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The purpose of this paper is to address the problem of control in a typical chaotic power system. Chaotic oscillations cannot only extremely endanger the stabilization of the power system but they can also not be controlled by adding the traditional controllers. So, the sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of the power system, eliminating control signal chattering and also show less control effort in comparison with the methods considered in previous literatures.

The sliding mode control based on a fuzzy supervisor can sufficiently ensure perfect tracking and controlling in the presence of uncertainties. Closed-loop stability is proved using the Lyapunov stability theory.

Closed-loop stability is proved using the Lyapunov stability theory. The simulation results show the effectiveness of the proposed method in damping chaotic oscillations of power system, eliminating control signal chattering and also less control effort in comparison with the methods considered in previous literatures.

Main contributions of the paper are as follows: the chaotic behavior of power systems with two uncertainty parameters and tracking reference signal for the control of generator angle and the controller signal are discussed; designing sliding mode control based on a fuzzy supervisor in order to practically implement for the first time; while the generator speed is constant, the proposed controller will enable the power system to go in any desired trajectory for generator angle at first time; stability of the closed-loop sliding mode control based on the fuzzy supervisor system is proved using the Lyapunov stability theory; simulation of the proposed controller shows that the chattering is low control signal.

The paper is concerned with the different aspects of mathematical modelling and analysis in dynamics of complex non‐linear systems, that are generated by applied problems of engineering practice. Main aims are the problems of optimal (in some sense) mechanical‐mathematical modelling and the regular schemes of decomposition. The critical step in the use of mathematics for solving complex engineering problems is the building of a suitable mathematical model, that, generally speaking, is the result of combining the mathematical formalized procedures as well as heuristic (non‐formalized) manners (conjunction of rigorous science and free art). This work advocates a novel approach to the building process of mathematical models, presenting an overview of concepts and techniques needed for modelling, via comprehension of modelling problem as singularly perturbed one. Here uniform methodology, based on methods of Lyapunov theory, Perturbations theory [Asymptotic method in theory of non‐linear oscillations (1963)] in accordance with Stability postulate and Singularity postulate is developed. This asymptotic approach (called – LPSS approach) allows to elaborate the general conception of the modelling; to determine the conditions of qualitative equivalence between full model and simplified model. As applications, the different examples of concrete physical nature are considered.

The purpose of this paper is to propose a stability analysis and control synthesis for achieving passivity properties of a class of continuous‐time nonlinear systems. These nonlinear systems are represented via continuous affine Takagi‐Sugeno (T‐S) fuzzy models, which played an important role in nonlinear control systems. The affine T‐S fuzzy models are more approximate than homogeneous T‐S fuzzy models for modeling nonlinear systems. Using the energy concept of passivity theory with Lyapunov function, the conditions are derived to ensure the passivity and stability of nonlinear systems. Based on the parallel distribution compensation (PDC) technique, this paper proposes a fuzzy controller design approach to achieve the passivity and stability for the continuous affine T‐S fuzzy systems.

For solving stability and stabilization problems of affine T‐S fuzzy models, the conversion techniques and passive theory are employed to derive the stability conditions. By applying the linear matrix inequality technique, a modified iterative linear matrix inequality algorithm is proposed to determine and update the auxiliary variables for finding feasible solutions of these stability conditions.

By studying the numerical example, the proposed design technique of this paper is an effectiveness and useful approach to design the PDC‐based fuzzy controller. From the simulation results, the considered nonlinear system with external disturbances driven by proposed design fuzzy controller is stable and strictly input passive.

This paper is interesting for designing fuzzy controller to guarantee the stability and strict input passivity of affine T‐S fuzzy models.

This paper is aimed at investigating a novel chemical oscillating chaotic system with different attractors at fixed parameters. The typical dynamical behavior of the new chemical oscillating system is discussed, and it is found that the state selection is dependent on initial values. Then, the stabilization problem of the chemical oscillating attractors is investigated analytically and numerically. Subsequently, the novel electronic circuit of the proposed chemical oscillating chaotic system are constructed, and the influences of the changes of circuit parameters on chemical oscillating chaotic attractors are investigated.

The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. Moreover, the active control and adaptive control methods are presented to make the chemical oscillating chaotic systems asymptotically stable at the origin based on the Lyapunov stability theory. The influences on chemical oscillating chaotic attractors are also verified by changing the circuit parameters.

It is found that the active control method is easier to be realized by using physical components because of its less control signal and lower cost. It is also confirmed that the adaptive control method enjoys strong anti-interference ability because of its large number of selected controllers. What can be seen from the simulation results is that the chaotic circuits are extremely dependent on circuit parameters selection. Comparisons between MATLAB simulations and Multisim simulation results show that they are consistent with each other and demonstrate that changing attractors of the chemical oscillating chaotic system exist. It is conformed that circuit parameters selection can be effective to control and realize chaotic circuits.

The different attractors of the novel chemical oscillating chaotic system are investigated by changing the initial values under fixed parameters. The characteristic of the chemical oscillating attractor is that the basin of attraction of the three-dimensional attractor is located in the first quadrant of the eight quadrants of the three-dimensional space, and the ranges of the three variables are positive. This is because the concentrations of the three chemical substances are all positive.

The purpose of this paper is to investigate the neural-network-based containment control of multi-agent systems with unknown nonlinear dynamics. Moreover, communication constraints are taken into account to reflect more realistic communication networks.

Based on the approximation property of the radial basis function neural networks, the control protocol for each agent is designed, where all the information is exchanged in the form of sampled data instead of ideal continuous-time communications.

By utilizing the Lyapunov stability theory and the Lyapunov–Krasovskii functional approach, sufficient conditions are developed to guarantee that all the followers can converge to the convex hull spanned by the stationary leaders.

As ideal continuous-time communications of the multi-agent systems are very difficult or even unavailable to achieve, the neural-network-based containment control of nonlinear multi-agent systems is solved under communication constraints. More precisely, sampled-data information is exchanged, which is more applicable and practical in the real-world applications.

This paper aims to investigate the distributed coordinated fuzzy tracking problems for multiple mechanical systems with nonlinear model uncertainties under a directed communication topology.

The dynamic leader case is considered while only a subset of the follower mechanical systems can obtain the leader information. First, this paper approximates the system uncertainties with finite fuzzy rules and proposes a distributed adaptive tracking control scheme. Then, this paper makes a detailed classification of the system uncertainties and uses different fuzzy systems to approximate different kinds of uncertainties. Further, an improved distributed tracking strategy is proposed. Closed-loop systems are investigated using graph theory and Lyapunov theory. Numerical simulations are performed to verify the effectiveness of the proposed methods.

Based on fuzzy control and adaptive control theories, the desired distributed coordinated tracking control strategies for multiple uncertain mechanical systems are developed.

Compared with most existing literature, the proposed distributed tracking algorithms use fuzzy control and adaptive control techniques to cope with system nonlinear uncertainties of multiple mechanical systems. Moreover, the improved control strategy not only reduces fuzzy rules but also has higher control accuracy.

The purpose of this paper is to propose a guaranteed cost control design procedure for model-based cyber–physical assembly (CPA) systems. To reflect the cyber–physical environment, the network-induced delays and disturbances are introduced in the mathematical model.

Based on the linear matrix inequality approach, the guaranteed cost controller is designed such that the guaranteed cost can be satisfied and the corresponding convex optimization algorithm is provided. Moreover, H-infinity theory is used to deal with the disturbance with the given H-infinity attenuation level.

By constructing appropriate Lyapunov–Krasovskii functionals, delay-dependent sufficient conditions are established in terms of linear matrix inequalities and the controller design procedure is given.

A simplified CPA model is given based on which the designed controller can allow us to control the closed-loop CPA systems with the guaranteed cost.

The quad‐rotor is an under‐actuation, strong coupled nonlinear system with parameters uncertainty, unmodeled disturbance and drive capability boundedness. The purpose of the paper is to design a flight control system to regulate the aircraft track the desired trajectory and keep the attitude angles stable on account of these issues.

Considering the dynamics of a quad‐rotor, the closed‐loop flight control system is divided into two nested loops: the translational outer‐loop and the attitude inner‐loop. In the outer‐loop, the translational controller, which exports the desired attitude angles to the inner‐loop, is designed based on bounded control technique. In consideration of the influence of uncertain rotational inertia and external disturbance, the backstepping sliding mode approach with adaptive gains is used in the inner‐loop. The switching control strategy based on the sign functions of sliding surface is introduced into the design procedure with respect to the input saturation.

The validity of the proposed flight control system was verified through numerical simulation and prototype flight experiment in this paper. Furthermore, with relation to the flying, the motor speed is kept in the predetermined scope.

This article introduces a new flight control system designed for a quad‐rotor.

The objective of this research is to investigate various neural network (NN) observer techniques for sensors fault identification and diagnosis of nonlinear system in consideration of numerous faults, failures, uncertainties and disturbances. For the importunity of increasing the faults diagnosis and reconstruction preciseness, a new technique is used for modifying the weight parameters of NNs without enhancement of computational complexities.

Various techniques such as adaptive radial basis functions (ARBF), conventional radial basis functions, adaptive multi-layer perceptron, conventional multi-layer perceptron and extended state observer are presented. For increasing the fault detection preciseness, a new technique is used for updating the weight parameters of radial basis functions and multi-layer perceptron (MLP) without enhancement of computational complexities. Lyapunov stability theory and sliding-mode surface concepts are used for the weight-updating parameters. Based on the combination of these two concepts, the weight parameters of NNs are updated adaptively. The key purpose of utilization of adaptive weight is to enhance the detection of faults with high accuracy. Because of the online adaptation, the ARBF can detect various kinds of faults and failures such as simultaneous, incipient, intermittent and abrupt faults effectively. Results depict that the suggested algorithm (ARBF) demonstrates more confrontation to unknown disturbances, faults and system dynamics compared with other investigated techniques and techniques used in the literature. The proposed algorithms are investigated by the utilization of quadrotor unmanned aerial vehicle dynamics, which authenticate the efficiency of the suggested algorithm.

The proposed Lyapunov function theory and sliding-mode surface-based strategy are studied, which shows more efficiency to unknown faults, failures, uncertainties and disturbances compared with conventional approaches as well as techniques used in the literature.

For improvement of the system safety and for avoiding failure and damage, the rapid fault detection and isolation has a great significance; the proposed approaches in this research work guarantee the detection and reconstruction of unknown faults, which has a great significance for practical life.

In this research, two strategies such Lyapunov function theory and sliding-mode surface concept are used in combination for tuning the weight parameters of NNs adaptively. The main purpose of these strategies is the fault diagnosis and reconstruction with high accuracy in terms of shape as well as the magnitude of unknown faults. Results depict that the proposed strategy is more effective compared with techniques used in the literature.

This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical behaviors of the new hyper-chaotic system are discussed in detail. The control problem of these hyper-chaotic attractors is also investigated analytically and numerically. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components.

The adaptive control method is derived to achieve chaotic synchronization and anti-synchronization of the novel hyper-chaotic system with unknown parameters by making the synchronization and anti-synchronization error systems asymptotically stable at the origin based on Lyapunov stability theory. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Multisim simulations and electronic circuit experiments are consistent with MATLAB simulation results and they verify the existence of these hyper-chaotic attractors.

Comparisons among MATLAB simulations, Multisim simulation results and physical experimental results show that they are consistent with each other and demonstrate that changing attractors of the hyper-chaotic system exist.

The goal of this paper is to construct a new four-dimensional hyper-chaotic system with different attractors as certain parameters vary. The adaptive synchronization and anti-synchronization laws of the novel hyper-chaotic system are established based on Lyapunov stability theory. The corresponding electronic circuits for the novel hyper-chaotic system with different attractors are also implemented to illustrate the accuracy and efficiency of chaotic circuit design.