Tracking control of chaotic spinning disks via nonlinear dynamic output feedback with input constraints

In many control engineering applications, it is impossible or expensive to measure all the states of the dynamical system and only the system output is available for controller design. In this study, a new dynamic output feedback control algorithm is proposed to stabilize the unstable periodic orbit of chaotic spinning disks with incomplete state information. The proposed control structure is based on the T‐S fuzzy systems. This investigation also introduces a new design procedure to satisfy a constraint on the T‐S fuzzy dynamic output feedback control signal. This procedure is independent of the exact value of initial states. Finally, computer simulations are accomplished to illustrate the performance of the proposed control algorithm. © 2015 Wiley Periodicals, Inc. Complexity 21: 148–159, 2016     

Sampled‐data reliable stabilization of T‐S fuzzy systems and its application

In this article, based on sampled‐data approach, a new robust state feedback reliable controller design for a class of Takagi–Sugeno fuzzy systems is presented. Different from the existing fault models for reliable controller, a novel generalized actuator fault model is proposed. In particular, the implemented fault model consists of both linear and nonlinear components. Consequently, by employing input‐delay approach, the sampled‐data system is equivalently transformed into a continuous‐time system with a variable time delay. The main objective is to design a suitable reliable sampled‐data state feedback controller guaranteeing the asymptotic stability of the resulting closed‐loop fuzzy system. For this purpose, using Lyapunov stability theory together with Wirtinger‐based double integral inequality, some new delay‐dependent stabilization conditions in terms of linear matrix inequalities are established to determine the underlying system's stability and to achieve the desired control performance. Finally, to show the advantages and effectiveness of the developed control method, numerical simulations are carried out on two practical models. © 2016 Wiley Periodicals, Inc. Complexity 21: 518–529, 2016     

A simple method of chaos control for a class of chaotic discrete-time systems

In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called “odd eigenvalues number limitation” of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system.     

Delay-dependent nonfragile guaranteed cost control for nonlinear time-delay systems

This paper concerns the nonfragile guaranteed cost control problem for a class of nonlinear dynamic systems with multiple time delays and controller gain perturbations. Guaranteed cost control law is designed under two classes of perturbations, namely, additive form and multiplicative form. The problem is to design a memoryless state feedback control law such that the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties. Based on the linear matrix inequality (LMI) approach, some delay-dependent conditions for the existence of such controller are derived. A numerical example is given to illustrate the proposed method.     

Adaptive output feedback asymptotic stabilization of nonholonomic systems with uncertainties

A global adaptive output feedback control strategy is presented for a class of nonholonomic systems in generalized chained form with drift nonlinearity and unknown virtual control parameters. The purpose is to design a nonlinear output feedback switching controller such that the closed-loop system is globally asymptotically stable. By using the input-state scaling technique and an integrator back-stepping approach, an output feedback controller is given. A filter of observer gain is introduced for state and parameter estimates. Meanwhile, in order to avoid the over-parameters, a tuning function technique is utilized. A novel switching control strategy based on the output measurement of the first subsystem rather than time is used to overcome the uncontrollability of the x₀-subsystem in the origin. The proposed controller can guarantee that all the system states globally converge to the origin, while other signals maintain bounded. The numerical simulation testifies the effectiveness.     

Study on chaos control of second-order non-autonomous phase-locked loop based on state observer

With system parameters falling into a certain area, the second-order non-autonomous phase locked loop (PLL) is experiencing chaotic behavior which is undesirable in system, where it is necessary to estimate the phase of a received signal. In order to control chaos in PLL and drive it to the locked state, dynamical equation for phase error model of PLL is firstly derived. Then, the state values of phase and transient frequency errors were estimated by a state observer. Moreover, by exploiting these state estimations, a non-linear feedback controller is designed. Since the presented controller does not need to change the controlled system structure and not to use any information of system except the system state variables, the designed controller is simple and desirable. Simulation results show that the presented control law is very effective.     

Dynamic output feedback fault tolerant controller design for discrete-time switched systems with actuator fault

This paper investigates the problem of dynamic output feedback fault tolerant controller design for discrete-time switched systems with actuator fault. By using reduced-order observer method and switched Lyapunov function technique, a fault estimation algorithm is achieved for the discrete-time switched system with actuator fault. Then based on the obtained online fault estimation information, a switched dynamic output feedback fault tolerant controller is employed to compensate for the effect of faults by stabilizing the closed-loop systems. Finally, an example is proposed to illustrate the obtained results.     

Delayed state feedback and chaos control for time-periodic systems via a symbolic approach

This paper presents a symbolic method for a delayed state feedback controller (DSFC) design for linear time-periodic delay (LTPD) systems that are open loop unstable and its extension to incorporate regulation and tracking of nonlinear time-periodic delay (NTPD) systems exhibiting chaos. By using shifted Chebyshev polynomials, the closed loop monodromy matrix of the LTPD system (or the linearized error dynamics of the NTPD system) is obtained symbolically in terms of controller parameters. The symbolic closed loop monodromy matrix, which is a finite dimensional approximation of an infinite dimensional operator, is used in conjunction with the Routh–Hurwitz criterion to design a DSFC to asymptotically stabilize the unstable dynamic system. Two controllers designs are presented. The first design is a constant gain DSFC and the second one is a periodic gain DSFC. The periodic gain DSFC has a larger region of stability in the parameter space than the constant gain DSFC. The asymptotic stability of the LTPD system obtained by the proposed method is illustrated by asymptotically stabilizing an open loop unstable delayed Mathieu equation. Control of a chaotic nonlinear system to any desired periodic orbit is achieved by rendering asymptotic stability to the error dynamics system. To accommodate large initial conditions, an open loop controller is also designed. This open loop controller is used first to control the error trajectories close to zero states and then the DSFC is switched on to achieve asymptotic stability of error states and consequently tracking of the original system states. The methodology is illustrated by two examples.     

Nonfragile H∞ output tracking control for uncertain singular Markovian jump delay systems with network‐induced delays and data packet dropouts

This article deals with the problem of nonfragile H_∞ output tracking control for a kind of singular Markovian jump systems with time‐varying delays, parameter uncertainties, network‐induced signal transmission delays, and data packet dropouts. The main objective is to design mode‐dependent state‐feedback controller under controller gain perturbations and bounded modes transition rates such that the output of the closed‐loop networked control system tracks the output of a given reference system with the required H_∞ output tracking performance. By constructing a more multiple stochastic Lyapunov–Krasovskii functional, the novel mode‐dependent and delay‐dependent conditions are obtained to guarantee the augmented output tracking closed‐loop system is not only stochastically admissible but also satisfies a prescribed H_∞‐norm level for all signal transmission delays, data packet dropouts, and admissible uncertainties. Then, the desired state‐feedback controller parameters are determined by solving a set of strict linear matrix inequalities. A simple production system example and two numerical examples are used to verify the effectiveness and usefulness of the proposed methods. © 2015 Wiley Periodicals, Inc. Complexity 21: 396–411, 2016     

Self-organizing adaptive wavelet CMAC backstepping control system design for nonlinear chaotic systems

A novel self-organizing wavelet cerebellar model articulation controller (CMAC) is proposed. This self-organizing wavelet CMAC (SOWC) can be viewed as a generalization of a self-organizing neural network and of a conventional CMAC, and it has better generalizing, faster learning and faster recall than a self-organizing neural network and a conventional CMAC. The proposed SOWC has the advantages of structure learning and parameter learning simultaneously. The structure learning possesses the ability of on-line generation and elimination of layers to achieve optimal wavelet CMAC structure, and the parameter learning can adjust the interconnection weights of wavelet CMAC to achieve favorable approximation performance. Then a SOWC backstepping (SOWCB) control system is proposed for the nonlinear chaotic systems. This SOWCB control system is composed of a SOWC and a fuzzy compensator. The SOWC is used to mimic an ideal backstepping controller and the fuzzy compensator is designed to dispel the residual of approximation errors between the ideal backstepping controller and the SOWC. Moreover, the parameters of the SAWCB control system are on-line tuned by the derived adaptive laws in the Lyapunov sense, so that the stability of the feedback control system can be guaranteed. Finally, two application examples, a Duffing–Holmes chaotic system and a gyro chaotic system, are used to demonstrate the effectiveness of the proposed control method. The simulation results show that the proposed SAWCB control system can achieve favorable control performance and has better tracking performance than a fuzzy neural network control system and a conventional adaptive CMAC.     

广义不确定周期时变系统的鲁棒非脆弱控制

研究了状态矩阵具有不确定性的广义周期时变系统的鲁棒非脆弱控制问题.利用线性矩阵不等式(LMI)方法,分别对控制器增益具有加法式摄动和乘法式摄动两种情形加以讨论,而非脆弱控制器的设计可以通过求解一组线性矩阵不等式得到.最后,数值例子说明了所给方法的有效性.     

一类时滞非完整系统的反馈控制问题的研究

针对一类具有时滞项的非完整系统,研究了其反馈控制器的设计问题.采用状态转换技术和反推方法,设计了不依赖于时滞的反馈控制器.同时为了处理初值为零的情况,提出了一种新颖的基于第一个子系统输出值的切换控制策略,最后通过仿真算例说明了控制器的有效性.     

Hybrid output regulation for linear impulsive systems with aperiodic jumps: A discrete-time feedback controller design approach

This paper is concerned with the problem of hybrid output regulation for a class of linear impulsive systems with aperiodic jumps. Firstly, by leveraging time-dependent Lyapunov function technique and impulsive control theory, sufficient conditions for achieving output regulation are obtained in state feedback case. Then, the results are extended to error feedback case by constructing an impulsive observer. In this framework, two novel hybrid controllers are designed. Such controllers only need the discrete-time system state or error signal for feedback. The complete procedures for controller designs are also presented. Finally, two illustrative examples, including a numerical example and an LC circuit, are given to show the validity and applicability of the proposed control laws.     

基于观测器的非严格反馈时滞非线性系统的神经网络自适应控制

针对一类非严格反馈的时滞非线性系统,研究了一类基于观测器的自适应神经网络控制问题.针对系统中存在未知状态变量的问题,设计了一个状态观测器.利用反步法和径向基神经网络的逼近特性,提出了一种自适应神经网络输出反馈控制方法.所设计的控制器保证了闭环系统中所有信号的半全局一致有界性.最后,通过仿真验证了所提控制方法的有效性.     

模糊输入时滞系统的输出反馈控制及稳定性分析

针对一类状态不可测的模糊输入时滞系统,应用平行分布补偿算法(PDC),设计了模糊观测器,提出了基于模糊观测器的输出反馈控制方法,给出了保证模糊时滞系统渐近稳定的新的充分条件.应用广义Lyapunov函数和线性矩阵不等式方法,证明了模糊输入时滞系统的渐近稳定性,同时给出了控制和观测增益矩阵的分离设计算法.仿真结果进一步验证了所提出的方法和条件的有效性.     

An entire strategy for precise system tracking control of a revolving thin flexural link,part I: Finite element modeling and direct tuning controller design

An entire control strategy including a design based model, controller design, and system output modification for a distributed parameter system is illuminated by application to feedback control of a revolving thin flexural link. In Part I, a very realizable actuator and a sensor, which uses a motor and a tachometer, are applied to design the control system. The finite element modeling and the state space representation are obtained for the purpose of control system analysis and computer simulation. Instead of relying on parameter identification subroutines, a controller design based on directly tuning the parameter of the gain makes the closed-loop absolutely stable and good for system tracking control. This control system design scheme is robust, insensitive to system parameter changes, and this algorithm cannot depend on traditionally priori knowledge such as the system dimension, exact model, or observer design. The performance included in the presence of all the high frequency dynamics can be effectively shown through the computer simulation, and one is led to speculate that this design scheme may perform quite well in the real world implementation.     

一类不确定性非线性系统的状态反馈鲁棒自适应控制器的设计与分析

该文考虑一类具有一般不确定性和部分参数未知的非线性系统（1），设计出一种用于跟踪参考信号的状态反馈鲁棒自适应控制器，此控制器对系统参数和状态的不确定性具有鲁棒性，能保证闭环系 统的全局稳定性，并解决了ε 跟踪问题. 仿真结果表明，所设计的鲁棒自适应控制系统具有良好的跟踪性能， 而且控制量在容许控制的范围之内.     

Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems

In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua’s chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system.     

离散交通流模型的反馈线性化与拥堵控制

在自动化高速公路环境下,提出一种改进的宏观离散交通流模型密度控制方法.利用反馈线性化方法,将宏观离散交通流模型转换为一般容易处理的线性系统模型,简化了密度控制器的设计.利用线性系统中具有输入变换的跟踪反馈控制方法,对线性化后的系统模型设计控制律.通过控制该线性系统的状态变量,间接稳定离散交通流模型中的交通流密度,达到对道路交通流拥堵的控制.同时给出设计方法和步骤,仿真实例说明了方法的实用性.     

Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators

This paper deals with the problem of control and synchronization of coupled second-order oscillators showing a chaotic behavior. A classical feedback controller is first used to stabilize the system at its equilibrium. An adaptive observer is then designed to synchronize the states of the master and slave oscillators using a single scalar signal corresponding to an observable state variable of the driving oscillator. An interesting feature of the proposed approach is that it can be used for chaos control as well as synchronization purposes. Numerical simulations results confirming the analytical predictions are shown and pspice simulations are also performed to confirm the efficiency of the proposed control scheme.