This article focuses on dynamic integral sliding mode control (SMC) of uncertain Takagi–Sugeno fuzzy delayed systems on time scales. SMC approaches for both continuous-and discrete-time fuzzy delayed systems are designed in a unified framework. First, we design a dynamic controller to guarantee global asymptotic stabilization (GAS) withH∞performance of the addressed systems. Second, to better adapt to the uncertainty characteristics of fuzzy models, an integral sliding mode surface (SMS) considering states, inputs, and uncertainties is proposed, which is an important contribution of this article. By utilizing the Lyapunov function and timescale calculus, it is shown that all states of the addressed control system can be driven close enough to the SMS and global asymptotic convergence (GAC) of the sliding motion can be ensured under matrix inequality criteria. In addition, the chattering phenomenon near the origin of discrete-time SMC system can be avoided in this article. Finally, three simulation examples are offered to illustrate the feasibility of the proposed control schemes.

This article develops a methodology employing partial differential equations (PDEs) to facilitate the exponential deployment of large-scale heterogeneous nonlinear multiagent systems (MASs). The considered MASs comprise a multitude of nonlinear first-order agents (FOAs) and second-order agents (SOAs). Two heterogeneous nonlinear PDEs are established to model the considered MASs by designing appropriate network communication protocols. Unlike previous PDE-based approaches for multiagent deployment, the topological weights between neighboring agents are defined as series-dependent. An informed agent, which is able to measure the location information of other agents and transmit its location information to neighboring agents through the communication network, is placed between the final FOA and the initial SOA. This novel network-based control scheme is referred to as single-point control, which could ensure the well-posedness and exponential stability of the error system. Accordingly, pointwise and distributed measurements are employed for delay-free and time-delayed cases, respectively. Numerical examples are provided in 3-D space to substantiate the obtained theoretical results.

This article investigates the practical finite-time spatial deployment of a class of large-scale heterogeneous nonlinear multi-agent systems (MASs), for which a novel hybrid analysis methodology based on ordinary differential equations (ODEs) coupled with partial differential equations (PDEs) is proposed. The assumption is made that a portion of the agents is sparsely distributed in space, while the other portion is densely distributed. By designing appropriate network communication protocols (NCPs), the dynamics of MASs are represented by a hybrid model consisting of several ODEs and a PDE. Particularly, the network topological weights are specifically designed as semi-Markov switched to better align with real communication situations of MASs, while complying with inconsistent switching rules. Moreover, for delay-free and time-delayed cases, this article proposes two novel projection-based adaptive neural control schemes and obtains two design criteria of controller gains, such that the practical finite-time stability of the tracking error systems could be guaranteed. Finally, numerical examples are provided to illustrate the effectiveness of the developed approaches.

For large-scale heterogeneous nonlinear multi-agent systems (MASs) consisting of abundant first-order and second-order agents, this paper presents a novel framework based on partial differential equations (PDEs) to facilitate their practically finite-time deployment in 2D or 3D space. First, through designing appropriate network communication protocols (NCPs), a heterogeneous nonlinear PDE model composed of a heat equation and a damped wave equation is constructed to characterize the collective dynamics of considered heterogeneous nonlinear MASs. Second, a single-point control strategy and a double-boundary control strategy are proposed, which could not only ensure the well-posedness of the closed-loop heterogeneous PDEs but also enable the finite-time deployment of multi agents. Notably, to better align with real MASs and operating environment, the network topologies and controllers are designed to be semi-Markov switched, while adhering to multiple asynchronous switching rules. Third, with the designed NCPs and control schemes, several sufficient conditions are derived to guarantee the practically finite-time stability of error systems. Finally, two numerical examples and an application example are conducted to validate effectiveness and practicability of the developed approaches.

For a class of 2-D spatial distributed parameter systems (DPSs) with space-dependent diffusivity, this article aims to achieve exponential realization of their desired profiles. To reduce the number of required sensors and actuators, a planar output feedback boundary control strategy is proposed with combining two nonfull-domain measurement methods, boundary collocated measurement and planar linear measurement, in which only two boundaries of the considered 2-D spatial DPSs are controlled and a little output information is measured. Moreover, by employing the Poincaré-Wirtinger inequality and variable substitution dexterously, the final exponential convergence criteria of the error system can be obtained with method of "Diverse treatment for same term." Finally, we provide a general numerical example and an application example in 2-D heat conduction systems to illustrate the effectiveness and practicability of the proposed measurement and control schemes.

This article considers both the semi-Markov jumping phenomenon and spatial distribution characteristics when investigating the exponential stabilization of memristive neural networks (MNNs). The introduction of the semi-Markov jumping parameters relaxes the restriction on the sojourn time of Markovian MNNs. To increase the operability while ensuring control effect, a novel event-based spatially pointwise-piecewise switching control scheme is presented under a unified spatial division criterion, in which the pointwise and piecewise control can switch according to the preset event condition for the applicability to different control requirements. Moreover, by constructing a semi-Markov Lyapunov functional and utilizing the properties of the considered cumulative distribution function, the final exponential stabilization criterion and two related corollaries are obtained. Finally, simulation results illustrate the effectiveness and superiority of the proposed control strategy.

Seldom existing studies directly focus on the control issues of 2-D spatial partial differential equation (PDE) systems, although they have strong application backgrounds in production and life. Therefore, this article investigates the finite-time control problem of a 2-D spatial nonlinear parabolic PDE system via a Takagi–Sugeno (T–S) fuzzy boundary control scheme. First, the overall fuzzy system model is constructed using T–S fuzzy rules to approximate the original nonlinear system. Second, based on the planar distributed measurement, boundary collocated measurement, and linear measurement methods, three novel kinds of fuzzy boundary controllers are designed, respectively. Then, by employing the variable substitution and integral inequality techniques, three criteria that ensure the finite-time boundness of the considered system are obtained. Finally, simulations of main results are provided to verify the effectiveness and practicability of the proposed measurement and control schemes.

This work investigates the problems of decentralized fault estimation within a finite-time interval (FTI) and fault-tolerant control for nonlinear interconnected distributed parameter systems under the situation of unpredictable faults. First, the fault estimator using interconnected information is designed to estimate the occurred faults over an FTI. Second, the designed fault-tolerant controller has a non-fragile characteristic and can make the considered system satisfy the prescribed performance index. Additionally, this article considers a real scenario where multiple switching channels exist in the network and supposes that the channel switching follows a Markovian switching law with discrete state. Furthermore, by establishing a global Lyapunov functional based on graph theory and employing the canonical Bessel–Legendre inequality method, the final results that are less conservative can be obtained reasonably. Finally, the feasibility, practicability and superiority of the main results are illustrated through three simulations.

For the considered reaction-diffusion inertial memristive neural networks (IMNNs), this article proposes a novel gain-scheduled generalized pinning control scheme, where three pinning control strategies are involved and$2^{n}$controller gains can be scheduled for different system parameters. Moreover, a time delay is considered in the controller to make it has a memory function. With the designed controller, drive-and-response systems can be synchronized within a finite-time interval. Note that the final finite-time synchronization criterion is obtained in the forms of linear matrix inequalities (LMIs) by introducing a memristor-dependent sign function into the controller and constructing a new Lyapunov–Krasovskii functional (LKF). Furthermore, by utilizing some improved integral inequality methods, the conservatism of the main results can be greatly reduced. Finally, three numerical examples are provided to illustrate the feasibility, superiority, and practicability of this article.

This paper interconnects N parabolic partial differential equations (PDEs) by a nonlinear coupling protocol to describe a class of large-scale distributed parameter systems, for which, based on the network communication, the issue of joint state and fault estimation is investigated. First, a generalized fault model, where the fault coefficient follows a semi-Markov switching law, is introduced into the system model. Then, to achieve joint state and fault estimation and ensure the estimation accuracy, a special augmented distributed estimator is designed with using associated information among subsystems. Note that the sampled-data and pointwise measurements are conjunctly employed, such that the network communication resources can be saved to a large extent. Moreover, based on the graph theory, a global Lyapunov-Krasovskii functional (LKF) is constructed to handle the nonlinear coupling function. As a result, an effective theorem is proposed to guarantee that both the state and fault estimation errors can converge to zero while satisfying a strictly (Ξ1,Ξ2,Ξ3)-λ- dissipative index. Finally, a numerical example and an application study on chemical non-isothermal tubular reactors are provided to illustrate the feasibility and practicality of this paper.

In this paper, a novel class of quaternion-valued memristive neural networks (QVMNNs) that considers both the spatial factor and Markov jump phenomenon is proposed, the finite/fixed-time anti-synchronization (F/FTAS) of which is investigated. It is worth mentioning that the considered master and slave systems are assumed to jump along two inconsistent Markov chains, which is a first attempt at the issue of the anti-synchronization of Markovian systems and may be more realistic than most existing Markovian systems' models. Then, a suitable feedback controller is designed, such that the error system can be finite/fixed-time stable. Moreover, by integrating algebraic inequality technologies and Lyapunov theory, a new F/FTAS theorem can be obtained for the proposed systems. Finally, this paper provides two examples, so that the rationality, superiority, and practical value of the main results can be illustrated.

An innovative class of drive-response systems that are composed of Markovian reaction-diffusion memristive neural networks, where the drive and response systems follow inconsistent Markov chains, is proposed in this article. For this kind of nonlinear parameter-varying systems, a suitable gain-scheduled controller that involves a mode and memristor-dependent item is designed, so that the error system is bounded within a finite-time interval. Moreover, by constructing a novel Lyapunov-Krasovskii functional and employing the canonical Bessel-Legendre inequality and free-weighting matrix method, the conservatism of the finite-time synchronization criterion can be greatly reduced. Finally, two numerical examples are provided to illustrate the feasibility and practicability of the obtained results.

A novel generalized neural network (NN), which includes Markovian jump parameters, inertial items, and reaction-diffusion terms, is proposed, and the issue of finite-time dissipative synchronization for this kind of NNs is discussed in this article. First, an appropriate variable substitution is employed so that the original second-order differential system is transformed into a first-order one. Second, a novel time-varying memory-based controller is designed to ensure the dissipative synchronization of the drive and response systems over a finite-time interval. Then, a new Lyapunov-Krasovskii function is processed by reciprocally convex combination and free-weighting matrix methods, therefore, a less conservative synchronization criterion is derived. Finally, by providing three examples, the feasibility, superiority, and practicality of the obtained results are illustrated.