Impulsive stabilization of fractional differential systems

This paper investigates the impulsive stabilization problem of fractional differential systems (FDSs in short). Both the global exponential stability and ultimate boundedness criteria are established using Lyapunov functions, algebraic inequality techniques and boundedness of Mittag-Leffler functions. It is shown that unstable and unbounded FDSs can be stable and bounded respectively under impulsive control. Examples and simulations are also provided to demonstrate the effectiveness of the derived theoretical results.     

Anti-windup adaptive PID control design for a class of uncertain chaotic systems with input saturation

In this paper, the stabilization problem of actuators saturation in uncertain chaotic systems is investigated via an adaptive PID control method. The PID control parameters are auto-tuned adaptively via adaptive control laws. A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation. The proposed control technique uses both the state-feedback and the output-feedback methodologies. Based on Lyapunov׳s stability theory, new anti-windup adaptive controllers are proposed. Demonstrative examples with MATLAB simulations are studied. The simulation results show the efficiency of the proposed adaptive PID controllers.     

Finite time stability and controller design for nonlinear impulsive sampled-data systems with applications

This paper investigates the finite time stability (FTS) for nonlinear impulsive sampled-data systems. By constructing an appropriated Lyapunov function and employing average impulsive interval (AII) method, some FTS criteria for the nonlinear impulsive sampled-data systems are derived in terms of linear matrix inequalities (LMIs), which can be easily verified via the LMI toolbox. The hybrid controller including sampled-data controller and impulsive controller is designed via the established LMIs. Moreover, the impulse effect considered in this paper including stabilizing impulse and destabilizing impulse. Our developed results are less conservative than the recent work in the literature. Finally, two numerical examples are provided to show the applications of the proposed criteria.     

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance.     

Improved robust stabilization method for linear systems with interval time-varying input delays by using Wirtinger inequality

This paper investigates the robust stabilization problem for uncertain linear systems with interval time-varying delays. By constructing novel Lyapunov–Krasovskii functionals and developing delay-partitioning approaches, some delay-dependent stability criteria are derived based on an improved Wirtinger׳s inequality and the reciprocally convex method. The proposed methods have improved the stability conditions without increasing much computational complexity. A state feedback controller design approach is also presented based on the proposed criteria. Numerical examples are finally given to illustrate the effectiveness of the proposed method.     

Partial stabilization of uncertain nonlinear systems

In this paper, the problem of robust partial stabilization is considered and two approaches for partial stabilization of uncertain nonlinear systems are presented. In these approaches, the nonlinear dynamical system is divided into two subsystems, which are called the first and the second subsystems. This division is done based on the required stability properties of the system's states. The reduced input vector (the vector that includes components of the input vector appearing in the first subsystem) is designed to asymptotically stabilize the first subsystem. In the first approach, a new partial stabilization technique, based on the first order sliding mode control idea is proposed. In the proposed method, hereafter called the partial sliding mode, a sliding surface is designed such that restricting the motion on this surface guarantees the stability of only the first part of the system's state. In the second approach, a Lyapunov-based controller is proposed for partial stabilization and then an additional feedback control is designed so that the overall feedback law guarantees a robust manner in the presence of uncertainties.     

Bonhoeffer-van der Pol方程中双吸引子的混沌控制

基于延时反馈混沌控制方法和相空间压缩法,提出一种改进的延时反馈混沌控制方法。该方法不仅可用于单个吸引子混沌系统的控制,而且由于克服了Pyragas控制方法的不能简便地将混沌系统稳定到嵌入在不同混沌吸引子内周期轨道的不足,也可以用于多个混沌吸引子混沌系统的控制。以Bonhoeffer-van der Pol系统为例,数值验证此改进方法用于两个混沌吸引子系统控制的有效性,结果表明,在延时反馈控制中增加适当的相空间限制器,可以快捷地将系统稳定在期望的周期轨道上。     

Stability analysis of sample data systems with input missing: A hybrid control approach

In this paper, we establish exponential stability criteria for the sampled-data impulsive control of the linear time-invariant system. With average impulse interval (AII), less conservative conditions are obtained on the exponential stability problem for the sampled-data systems. It is proved that when the AII of the impulsive sequences is fixed, the upper bound of the impulsive intervals could be very large, which guarantees the less conservativeness of the obtained result concerning the sampling intervals. The control input missing is also studied and we establish a new stability criterion for the exponential decay rate and the sampling period which is less conservative than the ones obtained for variable sampling intervals. Two examples are given to show the effectiveness of the obtained result.     

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

Optimistic value based optimal control for uncertain linear singular systems and application to a dynamic input-output model

In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained.     

Asynchronous control of discrete-time impulsive switched systems with mode-dependent average dwell time

This paper mainly studies the asynchronous control problem for a class of discrete-time impulsive switched systems, where “asynchronous” means the switching of the controllers has a lag to the switching of system modes. By using multiple Lyapunov functions (MLFs), the much looser asymptotic stability result of closed-loop systems is derived with a mode-dependent average dwell time (MDADT) technique. Based on the stability result obtained, the problem of asynchronous control is solved under a proper switching law. Moreover, the stability and stabilization results are formulated in form of matrix inequalities that are numerically feasible. Finally, an illustrative numerical example is presented to show the effectiveness of the obtained stability results.     

Improved results on delay-interval-dependent robust stability criteria for uncertain neutral-type systems with time-varying delays

In this paper, we consider the problem of delay-interval-dependent robust stability and stabilization of a class of linear uncertain neutral-type systems with time-varying delay. By constructing a candidate Lyapunov–Krasovskii functional (LKF), that takes into account the delay-range information appropriately, less conservative robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) to compute the maximum allowable upper bounds (MAUB) for the delay-interval within which the uncertain neutral-type system under consideration remains asymptotically stable. The verifiable stabilizability conditions and memoryless state feedback control design are stated. Finally, numerical examples are also designated to demonstrate the effectiveness and reduced conservatism of the developed results.     

非线性励磁控制器在线参数估计方法研究

在自适应方法基础上同时利用跟踪误差和预测误差,提出了一种非线性励磁控制器的复合自适应在线参数估计方法。该方法在保证系统稳定性和获得较小的跟踪误差基础上,更明显提高了参数估计的快速性和光滑性。数字仿真试验表明,设计的非线性自适应励磁控制器具有较强的参数自适应能力,且保证了系统的稳定性。     

Further improvement on delay-range-dependent robust absolute stability for Lur׳e uncertain systems with interval time-varying delays

This paper investigates improved delay-range-dependent robust absolute stability criteria for a class of Lur׳e uncertain systems with interval time-varying delays. By using delayed decomposition approach (DDA), a tighter upper bound of the derivative of Lyapunov functional can be obtained, and thus the proposed criteria give results with less conservatism compared with some previous ones. An integral inequality approach (IIA) is proposed to reduce the conservativeness in computing the allowable maximum admissible upper bound (MAUB) of the time-delay. The developed stability condition is expressed in terms of linear matrix inequality (LMI) that manipulates fewer decision variables and requires reduced computational load. Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

Finite-time stabilization for a class of nonholonomic feedforward systems subject to inputs saturation

This paper studies the problem of finite-time stabilization by state feedback for a class of uncertain nonholonomic systems in feedforward-like form subject to inputs saturation. Under the weaker homogeneous condition on systems growth, a saturated finite-time control scheme is developed by exploiting the adding a power integrator method, the homogeneous domination approach and the nested saturation technique. Together with a novel switching control strategy, the designed saturated controller guarantees that the states of closed-loop system are regulated to zero in a finite time without violation of the constraint. As an application of the proposed theoretical results, the problem of saturated finite-time control for vertical wheel on rotating table is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Detection and recovery of fault impulses via improved harmonic product spectrum and its application in defect size estimation of train bearings

The detection and recovery of impulsive signature play a vital role in the diagnosis and prognosis of rolling element bearings. Though different approaches have been proposed to deal with this problem so far, challenges still exist when they are applied to the bearings operating under harsh working conditions. The difficulties mainly come from the multi-resonance and multi-modulation characteristics of bearing vibration signals. To overcome this limitation, a new methodology for the detection and recovery of fault impulses is presented in this paper. First, an improved harmonic product spectrum (IHPS) is proposed to detect and identify the multiple modulation sources buried in a vibration signal. With this method, the fault-related impulsive features could be recognized, while the influence caused by non-fault modulation is eliminated. On this basis, a harmonic significance index is further established to quantify the diagnostic information contained in a narrow band signal. By utilizing this index, the optimal resonance band where the fault impulses are most significant could be accurately determined. Finally, IHPS and sideband product spectrum are integrated to reduce the in-band noise and further recover the fault impulses. The performance of this method is evaluated by both simulated data and real vibration data measured from a train wheel bearing with a naturally developed defect. Compared with Kurtogram and Protrugram, the proposed method can detect the resonance band more precisely even in the presence of heavy noise and other impulsive vibration sources. Moreover, with the impulses recovery scheme, the double impact phenomenon caused by a distributed defect is extracted successfully. Benefiting from this, the defect size of a bearing can be estimated from its vibration signal without dismantling, which makes it a promising tool for the bearing diagnosis and prognosis in industrial applications.     

Robust control of feedback linearizable large-scale systems

The design of decentralized controllers for a class of uncertain interconnected nonlinear systems is considered. The uncertainty considered here is time-varying and appears at each subsystem and interconnections. Two control techniques are explored. The first one, namely, the feedback linearization control, involves a known and autonomous nonlinear system. The second one, namely, the robust control, is especially suitable if any uncertainty and/or time-varying factors are involved in the nonlinear dynamics. These two controllers are combined to stabilize a class of large-scale nonlinear uncertain systems. Two decentralized robust controllers, nonadaptive and adaptive, are proposed and those results are proved.     

A delay decomposition approach to robust stability analysis of uncertain systems with time-varying delay

This paper is concerned with delay-dependent robust stability for uncertain systems with time-varying delays. The proposed method employs a suitable Lyapunov-Krasovskii's functional for new augmented system. Then, based on the Lyapunov method, a delay-dependent robust criterion is devised by taking the relationship between the terms in the Leibniz-Newton formula into account. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities (LMIs) which can be easily solved by various optimization algorithms. Numerical examples are included to show that the proposed method is effective and can provide less conservative results.     

Application of improved morphological filter to the extraction of impulsive attenuation signals

Rotating machinery response is often characterized by the presence of periodic impulses modulated by high-frequency harmonic components. It can be defined with three parameters, which are natural frequency, fault frequency and decay coefficient. In this paper, we propose an improved morphological filter for feature extraction of the above signals in the time domain. Firstly, an average weighted combination of open-closing and close-opening morphological operator, which eliminates statistical deflection of amplitude, is utilized to extract impulsive component from the original signal. Then, according to the geometric characteristic of impulsive attenuation component, the structure element is constructed with an impulsive attenuation function, and a new criterion is put forward to optimize the structure element. The proposed method is evaluated by simulated impulsive attenuation signals with different natural frequencies and vibration signals measured on defective bearings with outer race fault and inner race fault, respectively. Results show that the background noise can be fully restrained and the entire impulsive attenuation signal is well extracted, which demonstrates that the method is an efficient tool to extract impulsive attenuation component from mechanical signals.     

Non-fragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation

This paper proposes a new non-fragile stochastic control method to investigate the robust sampled-data synchronization problem for uncertain chaotic Lurie systems (CLSs) with time-varying delays. The controller gain fluctuation and time-varying uncertain parameters are supposed to be random and satisfy certain Bernoulli distributed white noise sequences. Moreover, by choosing an appropriate Lyapunov-Krasovskii functional (LKF), which takes full advantage of the available information about the actual sampling pattern and the nonlinear condition, a novel synchronization criterion is developed for analyzing the corresponding synchronization error system. Furthermore, based on the most powerful free-matrix-based integral inequality (FMBII), the desired non-fragile sampled-data estimator controller is obtained in terms of the solution of linear matrix inequalities. Finally, three numerical simulation examples of Chua's circuit and neural network are provided to show the effectiveness and superiorities of the proposed theoretical results.