Stabilizing the unstable periodic orbits of a chaotic system using model independent adaptive time-delayed controller

In this paper we deal with the control of chaotic systems. Knowing that a chaotic attractor contains a myriad of unstable periodic orbits (UPO’s), the aim of our work is to stabilize some of the UPO’s embedded in the chaotic attractor and which have interesting characteristics. First, using the input-to-state linearization method in conjunction with a time-delayed state feedback, we design a control signal that can achieve stabilization. Next, an adaptive time-delayed state feedback is proposed which shows at once efficiency and simplicity and circumvents the construction complexity of the first controller. Finally, we propose a reduced order sliding mode observer to estimate the necessary states for the design of an adaptive time delayed state feedback controller. This last controller has one main advantage, it in fact achieves UPO stabilization without using the system model. The efficacy of the proposed methods is illustrated by numerical simulations onto Chua’s system.     

Event-triggered robust adaptive control for uncertain nonlinear systems preceded by actuator dead-zone

It is both theoretically and practically important to investigate the problem of event-triggered adaptive tracking control for a class of uncertain nonlinear systems subject to actuator dead-zone, which aims at reducing communication rate and compensating actuator nonlinearity simultaneously. In this paper, to handle such a problem, an event-trigger based adaptive compensation scheme is proposed for the system preceded by actuator dead-zone. The challenges of this work can be roughly classified into two categories: how to compensate the nonsmooth dead-zone nonlinearity and how to eliminate the quantization signal effects caused by event-triggered strategy. To resolve the first challenge, a new decomposition of dead-zone mathematical model is employed so that dead-zone nonlinearity can be successively compensated by using robust approach. In addition, an adaptive controller and its triggering event are co-designed based on the relative threshold strategy, such that an asymptotic tracking performance can be ensured. The proposed scheme is proved to guarantee the globally bounded of all closed-loop signals and the asymptotic convergence performance of tracking error toward zero. The simulation results illustrate the effectiveness of our proposed control scheme.     

Directly adaptive fuzzy control of discrete-time chaotic systems by least squares algorithm with dead-zone

A new design scheme of directly adaptive fuzzy control for a class of discrete-time chaotic systems is proposed in this paper. The T-S fuzzy model is employed to represent the discrete-time chaotic systems. Then a fuzzy controller is designed and the unknown coefficients of the controller are identified by least squares algorithm with dead-zone. By Lyapunov method, all the signals involved in the closed-loop systems are shown to be bounded and the error between the system output and the reference output is proved to converge to a small neighborhood of zero. Simulation results demonstrate the effectiveness of the theoretical results.     

Adaptive interval type-2 fuzzy sliding mode control for unknown chaotic system

In this paper, a novel adaptive interval type-2 fuzzy sliding mode control (AIT2FSMC) methodology is proposed based on the integration of sliding mode control and adaptive interval type-2 fuzzy control for chaotic system. The AIT2FSMC system is comprised of a fuzzy control design and a hitting control design. In the fuzzy control design, an interval type-2 fuzzy controller is designed to mimic a feedback linearization (FL) control law. In the hitting control design, a hitting controller is designed to compensate the approximation error between the FL control law and the interval type-2 fuzzy controller. The parameters of the interval type-2 fuzzy controller, as well as the uncertainty bound of the approximation error, are tuned adaptively. The adaptive laws are derived in the sense of Lyapunov stability theorem, thus the stability of the system can be guaranteed. The proposed control system compared to adaptive fuzzy sliding mode control (AFSMC). Simulation results show that the proposed control systems can achieve favorable performance and robust with respect to system uncertainties and external disturbances.     

Adaptive fuzzy output feedback control of uncertain nonlinear systems with nonsymmetric dead-zone input

In this paper, we present an adaptive control scheme for a class of uncertain nonlinear system with unknown nonsymmetric dead-zone nonlinearity. It is assumed that the system states are unmeasurable. Therefore, an observer is designed to estimate those unmeasured states. The controller is designed by using the backstepping control design procedure. The proposed adaptive scheme requires only the information that the dead-zone slopes are bounded. The new control scheme ensures bounded-error trajectory tracking and the boundedness of all the signals in the closed-loop. The feasibility is investigated by an illustrative simulation example.     

Adaptive feedback control and synchronization of non-identical chaotic fractional order systems

This paper addresses the reliable synchronization problem between two non-identical chaotic fractional order systems. In this work, we present an adaptive feedback control scheme for the synchronization of two coupled chaotic fractional order systems with different fractional orders. Based on the stability results of linear fractional order systems and Laplace transform theory, using the master-slave synchronization scheme, sufficient conditions for chaos synchronization are derived. The designed controller ensures that fractional order chaotic oscillators that have non-identical fractional orders can be synchronized with suitable feedback controller applied to the response system. Numerical simulations are performed to assess the performance of the proposed adaptive controller in synchronizing chaotic systems.     

Property and evolution of the running-in attractor in an actual dynamic system

In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

     

Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control

In this paper, we apply the nonsingular terminal sliding mode control technique to realize the novel combination-combination synchronization between combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability theory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems. In theory, it is proved that the sliding mode technique can realize fast convergence for four different chaotic systems in the finite time. Some criteria and corollaries are derived for finite-time combination-combination synchronization of four different chaotic systems. Numerical simulation results are shown to verify the effectiveness and correctness of the combination-combination synchronization.     

Robust synchronization of two different fractional-order chaotic systems with unknown parameters using adaptive sliding mode approach

In this paper, an adaptive sliding mode control method is introduced to ensure robust synchronization of two different fractional-order chaotic systems with fully unknown parameters and external disturbances. For this purpose, a fractional integral sliding surface is defined and an adaptive sliding mode controller is designed. In this method, no knowledge of the bounds of parameters and perturbation is required in advance and the parameters are updated through an adaptive control process. The proposed scheme is global and theoretically rigorous. Two examples are given to illustrate effectiveness of the scheme, in which the synchronizations between fractional-order chaotic Chen system and fractional-order chaotic Rössler system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.

     

存在关节死区的空间机器人无扰快速终端滑模控制

针对机械臂一般操作过程中运动学的非完整特性进行运动规划时没有考虑机械臂与待抓取目标之间的关系与关节的实际特性, 研究了存在关节死区的漂浮基平面三连杆空间机械臂拦截目标前最后阶段的载体无扰动空间规划与控制. 首先根据拉格朗日第二类方程, 建立存在关节死区的载体位姿均不受控的漂浮基平面三连杆空间机械臂的动力学模型, 推导出三连杆空间机械臂反作用零空间的数学模型, 并对反作用零空间进行向量范数约束算法研究; 进而提出了一种具有抗干扰性与高收敛性的非奇异快速终端滑模控制算法实现系统的姿态无扰控制, 该方法采用变系数双幂次趋近率与非奇异快速终端滑模面相结合的方式, 提高系统状态收敛速度与抗干扰性. 为了消除机械臂关节存在的死区特性, 设计了自适应死区补偿器, 通过自适应控制来逼近死区特性的上界, 以消除关节死区对系统带来的影响, 确保跟踪控制的有效执行. 最后基于Lyapunov函数法证明了系统的稳定性, 并通过系统数值仿真结果验证了存在死区情况下机械臂的各关节角跟踪上无反应空间下的期望轨迹的同时载体的姿态处于稳定状态, 验证了所提方法的有效性.      

Adaptive control of a chaotic permanent magnet synchronous motor

This paper proposes a simple adaptive controller design method for a chaotic permanent magnet synchronous motor (PMSM) based on the sliding mode control theory which has given an effective means to design robust controllers for nonlinear systems with bounded uncertainties. The proposed sliding mode adaptive controller does not require any information on the PMSM parameter and load torque values, thus it is insensitive to model parameter and load torque variations. Simulation results are given to verify that the proposed method can be successfully used to control a chaotic PMSM under model parameter and load torque variations.     

Robust adaptive intelligent sliding model control for a class of uncertain chaotic systems with unknown time-delay

In this paper, a robust adaptive intelligent sliding model control (RAISMC) scheme for a class of uncertain chaotic systems with unknown time-delay is proposed. A sliding surface dynamic is appropriately constructed to guarantee the reachability of the specified sliding surface. Within this scheme, neuro-fuzzy network (NFN) is utilized to approximate the unknown continuous function. The robust controller is an adaptive controller used to dispel the unknown uncertainty and approximation errors. The adaptive parameters of the control system are tuned on-line by the derived adaptive laws based on a Lyapunov stability analysis. Using appropriate Lyapunov–Krasovskii (L–K) functional in the Lyapunov function candidate, the uncertainty caused by unknown time delay is compensated and the global asymptotic stability of the error dynamics system in the specified switching surface is accomplished. Finally, the proposed RAISMC system is applied to control a Hopfield neural network, Cellular neural networks, Rössler system, and to achieve synchronization between the Chen system with two time delays with Rössler system without time delay. The results are representative of outperformance of the proposed method in all cases.     

A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems

In this paper, a projective synchronization problem of master–slave chaotic systems is investigated. More specifically, a fuzzy adaptive controller is investigated for a projective synchronization of uncertain multivariable chaotic systems. The adaptive fuzzy-logic systems are used to approximate the unknown functions. A decomposition property of the control gain matrix is used in the controller design and the stability analysis. A Lyapunov approach is employed to derive the parameter adaptation laws and prove the boundedness of all signals of the closed-loop system as well as the exponential convergence of the synchronization errors to an adjustable region. Numerical simulations are performed to verify the effectiveness of the proposed synchronization scheme.     

Combination–combination synchronization among four identical or different chaotic systems

Based on one drive system and one response system synchronization model, a new type of combination–combination synchronization is proposed for four identical or different chaotic systems. According to the Lyapunov stability theorem and adaptive control, numerical simulations for four identical or different chaotic systems with different initial conditions are discussed to show the effectiveness of the proposed method. Synchronization about combination of two drive systems and combination of two response systems is the main contribution of this paper, which can be extended to three or more chaotic systems. A universal combination of drive systems and response systems model and a universal adaptive controller may be designed to our intelligent application by our synchronization design.     

Nonlinear system control using a self-organizing functional-linked neuro-fuzzy network

This study presents a self-organizing functional-linked neuro-fuzzy network (SFNN) for a nonlinear system controller design. An online learning algorithm, which consists of structure learning and parameter learning of a SFNN, is presented. The structure learning is designed to determine the number of fuzzy rules and the parameter learning is designed to adjust the parameters of membership function and corresponding weights. Thus, an adaptive self-organizing functional-linked neuro-fuzzy control (ASFNC) system, which is composed of a computation controller and a robust compensator, is proposed. In the computation controller, a SFNN observer is utilized to approximate the system dynamic and the robust compensator is designed to eliminate the effect of the approximation error introduced by the SFNN observer upon the system stability. Finally, to show the effectiveness of the proposed ASFNC system, it is applied to a chaotic system. The simulation results demonstrate that favorable control performance can be achieved by the proposed ASFNC scheme without any knowledge of the control plants and without requiring preliminary offline tuning of the SFNN observer.     

Adaptive control for electromechanical systems considering dead-zone phenomenon

The electromechanical gyrostat is a fourth-order nonautonomous system that exhibits very rich behavior such as chaos. In recent years, synchronization of nonautonomous chaotic systems has found many useful applications in nonlinear science and engineering fields. On the other hand, it is well known that the finite-time control techniques demonstrate good robustness and disturbance rejection properties. This paper studies the potential application of the finite-time control techniques for synchronization of nonautonomous chaotic electromechanical gyrostat systems in finite time. It is assumed that all the parameters of both drive and response systems are unknown parameters in advance. Moreover, the effects of dead-zone nonlinearities in the control inputs are also taken into account. Some adaptive controllers are introduced to synchronize two gyrostat systems in different scenarios within a given finite-time. Two illustrative examples are presented to demonstrate the efficiency and robustness of the proposed finite-time synchronization strategy.     

Adaptive sliding mode control of a chaotic nonsmooth-air-gap permanent magnet synchronous motor with uncertainties

Using the sliding mode control approach, a simple adaptive controller design method is proposed for a chaotic nonsmooth-air-gap permanent magnet synchronous motor (PMSM). The proposed method does not require the restrictive assumption that accurate information on the PMSM parameter and load torque values is available, thus it has robustness to model uncertainties. This paper analyzes the stability and convergence of the closed-loop control system, and this paper gives a discretized control algorithm for DSP implementation. Finally, this paper presents some simulation results to illuminate that the proposed method can effectively handle the controller design problem for a chaotic nonsmooth-air-gap PMSM under inaccurate information on the PMSM parameter and load torque values.     

Observer-based model reference adaptive control for unknown time-delay chaotic systems with input nonlinearity

Existence of unknown time-delay in the systems is a drastic restriction that it can menace the stability criteria and even deteriorate the performance system. This undesired case would be more intensified if that the uncertain input nonlinearity effects are also considered. To handle the input nonlinearities effects (results in dead-zone and/or hysteresis phenomena) and also unknown time-delay in the chaotic systems, this paper presents an observer-based Model Reference Adaptive Control (MRAC) scheme for a class of unknown time-delay chaotic systems with disturbances. This new method is a delay-independent variable-structure control method which is integrated with an observer system. The main task of the proposed approach is to accomplish a perfect tracking procedure such that unknown parameters are adapted via output estimation error. Furthermore, stability of the closed-loop system is achieved by means of the Lyapunov stability theory. Finally, the proposed methods are applied to some famous chaotic systems to verify the effectiveness of the proposed methods.     

Direct adaptive neural control of chaos in the permanent magnet synchronous motor

In this paper, a direct adaptive neural speed tracking control is addressed for the chaotic permanent magnet synchronous motor (PMSM) drive systems via backstepping. Neural networks are directly used to approximate unknown and desired control signals and a novel direct adaptive tracking controller is constructed via backstepping. The proposed adaptive neural controllers guarantee that the tracking error converges to a small neighborhood of the origin. Compared with the conventional backstepping method, the designed neural controller??s structure is very simple. Simulation results show that the proposed control scheme can suppress the chaos of PMSM and guarantees the perfect tracking performance even with the existence of unknown parameters.     

Synchronization of two different chaotic systems using novel adaptive interval type-2 fuzzy sliding mode control

In this paper, we use sliding mode control integrated with an interval type-2 fuzzy system for synchronization of two different chaotic systems in presence of system unmodeling and external disturbances. To reduce the chattering and improve the robustness of reaching phase of the Sliding Mode Control (SMC), an interval fuzzy type-2 logic controller is used. In addition, an adaptive interval type-2 fuzzy inference approximator is proposed (as equivalent control part of SMC) to approximate the unknown parts of the uncertain chaotic system. Using type-2 fuzzy systems makes more effective synchronization results in presence of system uncertainty and disturbances in comparison with type-1 fuzzy approximators. The stability analysis for the proposed control scheme is provided, and simulation results compare the performance of interval type-2 fuzzy and type-1 fuzzy controllers to verify the effectiveness of the proposed method.