Synchronization of chaotic systems under sampled-data control

The problem of global asymptotical synchronization of chaotic Lur??e systems using sampled-data controller is considered in this paper. Sufficient conditions are obtained in terms of effective synchronization linear matrix inequality using a piecewise sawtooth structure of the sampling in time by constructing the new discontinuous Lyapunov functionals. The sampled-data feedback control gain is obtained from the derived condition. The Chua system and horizontal platform system are taken for numerical demonstration to show the effectiveness of the proposed condition.     

Discontinuous Lyapunov functional approach to synchronization of time-delay neural networks using sampled-data

This paper investigates the synchronization problem of neural networks with time-varying delay under sampled-data control in the presence of a constant input delay. Based on the extended Wirtinger inequality, a discontinuous Lyapunov functional is introduced, which makes full use of the sawtooth structure characteristic of sampling input delay. A simple and less conservative synchronization criterion is given to ensure the master systems synchronize with the slave systems by using the linear matrix inequality (LMI) approach. The design method of the desired sampled-data controller is also proposed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.     

具有采样反馈的力控制系统稳定性

基于计算机的数字采样控制对离散信号进行运算并向作动器提供控制输入,是当前的主流控制技术.数字采样控制系统是这样一类控制系统,其控制对象由微分方程(组)描述,而控制律由离散采样信号给出.以采样PD(proportional-derivative)反馈作用下的单自由度力控制系统为例,基于离散系统的稳定性分析方法,研究采样控制律对控制系统稳定性的影响.为了突出采样反馈的作用,将系统取为无刚度、无阻尼的最简单形式.不同于已有研究假设位移采样信号与速度采样信号相互同步,本文研究当位移采样信号与速度采样信号不同步时受控系统的稳定性,发现位移采样信号与速度采样信号的采样周期不同组合对受控系统在增益平面上的稳定性区域有重要影响.结果表明,对所关心的三种数字采样反馈控制律,当位移采样信号滞后于速度采样信号一个采样周期时,受控系统具有最大的稳定性区域且对相同的增益值可以有最好的稳定效果.论文对这种现象进行分析,给出了一种力学解释.     

Sampled-data state estimation for delayed neural networks with Markovian jumping parameters

This paper is concerned with the sampled-data state estimation problem for a class of delayed neural networks with Markovian jumping parameters. Unlike the classical state estimation problem, in our state estimation scheme, the sampled measurements are adopted to estimate the concerned neuron states. The neural network under consideration is assumed to have multiple modes that switch from one to another according to a given Markovian chain. By utilizing the input delay approach, the sampling period is converted into a time-varying yet bounded delay. Then a sufficient condition is given under which the resulting error dynamics of the neural networks is exponentially stable in the mean square. Based on that, a set of sampled-data estimators is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using the available software. Finally, a numerical example is used to show the effectiveness of the estimation approach proposed in this paper.     

Robust H ∞ output tracking control for fuzzy networked systems with stochastic sampling and multiplicative noise

In this paper, the problem of robust sampled-data H _?? output tracking control is investigated for a class of fuzzy networked systems with stochastic sampling, multiplicative noise and time-varying norm-bounded uncertainties. For the sake of technical simplicity, only two different sampling periods are considered, their occurrence probabilities are given constants and satisfy Bernoulli distribution, and they can be extended to the case with multiple stochastic sampling periods. By using an input-delay method, the probabilistic system is transformed into a stochastic continuous time-delay system. A?new linear matrix inequality(LMI)-based procedure is proposed for designing state-feedback controllers, which would guarantee that the closed-loop networked system with stochastic sampling tracks the output of a given reference model well in the sense of H _??. Conservatism is reduced by taking the probability into account. Both network-induced delays and packet dropouts have been considered. Finally, an illustrative example is given to show the usefulness and effectiveness of the proposed H _?? output tracking design.     

An enhanced input-delay approach to sampled-data stabilization of T–S fuzzy systems via mixed convex combination

The problem of sampled-data control is investigated for Takagi–Sugeno (T–S) fuzzy systems with aperiodic sampling intervals based on an enhanced input-delay approach. Delay-dependent stability and stabilizability conditions for the closed-loop continuous nonuniformly sampled-data fuzzy systems are derived by constructing a novel discontinuous Lyapunov–Krasovskii (L–K) functional, which makes good use of not only the upper bound on the variable sampling interval, but also its sawtooth structure information about varying input delay often ignored in previous results. A bounding technique combined by reciprocally convex technics and linear convex combination is presented for acquiring the time derivative of the functional, wherein Jensen’s inequality and Wirtinger’s inequality are integratively employed. And a feasible solution of the obtained criterion formulated as parameterized linear matrix inequalities is ultimately conceived. A numerical example is given to show the effectiveness of the proposed method.     

Sampling-interval-dependent synchronization of complex dynamical networks with distributed coupling delay

The problem of sampled-data synchronization of complex dynamical networks with distributed coupling delay and time-varying sampling is discussed in this paper. Based on the input delay approach and two integral inequalities, a stability criterion is proposed for the error dynamics, which is sampling-interval-dependent. Based on the given criterion, the design method of the desired sampled-data controllers is also obtained in terms of the solution to linear matrix inequalities, which can be checked effectively by using available software. An example is given to illustrate the effectiveness of the proposed result.     

Robust reliable sampled-data control for offshore steel jacket platforms with nonlinear perturbations

In this article, we consider the robust reliable sample-data control problem for an offshore steel jacket platform with input time-varying delay and possible occurrence of actuator faults subject to nonlinear self-exited hydrodynamic forces. The main objective of this work is to design a state feedback reliable sample-data controller such that for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly exponentially stable. By constructing an appropriate Lyapunov–Krasovskii functional and using linear matrix inequality (LMI) approach, a new set of sufficient condition is derived in terms of LMIs for the existence of robust reliable sample-data control law. In particular, the uncertainty under consideration in system parameters includes linear fractional norm-bounded uncertainty. Further, Schur complement and Jenson’s integral inequality are used to substantially simplify the derivation in the main results. More precisely, the controller gain matrix for the nonlinear offshore steel jacket platform can be achieved by solving the LMIs, which can be easily facilitated by using some standard numerical packages. Finally, a numerical example with simulation result is provided to illustrate the applicability and effectiveness of the proposed reliable sampled-data control scheme.     

Exponential state estimation for delayed recurrent neural networks with sampled-data

In this paper, the sampled-data state estimation problem is investigated for a class of recurrent neural networks with time-varying delay. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator is constructed. By converting the sampling period into a bounded time-varying delay, the error dynamics of the considered neural network is derived in terms of a dynamic system with two different time-delays. Subsequently, by choosing an appropriate Lyapunov functional and using the Jensen??s inequality, a sufficient condition depending on the sampling period is obtained under which the resulting error system is exponentially stable. Then a sampled-data estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs) which can be solved by using available software. Finally, a numerical example is employed to demonstrate the effectiveness of the proposed sampled-data estimation approach.     

Design of fractional robust adaptive intelligent controller for uncertain fractional-order chaotic systems based on active control technique

In this paper, a robust fractional-order adaptive intelligent controller is proposed for stabilization of uncertain fractional-order chaotic systems. The intelligent neuro-fuzzy network is used to estimate unknown dynamics of system, while the neuro-fuzzy network parameters as well as the upper bounds of the model uncertainties, disturbances and approximation errors are adaptively estimated via separate adaptive rules. An SMC scheme, with a fractional-order sliding surface, is employed, as the controller to improve the velocity and performance of the proposed control system and to eliminate the unknown but bounded uncertainties, external disturbances and approximation errors. The Lyapunov stability theorem has been also employed to show the stability of the closed-loop system, robustness against uncertainties, external disturbances and approximation errors, while the control signal remains bounded. Explanatory examples and simulation results are given to confirm the effectiveness of the proposed procedure, which consent well with the analytical results.     

Fuzzy observer-based command filtered tracking control for uncertain strict-feedback nonlinear systems with sensor faults and event-triggered technology

For the trajectory tracking problem of nth-order uncertain nonlinear systems with sensor faults, a fuzzy controller based on command filtered and event-triggered technology is designed to improve the tracking error of the system. Concurrently, a fault-tolerant control scheme is introduced to effectively solve the problem of sudden output sensor failure. Additionally, the proposed controller can also greatly avoid complexity explosion problem of derivations of virtual control laws, which makes the design of the controller simpler. Furthermore, an effective observer is designed to solve the problem of system state immeasurability. Therefore, the proposed control scheme makes the design of the controller more convenient and flexible. According to Lyapunov stability theory, it is proved that all closed-loop signals are uniformly and ultimately bounded. Finally, two simulation examples of second-order nonlinear system and single-link robot show the effectiveness of the proposed scheme.

     

Periodic self-triggered intermittent sampled-data stabilization for stochastic complex networks

In this paper, a new class of periodic self-triggered intermittent control with sampled-data (PSICS) is designed to tackle the stabilization issue for stochastic complex networks with time delays and Lévy noise (SCNTL). Therein, the self-triggered scheme is propounded with regard to intermittent control which is periodic judgment, and there exists a sampled-data control in every intervals of periodic judgment in the control time (work time) of intermittent control. It is worth pointing out that PSICS possesses more flexibility in terms of applications and simpler design of triggered conditions, compared with some previously reported control strategies such as the control combines the advantages of the periodic sampling and self-triggered control. Meanwhile, by means of stability analysis, sampled-data control, intermittent control and event-driven control theory, a useful criterion is established to guarantee the exponential stability in mean square of SCNTL. Notably, the stabilization issue of single-link robot arms with time delays and Lévy noise via PSICS is studied, as a practical application of SCNTL. Ultimately, numerical simulations are utilized for illustration.

     

车辆主动悬架设计的约束H∞控制方法

针对线性离散时间系统,研究其时域硬约束下的H∞输出反馈控制问题。假定外界扰动能量有限,基于线性矩阵不等式处理方法,提出并证明了时域硬约束下H∞输出反馈控制器存在的充分条件,并应用于车辆主动悬架设计。四分之一车辆模型数值仿真结果表明,即使车辆模型参数存在不确定性,本文提出的控制器在提高车辆乘坐舒适性的同时,仍能很好地兼顾车辆的其他性能要求。     

Chaos bursting synchronization of mismatched Hindmarsh–Rose systems via a single adaptive feedback controller

Chaotic bursting synchronization of mismatched Hindmarsh–Rose neuron systems is investigated. Based on the Lyapunov stability theory, an adaptive feedback control scheme for the synchronization of the neuron systems is proposed when partially parameters of the response system are unknown and different with those of the drive system. Furthermore, in the proposed scheme, only a single adaptive feedback controller is needed, which is efficient and easy to implement. Finally, numerical simulations are provided to show the effectiveness of the developed methods.     

线性时滞系统的离散最优控制

介绍了对线性时滞系统进行最优控制的设计，将具有时滞控制的线性系统离散后引入增广状态向量。获得不显含时滞的差分方程，根据时滞量的两种分类情况采用连续和离散形式的性能指标函数导出了最优控制律。控制律包含当前状态和此前若干步状态向量的叠加，最优控制律直接从时滞方程中得到，可保证系统的稳定性，此方法亦适用于大时滞的情况。数值算例验证了控制策略的有效性。     

一种新型高精度大功率电动飞行仿真转台的驱动方案设计

针对一种新型电动飞行仿真转台高精度、大功率的突出特点,设计了十分有效的驱动方案。首先简要介绍了该电动飞行仿真转台的主要技术指标,然后提出了高精度大功率飞行仿真转台驱动方案的详细设计策略,驱动方案中采用PWM功率放大器驱动,最后给出了该驱动方案在飞行仿真转台控制系统中的设计实现。实际应用表明:该驱动方案可以很好地满足新型电动飞行仿真转台的高精度、大功率要求,具有很强的抗干扰性和鲁棒性,完全适合在高精度大功率电动仿真转台上应用。     

CONTROL CHAOS IN TRANSITION SYSTEM USING SAMPLED-DATA FEEDBACK

The method for controlling chaotic transition system was investigated using sampled- data . The output of chaotic transition system was sampled at a given sampling rate , then the sampled output was used by a feedbacks subsystem to construct a control signal for controlling chaotic transition system to the origin . Numerical simulations are presented to show the effectiveness and feasibility of the developed controller.     

A single adaptive controller with one variable for synchronizing two identical time delay hyperchaotic Lorenz systems with mismatched parameters

Time delays are ubiquitous in real world and are often sources of complex behaviors of dynamical systems. This paper addresses the problem of parameter identification and synchronization of uncertain hyperchaotic time-delayed systems. Based on the Lyapunov stability theory and the adaptive control theory, a single adaptive controller with one variable for synchronizing two identical time-delay hyperchaotic Lorenz systems with mismatch parameters is proposed. The parameter update laws and sufficient conditions of the scheme are obtained for both linear feedback and adaptive control approaches. Numerical simulations are also given to show the effectiveness of the proposed method.     

A switching fractional calculus-based controller for normal non-linear dynamical systems

In this paper, a fractional calculus-based terminal sliding mode controller is introduced for finite-time control of non-autonomous non-linear dynamical systems in the canonical form. A fractional terminal switching manifold which is appropriate for canonical integer-order systems is firstly designed. Then some conditions are provided to avoid the inherent singularities of the conventional terminal sliding manifolds. A non-smooth Lyapunov function is adopted to prove the finite time stability and convergence of the sliding mode dynamics. Afterward, based on the sliding mode control theory, an equivalent control and a discontinuous control law are designed to guarantee the occurrence of the sliding motion in finite time. The proposed control scheme uses only one control input to stabilize the system. The proposed controller is also robust against system uncertainties and external disturbances. Two illustrative examples show the effectiveness and applicability of the proposed fractional finite-time control strategy. It is worth noting that the proposed sliding mode controller can be applied for control and stabilization of a large class of non-autonomous non-linear uncertain canonical systems.