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This paper concentrates on the issues of input–output finite-time stability (IO-FTS) and finite-time boundedness (FTB) for stochastic Takagi–Sugeno fuzzy nonlinear systems. The novel sufficient criterion regarding IO-FTS and FTB is derived. A state observer is built, which can estimate state that are difficult to measure. Using the constructed state observer and an observer-based event-triggered protocol, the event-triggered controller is constructed. The observer gains and controller gains can be derived from the obtained sufficient conditions. Furthermore, the practicality and feasibility for the presented control scheme are proven using a numerical example and an example of an inverted pendulum on a trolley system. [ABSTRACT FROM AUTHOR]

This paper investigates the finite‐time H∞$$ {H}_{\infty } $$ control of Itô‐type stochastic nonlinear systems. Considering the transient performance and anti‐interference ability within a given limited time interval, the control strategy of stochastic nonlinear systems is researched. A new sufficient condition for mean‐square finite‐time boundedness for stochastic nonlinear system is developed. Due to the state components are not available, a state observer is designed. Based on the estimated state, an H∞$$ {H}_{\infty } $$ controller is proposed and Linear Matrix Inequality (LMI) conditions are given, which not only guarantee the mean‐square finite‐time boundedness but also satisfy the corresponding H∞$$ {H}_{\infty } $$ performance. Finally, two examples are given to demonstrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

The current work has proposed an approach to the controller design of a fuzzy non-singular terminal sliding mode (NTSM) for a type of planar systems with input saturation. On the basis of a modified version of NTSM, a category of saturated NTSM controller is first constructed to ensure that the states can reach the sliding surface and finite-time converge to the origin. On this basis, a fuzzy logic controller including two fuzzy input variables and a fuzzy output variable is developed to adaptively adjust the control gain such that the gain of the NTSM controller can be automatically minimized. This also implies that the chattering phenomenon encountered by most conventional sliding mode control (SMC) schemes can be significantly attenuated without sacrificing inherent properties. Finally, in comparison with a traditional SMC method, the superiority of the presented algorithm is confirmed by the comparative simulation results in terms of chattering alleviation and robustness. [ABSTRACT FROM AUTHOR]

This paper concerns the problem of robust H∞ sliding mode control for a class of singular stochastic nonlinear systems. Integral sliding mode control is developed to deal with this problem. Based on the integral sliding surface of the design and linear matrix inequality, a sufficient condition which guarantees the sliding mode dynamics is asymptotically mean square admissible and has a prescribed H∞ performance for a class of singular stochastic nonlinear systems is proposed. Furthermore, a sliding mode control law is synthesized such that the singular stochastic nonlinear system can be driven to the sliding surface in finite time. Finally, a numerical example is proposed to illustrate the effectiveness of the given theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the hybrid synchronization behavior in an array of coupled chaotic systems with ring connection, of which means complete synchronization (CS) and anti-synchronization (AS) could coexist. First, the anti-synchronization controllers are designed, which can transform the synchronization error dynamic system into a nonlinear system with an antisymmetric structure. Second, we investigate the complete synchronization behavior in such a chaotic system under the anti-synchronization control. After that, the stability conditions are given for reaching hybrid synchronization. Finally, numerical examples and simulation results are presented to verify and validate the hybrid synchronization behavior in coupled chaotic system. [ABSTRACT FROM AUTHOR]

• As a first attempt, the SMC problem of PDT switched nonlinear systems is addressed, and the dynamic ET mechanism is introduced to alleviate the limited bandwidth resources, which is more general. • With the dynamic ET mechanism, a new switched SMC law is constructed with the PDT switching strategy that is more general than DT and ADT switching strategies, which can match the subsystem one by one more reasonably and reduce the conservativeness to some extent. • Based on the Lyapunov function approach, some sufficient conditions, which can ensure both the reachability and globally uniform exponential stability with an H ∞ performance of the closed-loop PDT switched system, are derived. In this paper, the H ∞ sliding mode control problem of persistent dwell-time switched nonlinear systems is investigated. Due to the limited bandwidth resources, a dynamic event-triggered mechanism is introduced to alleviate the transmission burden. Considering that the system parameters are switched in accordance with the persistent dwell-time switching strategy, a novel switched sliding mode control law is constructed. Then, drawing on the Lyapunov function approach, sufficient conditions are derived, which not only ensure the reachability of the sliding region around the specified sliding surface but also guarantee the globally uniform exponential stability of the system with an H ∞ performance. Moreover, the specific form of the controller gains is derived by utilizing an efficient decoupling method. Eventually, the validity of the proposed method is validated by two numerical examples. [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]

• The fuzzy stabilization of CSs is investigated via a sampled-data strategy; • The cost-efficient sampled data controller is designed; • Contrasted with the existing results, our developed one is less conservative. This work focuses on addressing the sampled-data stabilization problem for chaotic nonlinear systems, where the Takagi-Sugeno (T-S) fuzzy model is employed to dispose of the nonlinearity in the system as well as the controller. Contrasted to the traditional control strategy, a more practical piecewise sampled-data controller is developed, where the input delay during the signal transmission is considered. By introducing an approved method for processing fuzzy items and a novel Lyapunov-Krasovskii functional which is inspired by the Wirtinger inequality, as well as an advanced inequality derivation technique, some sufficient conditions with less conservatism are put forward. Appropriate controller gains can be acquired via the solution of the convex optimization problem. At last, the advantages and feasibility of the method proposed are explained by two numerical examples. [ABSTRACT FROM AUTHOR]