On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach

Fuzzy Boundary Sampled-Data Control for Nonlinear Parabolic DPSs

For a nonlinear parabolic distributed parameter system (DPS), a fuzzy boundary sampled-data (SD) control method is introduced in this article, where distributed SD measurement and boundary SD measurement are respected. Initially, this nonlinear parabolic DPS is represented precisely by a Takagi-Sugeno (T-S) fuzzy parabolic partial differential equation (PDE) model. Subsequently, under distributed SD measurement and boundary SD measurement, a fuzzy boundary SD control design is obtained via linear matrix inequalities (LMIs) on the basis of the T-S fuzzy parabolic PDE model to guarantee exponential stability for closed-loop parabolic DPS by using inequality techniques and a acrlong LF. Furthermore, respecting the property of membership functions, we present some LMI-based fuzzy boundary SD control design conditions. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.

Pinning Spatiotemporal Sampled-Data Synchronization of Coupled Reaction-Diffusion Neural Networks Under Deception Attacks

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

Adaptive event-triggered extended dissipative synchronization of delayed reaction-diffusion neural networks under deception attacks

Under spatially averaged measurements (SAMs) and deception attacks, this article mainly studies the problem of extended dissipativity output synchronization of delayed reaction-diffusion neural networks via an adaptive event-triggered sampled-data (AETSD) control strategy. Compared with the existing ETSD control methods with constant thresholds, our scheme can be adaptively adjusted according to the current sampling and latest transmitted signals and is realized based on limited sensors and actuators. Firstly, an AETSD control scheme is proposed to save the limited transmission channel. Secondly, some synchronization criteria under SAMs and deception attacks are established by utilizing Lyapunov-Krasovskii functional and inequality techniques. Then, by solving linear matrix inequalities (LMIs), we obtain the desired AETSD controller, which can satisfy the specified level of extended dissipativity behaviors. Lastly, one numerical example is given to demonstrate the validity of the proposed method.

Practical Stabilization of Networked Takagi-Sugeno Fuzzy Systems via Improved Jensen Inequalities

This work addresses the problem of aperiodically sampled control for the networked Takagi-Sugeno (T-S) fuzzy systems, where the aperiodically sampled input is generated by a periodic sampler and an event-triggered mechanism (ETM). The purpose of ETM is used to reduce the computational and communication burdens. For guaranteeing controller robustness, the practical stability of T-S fuzzy systems is considered by using the Lyapunov method and linear matrix inequality (LMI) technique. As one of the most powerful inequalities for deriving stability criteria using LMIs, Jensen's inequality has recently been improved by various authors for the stability analysis of delayed systems. However, these results are conservative to obtain lower bounds for integrals with an exponential term. Inspired by this, improved integral inequalities are derived in this work, and they are applied to obtain practical stability criteria for aperiodically sampled control. Finally, a numerical example on flight control of a helicopter is given to illustrate the effectiveness of the obtained practical stability criteria. Furthermore, the effectiveness of the improved Jensen inequalities on the exponential stability criteria is illustrated by numerical comparisons.

Adaptive Control of Advanced G-L Fuzzy Systems with Several Uncertain Terms in Membership-Matrices

In this paper, a set of novel adaptive control strategies based on an advanced G-L (proposed by Ge-Li-Tam, called GLT) fuzzy system is proposed. Three main design points can be summarized as follows: (1) the unknown parameters in a nonlinear dynamic system are regarded as extra nonlinear terms and are further packaged into so-called nonlinear terms groups for each equation through the modeling process, which reduces the complexity of the GLT fuzzy system; (2) the error dynamics are further rearranged into two parts, adjustable membership function and uncertain membership function, to aid the design of the controllers; (3) a set of adaptive controllers change with the estimated parameters and the update laws of parameters are provided following the current form of error dynamics. Two identical nonlinear dynamic systems based on a Quantum-CNN system (Q-CNN system) with two added terms are employed for simulations to demonstrate the feasibility as well as the effectiveness of the proposed fuzzy adaptive control scheme, where the tracking error can be eliminated efficiently.

Stabilization of Interval Type-2 Fuzzy-Based Reliable Sampled-Data Control Systems

This article investigates the stabilization problem of the Takagi-Sugeno (T-S) fuzzy-based interval type-2 (IT-2) reliable sampled-data control system. Different from the existing studies, the information for the entire sampling interval with a relation of the augmented state vectors is considered for designing the reliable sampled-data control of IT-2 T-S fuzzy systems. In this regard, we construct the suitable looped Lyapunov-Krasovskii functional (LKF) with the information of the fuzzy membership function that feeds back the time derivative of the membership function to derive sufficient conditions. These sufficient conditions are established in the form of linear matrix inequalities (LMIs), which ensure the global asymptotic stability of T-S fuzzy systems under the designed control technique. Finally, the applicability and superiority of developed reliable sampled-data control techniques were validated by three practical systems.

Massive Maritime Path Planning: A Contextual Online Learning Approach

The ocean has been investigated for centuries across the world, and planning the travel path for vessels in the ocean has become a hot topic in recent decades as the increasing development of worldwide business trading. Planning such suitable paths is often based on big data processing in cybernetics, while not many investigations have been done. We attempt to find the optimal path for vessels in the ocean by proposing an online learning dispatch approach on studying the mission-executing-feedback (MEF) model. The proposed approach explores the ocean subdomain (OS) to achieve the largest average traveling feedback for different vessels. It balances the ocean path by a deep and wide search, and considers adaptation for these vessels. Further, we propose a contextual multiarmed bandit-based algorithm, which provides accurate exploration results with sublinear regret and significantly improves the learning speed. The experimental results show that the proposed MEF approach possesses 90% accuracy gain over random exploration and achieves about 25% accuracy improvement over other contextual bandit models on supporting big data online learning pre-eminently.

A hyperchaotic cycloid map with attractor topology sensitive to system parameters

We propose herein a novel discrete hyperchaotic map based on the mathematical model of a cycloid, which produces multistability and infinite equilibrium points. Numerical analysis is carried out by means of attractors, bifurcation diagrams, Lyapunov exponents, and spectral entropy complexity. Experimental results show that this cycloid map has rich dynamical characteristics including hyperchaos, various bifurcation types, and high complexity. Furthermore, the attractor topology of this map is extremely sensitive to the parameters of the map. The x--y plane of the attractor produces diverse shapes with the variation of parameters, and both the x--z and y--z planes produce a full map with good ergodicity. Moreover, the cycloid map has good resistance to parameter estimation, and digital signal processing implementation confirms its feasibility in digital circuits, indicating that the cycloid map may be used in potential applications.

Fuzzy Control Under Spatially Local Averaged Measurements for Nonlinear Distributed Parameter Systems With Time-Varying Delay

This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi-Sugeno (T-S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T-S fuzzy PDdE model and a Lyapunov-Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach.

Dissipativity Analysis for T-S Fuzzy System Under Memory Sampled-Data Control

The dissipative stability problem for a class of Takagi-Sugeno (T-S) fuzzy systems with variable sampling control is the focus of this paper. The controller signals are assumed to transmit with a constant delay. Our aim is to design the sampled-data controller such that the T-S fuzzy system is globally asymptotically stable with a (Q,S,R) - γ -dissipative performance index. The stability is analyzed by using a novel piecewise Lyapunov-Krasovskii functional (LKF) together with a looped-functional and free-matrix-based (FMB) inequality method. First, several useful linear matrix inequality (LMI) conditions are derived to verify the dissipative stability of the T-S fuzzy system and then the controller gains matrices are expressed by resorting the LMI approach with the maximal-allowable upper bound (MAUB) of sampling periods. The proposed LMI conditions can be easily solved by using the MATLAB tool box. Finally, the numerical example of a truck-trailer system is considered and analyzed by the proposed scheme to illustrate the benefit and superiority.

Further Study on Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model With Unknown Premise Variables via Average Dwell Time

This article further studies the problem of observer design for the continuous-time Takagi-Sugeno (T-S) fuzzy system with unmeasurable premise variables. A membership function-dependent Lyapunov function is designed to obtain the observer-based controller. Different from the existing results, a switching method is proposed to deal with the time derivative of membership functions. Several problems such as, too many parameters, and the small local stabilization region in the existing papers are solved by applying the switching method. In addition, two algorithms are designed to obtain the controller gains and observer gains. In the end, two examples are provided to demonstrate the effectiveness of the proposed approach.

An Improved Fuzzy Sampled-Data Control to Stabilization of T-S Fuzzy Systems With State Delays

This paper deals with the issue of sampled-data stabilization for T-S fuzzy systems (TSFSs) with state delays and nonuniform sampling. First, a fuzzy membership function (FMFs)-dependent approach is proposed, which uses information not only on both the delayed state and actual sampling pattern but also on the FMFs. Second, the inner sampling interval is split into flexible terminals, and a novel FMFs-dependent Lyapunov-Krasovskii functional (LKF) is constructed. Meanwhile, a fuzzy sampled-data controller (FSDC) with a switched topology is designed to solve the tricky issue on the estimation of FMFs-dependent terms. Then, based on the LKF methodology, the extended Wirtinger's inequality, and an improved reciprocally convex combination strategy, some relaxed criteria with both a larger sampling period and upper bound of time delays for achieving the stabilization of TSFSs are derived. Two numerical examples are presented to demonstrate the superiority and applicability of the proposed scheme.

A Switched Operation Approach to Sampled-Data Control Stabilization of Fuzzy Memristive Neural Networks With Time-Varying Delay

This paper investigates the issue of sampled-data stabilization for Takagi-Sugeno fuzzy memristive neural networks (FMNNs) with time-varying delay. First, the concerned FMNNs are transformed into the tractable fuzzy NNs based on the excitatory and inhibitory of memristive synaptic weights using a new convex combination technique. Meanwhile, a switched fuzzy sampled-data controller is employed for the first time to tackle stability problems related to FMNNs. Then, the novel stabilization criteria of the FMNNs are established using the fuzzy membership functions (FMFs)-dependent Lyapunov-Krasovskii functional. This sufficiently utilizes information from not only the delayed state and the actual sampling pattern but also the FMFs. Two simulation examples are presented to demonstrate the feasibility and validity of the proposed method.

A New Approach to Stabilization of Chaotic Systems With Nonfragile Fuzzy Proportional Retarded Sampled-Data Control

This paper is concerned with the problem of stabilization of chaotic systems via nonfragile fuzzy proportional retarded sampled-data control. Compared with existing sampled-data control schemes, a more practical nonfragile fuzzy proportional retarded sampled-data controller is designed, which involves not only a signal transmission delay but also uncertainties. Based on the Wirtinger inequality, a new discontinuous Lyapunov-Krasovskii functional (LKF), namely, Wirtinger-inequality-based time-dependent discontinuous (WIBTDD) LKF, is the first time to be proposed for sampled-data systems. With the WIBTDD LKF approach and employing the developed estimation technique, a less conservative stabilization criterion is established. The desired fuzzy proportional retarded sampled-data controller can be obtained by solving a set of linear matrix inequalities. Finally, numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.

Sampled-data control for linear time-delay distributed parameter systems

Some real systems have spatiotemporal dynamics and are time-delay distributed parameter systems (DPSs). The existence of time-delay may lead to system instability. The analysis and design of DPSs with time-delay is essentially more complicated. To take into account the factor of time-delay and fully enjoy the benefits of the digital technology in control engineering, it is a theoretical and practical value to consider the sampled-data control (SDC) problem of DPSs with time-delay. However, there are few attempts to solve the SDC problem of time-delay DPSs. In this paper, we introduce a SDC for linear time-delay DPSs described by parabolic partial differential equations (PDEs). A SDC design is developed in the formulation of spatial linear matrix inequalities (LMIs) by constructing an appropriate Lyapunov functional, which can stabilize exponentially the time-delay DPSs. This stabilization condition can be applied to either slowing-varying time delay or fast-varying one. Finally, simulation results of a numerical example are provided to illustrate the effectiveness of the proposed method.

Dissipativity-based non-fragile sampled-data control design of interval type-2 fuzzy systems subject to random delays

This paper investigates the β-dissipativity-based reliable non-fragile sampled-data control problem for a class of interval type-2 (IT2) fuzzy systems. In particular, it is allowed to have randomly occurring time-varying delays in the controller design, which are modeled by Bernoulli distributed white noise sequences. Precisely, the IT2 fuzzy model and the non-fragile sampled-data controller are formulated by considering the mismatched membership functions. By constructing an appropriate Lyapunov-Krasovskii functional, a set of delay-dependent conditions is derived to guarantee that the closed-loop IT2 fuzzy system is strictly <Q,S,R>-β-dissipative. Moreover, the gain matrices of feedback reliable non-fragile sampled-data controller are derived in terms of linear matrix inequalities (LMIs), which can be solved by using existing LMI solvers. Two numerical examples are eventually given to illustrate the applicability and effectiveness of the proposed controller design technique.

Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an -dimensional ( -D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic -D Cat matrices iteratively and then constructs the final -D Cat matrix by performing similarity transformation on one basic -D Cat matrix by the other. Given any number of positive LEs, it can generate an -D HCM with desired hyperchaotic complexity. Two illustrative examples of -D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct -D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.

On Stabilization of Quantized Sampled-Data Neural-Network-Based Control Systems

This paper investigates the problem of stabilization of sampled-data neural-network-based systems with state quantization. Different with previous works, the communication limitation of state quantization is considered for the first time. More specifically, it is assumed that the sampled state measurements from sensor to the controller are quantized via a quantizer. To reduce conservativeness, a novel piecewise Lyapunov-Krasovskii functional (LKF) is constructed by introducing a line-integral type Lyapunov function and some useful terms that take full advantage of the available information about the actual sampling pattern. Based on the new LKF, much less conservative stabilization conditions are derived to obtain the maximal sampling period and the minimal guaranteed cost control performance. The desired quantized sampled-data three-layer fully connected feedforward neural-network-based controllers are designed by a linear matrix inequality approach. A search algorithm is given to find the optimal values of tuning parameters. The effectiveness and advantage of proposed method are demonstrated by the numerical simulation of an inverted pendulum.

Sampled-Data Fuzzy Control for Nonlinear Coupled Parabolic PDE-ODE Systems

In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.

A Switched System Approach to Exponential Stabilization of Sampled-Data T-S Fuzzy Systems With Packet Dropouts

This paper investigates the problem of exponential stabilization for sampled-data Takagi-Sugeno (T-S) fuzzy control systems with packet dropouts. An input delay approach is adopted to model the sample-and-hold behavior with a time-varying delayed control input, and a switched system approach is proposed to model the data-missing phenomenon. On this basis, the sampled-data T-S fuzzy control system with packet dropouts is modeled as a switched T-S fuzzy system with time-varying delay. The objective is to design a sampled-data fuzzy controller to guarantee the exponential stability of the resulting closed-loop system. Based on a new piecewise time-dependent Lyapunov functional, a novel sufficient condition is derived for the existence of exponentially stabilizing sampled-data fuzzy controllers. All the solutions to the problem are formulated in the form of linear matrix inequalities. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

Dynamic Parameter-Control Chaotic System

This paper proposes a general framework of 1-D chaotic maps called the dynamic parameter-control chaotic system (DPCCS). It has a simple but effective structure that uses the outputs of a chaotic map (control map) to dynamically control the parameter of another chaotic map (seed map). Using any existing 1-D chaotic map as the control/seed map (or both), DPCCS is able to produce a huge number of new chaotic maps. Evaluations and comparisons show that chaotic maps generated by DPCCS are very sensitive to their initial states, and have wider chaotic ranges, better unpredictability and more complex chaotic behaviors than their seed maps. Using a chaotic map of DPCCS as an example, we provide a field-programmable gate array design of this chaotic map to show the simplicity of DPCCS in hardware implementation, and introduce a new pseudo-random number generator (PRNG) to investigate the applications of DPCCS. Analysis and testing results demonstrate the excellent randomness of the proposed PRNG.

$n$ -Dimensional Discrete Cat Map Generation Using Laplace Expansions

Different from existing methods that use matrix multiplications and have high computation complexity, this paper proposes an efficient generation method of n -dimensional ( [Formula: see text]) Cat maps using Laplace expansions. New parameters are also introduced to control the spatial configurations of the [Formula: see text] Cat matrix. Thus, the proposed method provides an efficient way to mix dynamics of all dimensions at one time. To investigate its implementations and applications, we further introduce a fast implementation algorithm of the proposed method with time complexity O(n⁴) and a pseudorandom number generator using the Cat map generated by the proposed method. The experimental results show that, compared with existing generation methods, the proposed method has a larger parameter space and simpler algorithm complexity, generates [Formula: see text] Cat matrices with a lower inner correlation, and thus yields more random and unpredictable outputs of [Formula: see text] Cat maps.

Novel Fuzzy Modeling and Synchronization of Chaotic Systems With Multinonlinear Terms by Advanced Ge-Li Fuzzy Model

Ge and Li proposed an alternative strategy to model and synchronize two totally different nonlinear systems in the end of 2011, which provided a new version for fuzzy modeling and has been applied to several fields to simplify their modeling works and solve the mismatch problems [1]-[17]. However, the proposed model limits the number of nonlinear terms in each equation so that this model could not be used in all kinds of nonlinear dynamic systems. As a result, in this paper, a more efficient and comprehensive advanced-Ge-Li fuzzy model is given to further release the limitation and improve the effectiveness of the original one. The novel fuzzy model can be applied to all kinds of complex nonlinear systems--this is the universal strategy and only m x 2 fuzzy rules as well as two linear subsystems are needed to simulate nonlinear behaviors (m is the number of states in a nonlinear dynamic system), whatever the nonlinear terms are copious or complicated. Further, the fuzzy synchronization of two nonlinear dynamic systems with totally distinct structures can be achieved via only two sets of control gains designed through the novel fuzzy model as well as its corresponding fuzzy synchronization scheme. Two complicated dynamic systems are designed to be the illustrations, Mathieu-Van der pol system with uncertainties and Quantum-cellular neural networks nano system with uncertainties, to show the effectiveness and feasibility of the novel fuzzy model.

H∞ Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model With Unknown Premise Variables via Nonquadratic Lyapunov Function

This paper deals with the problem of observer design for continuous-time Takagi-Sugeno fuzzy models with unmeasurable premise variables. First, in order to improve the existing results of observer design, a new method is proposed to bound the time derivatives of the membership function. Then, by applying the nonquadratic Lyapunov function and the matrix decoupling technique, the controller gains and observer gains are designed to guarantee that the error system is asymptotically stale. Furthermore, better H ∞ performance can be obtained by solving an optimization problem. All of the results are presented as linear matrices inequalities and three examples are provided to demonstrate the merits of the proposed approach.

Robust Frequency-Domain Constrained Feedback Design via a Two-Stage Heuristic Approach

Based on a two-stage heuristic method, this paper is concerned with the design of robust feedback controllers with restricted frequency-domain specifications (RFDSs) for uncertain linear discrete-time systems. Polytopic uncertainties are assumed to enter all the system matrices, while RFDSs are motivated by the fact that practical design specifications are often described in restricted finite frequency ranges. Dilated multipliers are first introduced to relax the generalized Kalman-Yakubovich-Popov lemma for output feedback controller synthesis and robust performance analysis. Then a two-stage approach to output feedback controller synthesis is proposed: at the first stage, a robust full-information (FI) controller is designed, which is used to construct a required output feedback controller at the second stage. To improve the solvability of the synthesis method, heuristic iterative algorithms are further formulated for exploring the feedback gain and optimizing the initial FI controller at the individual stage. The effectiveness of the proposed design method is finally demonstrated by the application to active control of suspension systems.