This paper investigates observer-based event-triggered sliding mode control of delayed semi-Markov jump discrete singular systems under randomly occurring false data injection attacks and network-induced communication restrictions. Error dynamics and observer systems are modeled as semi-Markov jump systems with time-varying time delay using an improved time delay analysis technique. The stochastic admissibility of the augmented system is analyzed using the semi-Markov kernel method, and adequacy criteria that facilitate numerical detection are derived from new Lyapunov functions. A mode-independent sliding surface is designed and its reachability is ensured. Finally, the effectiveness of the proposed scheme is illustrated by simulation examples.

This article devotes to investigate the fuzzy optimal consensus problem for multiagent systems (MASs) subject to denial-of-service (DoS) attacks by using the dynamic event-triggered (DET) strategy. The interval type-2 (IT2) fuzzy systems are employed to model the MASs, which combines with the DET fuzzy controller to establish a closed-loop system. Moreover, two piecewise functions are designed, and the triggered interval in a DoS period is decomposed into some subsets with a sampling interval. Therefore, the closed-loop system is reconstructed to facilitate stability analysis. The piecewise Lyapunov-Krasovskii functional is designed, and the system stability is deduced with and without DoS attacks, respectively. By considering the relationship of the piecewise Lyapunov functional, all agents are ensured to be exponentially stable, and the closed-loop system satisfies an optimal control performance. Two examples show the feasibility of the proposed theory finding. Note to Practitioners—Cyberattacks lead to control failure or data breach of MASs due to data tampering and communication interruption. Besides, the controller based on DET mechanism can save limited network resources. Hence, this research focuses on MASs with parameter uncertainties under DoS attacks in interval type-2 fuzzy form, and a DET fuzzy control scheme is proposed to guarantee system security. The Lyapunov-Krasovskii functional with sampling information is constructed to promote stability verification, and slack matrices are also introduced. This study aims to reveal the design principles of DET fuzzy secure control scheme for MASs under DoS attacks. The conducted stability analysis and DET strategy adapt to the background of engineering application.

This paper addresses a class of sliding mode control (SMC) strategies for high-frequency sampled systems with uncertainties, utilizing a generalized Delta operator reaching law. First, Delta operator sampled systems are regarded as a bridge in the unified research framework of discrete-time systems and continuous-time systems. With the increase of sampling frequency, Delta operator sampled systems can maintain consistent stability with their corresponding continuous models. Then, a generalized reaching law by Delta operator is presented, which can degenerate into multiple existed reaching laws under certain conditions. And then, the reaching condition, quasi-sliding mode (QSM) band, and finite time reachability of the proposed generalized Delta operator reaching law are analyzed. Next, sliding mode controllers are designed separately for both matched uncertainty and unmatched uncertainty cases. With the effect of these controllers, Delta operator SMC systems exhibit desirable dynamic characteristics. Finally, two examples on truck-trailer system and ball-beam system demonstrate the effectiveness of Delta operator sliding mode controllers, and show efficient performance in stabilizing high-frequency sampled systems with uncertainties. These scenarios illustrate the potential of the proposed strategies for practical applications. Note to Practitioners—This work aims to develop sliding mode control strategy for Delta operator sampled systems, which is of fundamental significance in the fields of high-frequency sampled control. We propose a generalized Delta operator reaching law and provide a unified framework for high-frequency sampled discrete-time systems and their corresponding continuous-time systems, addressing practical challenges in areas, such as high-speed motors, supercomputing, and network transmission. The reaching condition, quasi-sliding mode bandwidth, and finite time reachability of the proposed generalized Delta operator reaching law are fully considered. Given that the effects of unknown matched or unmatched uncertainties, sliding mode controllers based on Delta operator are designed, which are applied to truck-trailer system and ball-beam system.

The information interaction between agents in this paper is described using Markov switching topology, and an adaptive neural-network sliding mode (ANNSM) controller is proposed to address the admissible consensus problem for discrete-time nonlinear singular multi-agent systems (SMASs) with external disturbances. For the reason of approximating the nonlinear part online and overcoming the bounded difficulty, the radial basis function (RBF) based on neural network (NN) is introduced. When designing the state observer, a disturbance observer assisted by an adaptive update law is established for the purpose of estimating the external disturbance and the NN residual error. Next, an ANNSM control method related to the Markov switching topology is proposed based on the designed disturbance observer, and the Lyapunov stability theory demonstrates that the system achieves admissible bounded consensus. Finally, simulation studies on a numerical example and a distributed microgrid model to demonstrate the effectiveness of the proposed controller.

This study considers a dynamic event-triggered fuzzy${\mathcal {H}}_{\infty }$consensus problem for multiagent systems (MAS) characterized by parameter uncertainties and external disturbances in interval type-2 (IT2) fuzzy form. The proposed control strategy aims to minimize data transmission by triggering control events dynamically. Stability analysis is conducted by Lyapunov stability theory, and more mathematical tools are introduced to relax the sufficient condition and demonstrate the${\mathcal {H}}_{\infty }$consensus. The developed control scheme ensures the consensus among agents, enhancing the overall system performance in the presence of uncertainties and disturbances. Finally, three examples exhibit the validity of the suggested controller.

In this article, a novel distributed prescribed-time consensus tracking control strategy is presented for heterogeneous nonlinear multi-agent systems (MASs) under deception attacks and actuator faults. Since the original states of the studied system are unavailable under deception attacks, we present a new coordinate transformation technique considering the compromised states and the outputs of command filters to design the corresponding controller. Then, to handle the unknown control gains caused by actuator faults, the rational adaptive laws are cleverly designed for the upper bounds involving the unknown control gains. Besides, by introducing a time-varying constraint function in the backstepping design process, a new adaptive prescribed-time controller is constructed in this paper, such that the prescribed-time tracking control problem of the heterogeneous nonlinear MASs is converted into the constraint problem of the tracking errors. Through the Lyapunov stability analysis, the final results prove that the whole signals in the closed-loop MASs remain bounded and the tracking errors can converge to the pre-set region in the predefined time. Finally, the simulation results demonstrate the availability of the developed control method.Note to Practitioners—This paper investigates the distributed prescribed-time consensus tracking control problem for heterogeneous nonlinear MASs, whose models can be extended to more complex industrial applications, such as flexible manipulators, series elastic actuators and electric systems. In certain practical scenarios, security and fault problems are inevitable. Hence, it is challenging to design a control strategy that achieves distributed consensus tracking control in an insecure network environment. Furthermore, the proposed approach based on the time-varying constraint function ensures the system stability within the predefined time, which provides a viable strategy for engineering applications.

This article delves into the predefined-time output-feedback leader-following consensus problem of uncertain pure-feedback nonlinear multiagent systems for the first time. To streamline subsequent design, the original systems in pure-feedback form are first transformed into canonical systems. Following this, a distributed predefined-time extended state observer (ESO) and a local predefined-time ESO are developed to reconstruct the unknown states/lumped disturbance of the transformed leader system and follower systems, respectively. Based on the estimated states and utilizing a bounded regulation function, two nonsingular and nonconservative predefined-time control laws are formulated to achieve consensus tracking. The proposed method showcases the following advantages: 1) the actual convergence time rather than the upper bound of the convergence time (UBCT) of the tracking errors can be explicitly specified a priori regardless of the initial conditions in a bounded region, optimizing control energy usage and 2) the system overshoot could be effectively reduced by selecting appropriate parameters for the regulation function. Finally, numerical examples are conducted to verify the obtained results.

This article concerns innovative adaptive sliding mode control governed by an observer for a time-varying fuzzy system constrained by fractional Brownian motion with$H \in (\frac{1}{2},1)$under Markovian jump with uncertain transition rates. First, for an uncertain signal, a Takagi-Sugeno (T-S) observer is constructed. Furthermore, in accordance with the unique feature of the coefficient matrix for an uncertain block, the observation system is divided into two low-order subsystems through regular transformation. Subsequently, a common and fixed sliding surface function that does not change with jump is constructed; this is one of the characteristics that differ from the characteristics of the integral switching surface designed by many researchers who have studied the Markovian jump. An adaptive controller is also designed and finite-time reachability analysis is performed by using it. Additionally, a stochastic stability study is performed by constructing Lyapunov--Krasovskii functional, introducing slack matrices and utilizing linear matrix inequalities. Finally, a numerical simulation was conducted to verify the reliability of the proposed approach.

In this article, the projective synchronization of uncertain fractional-order (FO) reaction-diffusion systems is studied for the first time via the fractional adaptive sliding mode control (SMC) method. A FO integral type switching function is designed, and corresponding adaptive SMC laws are derived which ensure the FO sliding mode surface (SMS) is reachable after a finite time interval. The improved version of these control laws which have smaller oscillation and better control performance are also derived. A new lemma for proving the finite-time reachability of the FO SMS is developed. At last, numerical examples are provided to verify the effectiveness of our theories.

The fractional-order (FO) nonlinear differential system with state-dependent (SD) delayed impulses (DI) is considered in this brief. The considered impulses are related to the delayed state of the system and the delays are SD. A novel lemma for the monotonicity of the solution of Caputo's FO derivative equation is given. By means of linear matrix inequality (LMI) and several comparative arguments, criteria of uniform stability, uniform asymptotical stability, and Mittag-Leffler stability are obtained. Compared with other works on integer-order (IO) impulsive delayed systems with SD delays or fixed delays, how to impose constraints on parameters and impulses is explored, without imposing the boundedness on the state delays. Two examples are implemented to examine the practicality and sharpness of our theoretical analysis.

In this chapter, the synchronization problem between two coupled hyperbolic neural networks (CHNNs) with delays is studied. A simple but effective impulsive pinning controller strategy is designed to achieve exponentially outer synchronization on two CHNNs. To get rid of strict restrictions on delays, the Lyapunov functional approach, the comparison principle and the average impulsive interval method are used to investigate the outer synchronization problem, and a novel criterion is obtained. Furthermore, an example is presented to show our results are new and satisfactory.

In this article, the finite-time observer-based sliding-mode control (SMC) problem is considered for stochastic Markovian jump systems (MJSs) with a deterministic switching chain (DSC) subject to time-varying delay and packet losses (PLs). First, the stochastic MJSs with DSC are appropriately modeled and the PLs case is characterized by using some Bernoulli random variables. Then, a nonfragile finite-time bounded sliding-mode observer is designed. Our objective is to propose a finite-time observer-based SMC approach such that for the above addressed system, the finite-time boundedness in a certain time interval can be guaranteed by giving sufficient criteria via the stochastic analysis skills and average dwell time (ADT) method. Moreover, a new robust finite-time sliding-mode controller can be designed to ensure reachability of the common sliding surface in the estimation space. Finally, a numerical example is provided to illustrate our theoretical results.

The stability of fractional-order (FO) nonlinear system with state-dependent delays (SDDs) is investigated. Unlike the usual time-dependent delays, the state-dependent (SD) delays make the size of the delays relative to the states, which makes the system uncertain when historical state information would be used. A Lemma on Riemann-Liouville derivative is first given to ensure the monotonicity of the considered function. Then, based on the Lyapunov method, several sufficient criteria are presented to guarantee the Mittag-Leffler stability of the discussed systems. In the end, three examples are applied to illustrate the correctness and applicability of our theoretical conclusions, including practical applications in submarine positioning models.

This work focuses on the robust leader-follower synchronization navigation for the under-actuated vessels with only independent the surge control force and the yaw moment. The ocean disturbances and thruster saturation are simultaneously addressed. A virtual vessel placed at the relative distance with the moving main vessel alleviates the requirements on main vessel’s velocity measurements. The disturbance estimation performance is achieved by utilizing the disturbance observer. The additional controls produce the filtered non-achievable command control signals due to the thrust saturation effects. The filtered signals correct feedback errors for avoiding disturbance estimation and rejection compromise. The dynamic surface control technique is employed to derive the under-actuated synchronization control laws. By employing first-order filters, the differential terms are replaced by the algebraic operations such that the control is convenient to implement. It is analyzed that the supply vessel control system is semi-globally stable and the synchronization navigation along with the main vessel is ensured with the small errors. Simulations in the different disturbance cases validate the synchronization scheme.

In this article, we mainly consider the existence of solutions and global Mittag-Leffler stability of delayed fractional-order coupled reaction-diffusion neural networks without strong connectedness. Using the Leary-Schauder's fixed point theorem and the Lyapunov method, some criteria for the existence of solutions and global Mittag-Leffler stability are given. Finally, the correctness of the theory is verified by a numerical example.

As a generation of the real-valued neural network (RVNN), complex-valued neural network (CVNN) is based on the complex-valued (CV) parameters and variables. The fractional-order (FO) CVNN with linear impulses and fixed time delays is discussed. By using the sign function, the Banach fixed point theorem, and two classes of activation functions, some criteria of uniform stability for the solution and existence and uniqueness for equilibrium solution are derived. Finally, three experimental simulations are presented to illustrate the correctness and effectiveness of the obtained results.

This brief is devoted to exploring the global Mittag-Leffler (ML) synchronization problem of fractional-order memristor neural networks (FOMNNs) with leakage delay via a hybrid adaptive controller. By applying Fillipov's theory and the Lyapunov functional method, the novel algebraic sufficient condition for the global ML synchronization of FOMNNs is derived. Finally, a simulation example is presented to show the practicability of our findings.

In this article, a decentralized adaptive finite-time tracking control scheme is proposed for a class of nonstrict feedback large-scale nonlinear interconnected systems with disturbances. First, a practical almost fast finite-time stability framework is established for a general nonlinear system, which is then applied to the design of the large-scale system under consideration. By fusing command filter technique and adaptive neural control and introducing two smooth functions, the "singular" and "explosion of complex" problems in the backstepping procedure are circumvented, while the obstacles caused by unknown interconnections are overcome. Moreover, according to the framework of practical almost fast finite-time stability, it is shown that all the closed-loop signals of the large-scale system are almost fast finite-time bounded, and the tracking errors can converge to arbitrarily small residual sets predefined in an almost fast finite time. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed finite-time decentralized control scheme.

This paper is devoted to the interval type-2 (IT2) fuzzy exponential stability for nonlinear networked sampled-data control systems with random communication links. By using the input delay approach, the designed networked IT2 fuzzy sampled-data controller can be applied in the continuous-time controlled plant, and the continuous-time Lyapunov-Krasovskii functional (LKF) is constructed. Based on the LKF theory, the stability analysis is conducted in the sense of mathematical expectation, and the sufficient conditions are determined in terms of the linear matrix inequalities. Then, the IT2 fuzzy networked controller is developed such that the networked closed-loop control system is exponentially stable. Finally, the simulation results are used to demonstrate the efficiency of the proposed design. The merits of the proposed algorithm are also shown by some comparative results.

This paper deals with the issue of reliable sliding mode control for descriptor systems with semi-Markov parameters using the Takagi-Sugeno fuzzy model, in which an average dwell time approach is utilized to tackle generic uncertain transition rates (TRs). From the analysis of the inner mechanism of switching singular system, a continuous sliding surface function is proposed. Different from continuity with probability one for stochastic systems, the absolute continuity of system solution is a key point in this paper being ensured for application of the average dwell time approach. Then, the mean-square exponential stability of the obtained sliding mode is analyzed based on two types of uncertain TRs. Moreover, a sliding mode controller is constructed to ensure the reachability condition in finite time. Lastly, the method is verified numerically by a single-link robot arm model.

This paper is concerned with the problem of interval type-2 (IT2) fuzzy sampled-data H∞control for nonlinear networked control systems with parameter uncertainties, data dropout, and transmission delay. The IT2 fuzzy system used to describe the networked control systems and the IT2 networked sampled-data controller implemented by a zero-order holder is connected in the closed-loop system. By means of the input delay approach, the resulting closed-loop system is converted into a continuous-time delayed system. Subsequently, the continuous-time Lyapunov-Krasovskii functional theory is used to carry out the stability analysis. Some slack matrices and the bound information in membership functions are introduced to obtain the relaxed sufficient conditions formed by the linear matrix inequalities, which guarantee the anticipant H∞performance. Finally, the efficiency and merits of the proposed design method are verified by four practical systems.

This paper is focused on the event-triggered fuzzy sliding-mode control of networked control systems regulated by semi-Markov process. First, through movement-decomposition method, the networked control system is transformed into two lower-order subsystems. Then, an event-triggered scheme based on a delay system model approach is proposed in designing the switching surface and obtaining the sliding mode dynamics. Furthermore, a fuzzy sliding-mode controller is developed to realize reachability of a predefined switching surface and desirable sliding motion. Moreover, in terms of linear matrix inequality method, sufficient conditions for stochastic stability of the obtained sliding mode dynamics is developed in the sense of generally uncertain transition rates. Finally, the applicability of the proposed results are verified numerically on the single-link robot arm system.

This paper is concerned with finite-time sliding mode control (SMC) of continuous-time semi-Markovian jump systems with immeasurable premise variables via fuzzy approach. First, an integral sliding surface is constructed based on fuzzy observer. Second, an observer-based SMC law is synthesized to guarantee finite-time reachability of the predefined sliding surface before the prescribed time. Third, through finite-time boundedness analysis, the required boundedness performance is conducted at the reaching phase first and then the sliding motion phase, respectively. Furthermore, sufficient conditions in terms of linear matrix inequalities (LMIs) are established to guarantee the required boundedness performance of the overall closed-loop controlled system during the two phases with generally uncertain transition rates (TRs) simultaneously. Finally, a practical example is given to show the validity of the established method numerically.

In this paper the mathematical model of six-phase induction motor is established. Then the phase-fault SVPWM algorithm is put forward, and the simulation model is built in MATLAB to verify the feasibility of the algorithm. The system simulation and experiment of phase-fault of the six-phase induction machine are performed.

There is a disadvantage of the traditional SVPWM techniques of six-phase motors, it does not consider the synthesizing vector in harmonic subspace. This thesis proposes modified SVPWM techniques based on twelve vectors. The novel techniques are simulated in Matlab/Simulink system and simulation results are given. Finally the SVPWM techniques are realized in the practical platform.

For constrained three-link manipulation robots it is shown how the complexity of controlling anthropomorphic arm-like manipulators can be considerable ameliorated by designing a sliding-mode control. First, a representation singular system model of three-link manipulators is established by employing constrained equations and corresponding descriptions of force restriction. Then sliding-mode control with constrained control inputs for three-link manipulator is expatiated as appropriate. Based on quadratic performance index, the optimal sliding mode switching function for three-link manipulator system is derived and a modified reaching law on the grounds of the singular model is constructed using a power function. Then the sliding mode controller for three-link constrained manipulator is designed using the proposed reaching law. Using PUMA-560 the efficiency of the proposed method is demonstrated via the obtained simulation results.