large output scale. Third, given some reasonable assumptions, a distributed finite‐time output consensus tracking controller is proposed to guarantee that the tracking error converges to an adjustable small region around the origin in a finite time and that the output constraints of all subsystems are not violated. The result with output constraints can also be extended to the case without output constraints. Finally, simulation verifications also confirm the benefits and effectiveness of the proposed control methods. [ABSTRACT FROM AUTHOR]

This paper addresses the adaptive finite-time consensus tracking problem for high-order nonlinear multi-agent systems (MASs) with powers of positive odd rational numbers under prescribed performance. Since the virtual and actual control parts of the dynamics of each follower agent are power functions containing positive odd rational numbers, the method of adding a power integrator is used to overcome the controller design difficulties caused by the power functions. With the aid of a finite-time performance function (FTPF) and neural networks (NNs), a distributed adaptive finite-time consensus tracking controller with prescribed tracking performance is properly designed by the backstepping process. It is shown that the proposed control strategy can guarantee that the consensus tracking error converges to an arbitrarily small neighborhood around zero at any settling time, while all signals of the closed-loop system are semi-globally practical finite-time stable (SGPF-stable). Finally, a simulation example is presented to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]