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In this paper, the problem of distributed containment control for pure-feedback nonlinear multiagent systems under a directed graph topology is investigated.The dynamics of each agent are molded by high-order nonaffine pure-feedback form. Neural networks are employed to identify unknown nonlinear functions, and dynamic surface control technique is used to avoid the problem of explosion of complexity inherent in backstepping design procedure. The Frobenius norm of the ideal neural network weighting matrices is estimated, which is helpful to reduce the number of the adaptive tuning law and alleviate the networked communication burden. The proposed distributed containment controllers guarantee that all signals in the closed-loop systems are cooperatively semiglobally uniformly ultimately bounded, and the outputs of followers are driven into a convex hull spanned by the multiple dynamic leaders. Finally, the effectiveness of the developed method is demonstrated by simulation examples.

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SUMMARYThe problem of global adaptive state regulation is investigated via output feedback for uncertain feedforward nonlinear time-delay systems. Compared with existing results, our control schemes can be applicable to more general nonlinear time-delay systems because of combining the low-gain scaling approach with the backstepping method. In particular, we allow that there exist uncertain output function and uncertain growth rate imposed on nonlinear terms. Also, one considers a class of nonlinear systems with main-axis delay. By the Lyapunov-Krasovskii theorem, delay-independent controllers are proposed by constructing novel lowgain observers driven by system input, to regulate the states of original system while all the closed-loop signals are globally bounded. Furthermore, two examples are given to illustrate the usefulness of our results.

This paper studies the distributed consensus tracking control problem of multiple uncertain non-linear strict-feedback systems under a directed graph. The command filtered backstepping approach is utilised to alleviate computation burdens and construct distributed controllers, which involves compensated signals eliminating filtered error effects in the design procedure. Neural networks are employed to estimate uncertain non-linear items. Using a Lyapunov stability theorem, it is proved that all signals in the closed-looped systems are semi-globally uniformly ultimately bounded. In addition, consensus errors converge to a small neighbourhood of the origin by adjusting the appropriate design parameters. Finally, simulation results are presented to demonstrate the effectiveness of the developed control design approach.