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Two kinds of finite-time complex function synchronization for multiple complex-variable chaotic systems are investigated. Both the transmission mode and combination mode are respectively considered. By considering complex functions as the scaling factors, the definitions of the two different synchronization mechanisms are established, and the appropriate schemes are proposed to guarantee the finite-time stability of all error systems. Furthermore, two verifiable criteria are derived to synchronize multi-systems. Finally, detailed simulation analysis is provided to validate the effectiveness of all innovations. [ABSTRACT FROM AUTHOR]

This paper mainly investigates two kinds of sliding mode synchronization (SMS) for multiple chaotic systems with unknown parameters and disturbances. Both multiple coupled systems and uncoupled systems are considered. For multiple uncoupled chaotic systems (MUCSs), the sliding mode control scheme is designed to ensure that multiple response systems synchronize with one drive system under the effects of external disturbances, and the appropriate adaptive laws are proposed to estimate unknown parameters. For multiple coupled chaotic systems (MCCSs), the definition of transmission synchronization is given first. Furthermore, a special integral sliding surfaces is selected, and the corresponding controllers with the compensation terms are developed to realize SMS between every drive chaotic system and every respond system in transmission mode. Finally, some numerical examples are presented to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization of multiple chaotic systems with unknown parameters using adaptive control method, and two kinds of different synchronization modes are considered here. One is that more response systems synchronize with one drive system, and the other is the ring transmission synchronization, which guarantees that all chaotic systems can synchronize with each other. The definition of adaptive synchronization of multiple chaotic systems with unknown parameters is given, and then based on the idea of adaptive control method, adaptive laws are derived to estimate the unknown parameters, and nonlinear adaptive controllers are developed to ensure the asymptotical stability of two classes of error systems. Finally, simulation results are presented to verify the effectiveness of proposed synchronization schemes. [ABSTRACT FROM AUTHOR]

This paper focuses on the distributed adaptive finite-time control problem for nonlinear multi-agent systems (MASs). The fast practical finite-time criterion is extended to MASs. As such, a distributed adaptive finite-time protocol is established based on the recursion algorithm and neural networks (NNs), which provides a solution to cope with the adaptive finite-time regulate problem. Moreover, the proposed scheme is able to address the singular problem existing in the adaptive fuzzy/NN practical finite-time control. Furthermore, a simpler adaptive law is constructed. Finally, the presented method is applied to multiple robotic systems to illustrate its effectiveness. [ABSTRACT FROM AUTHOR]

• This is the first work to design a finite-time controller with a new adaptive mechanism by constructing a novel preset region. The dynamical change of the control gain is dependent on the case whether the state trajectories enter or leave a pre-designed domain or not. • The novel adaptive control strategy is presented to avoid the overestimation of the developed adaptive gain based on the adding a power integrator technique and the Lyapunov method. Meanwhile, the novel practical adaptive finite-time controller could improve the dynamic performance of systems and reduce the potential chattering influence. • In practical applications, the system states are usually finite-time stabilized to a neighborhood of the origin, rather than the origin. From this point of view, the investigation of practical finite-time stability (PFTS) for nonlinear systems is more meaningful. In this paper, the PFTS of second-order nonlinear systems has been verified under the developed adaptive finite-time controller. This paper considers the practical adaptive finite-time stabilization problem for a class of second-order systems. Based on the adding a power integrator technique and the adaptive method, a novel adaptive control strategy is presented to assure the trajectories of the closed-loop systems converge to a small neighborhood of the origin in a finite time. Under the adaptive control strategy, the dynamical change of control gain is dependent on the cases whether the state trajectories enter or leave a pre-designed domain or not. In addition, the practical finite-time stability (PFTS) of systems is testified via utilizing the Lyapunov method and adaptive mechanism. Last of all, the validity of the obtained practical adaptive finite-time algorithm is verified via simulation results. [ABSTRACT FROM AUTHOR]

• A modified design process of finite-time control (FTC) is achieved by utilizing prescribed performance control (PPC) and pre-assigned finitetime function (PFTF). • The states can converge to a predefined region within the pre-assigned finite-time. • The proposed method is more flexible and simpler since the convergence time is not related with the design parameters and initial values. • Nussubaum gain is employed to tackle the FTC problem for parameter systems with unknown signs. This paper mainly studies an adaptive finite-time control problem for a kind of uncertain strict feedback systems with unknown control gains. First, the original strict-feedback system is transformed into a pure-feedback system. And then, we propose a modified adaptive finite-time design idea on the basis of the property of pre-assigned finite-time function (PFTF) and Nussbaum gain. The designed controller can make sure that all states converge to an arbitrarily region in finite-time and signals in the closed-loop system are finite-time bounded. Moreover, the presented controller is smooth and the settling time does not rely on the initial values and design parameters. Finally, the simulation study is made to illustrate the innovativeness for the proposed scheme. [ABSTRACT FROM AUTHOR]