Terminal sliding mode control without singular for a class of uncertain system

An improved nonsingular terminal sliding mode method is proposed for a class of nonlinear systems with unmodeled dynamics. The proposed method can effectively avoid the singularity problem. The stability of the proposed procedure which could guarantee the robustness against uncertain unmodeled dynamic and external disturbances is proven by using the Lyapunov theory in finite time. An example is given to show the proposed improved terminal sliding mode control law without singular effectively. © 2016 Wiley Periodicals, Inc. Complexity 21: 566–572, 2016     

Finite-time chaos control via nonsingular terminal sliding mode control

This paper considers the nonsingular terminal sliding mode control for chaotic systems with uncertain parameters or disturbances. The switching surface is designed technically to realize fast convergence. The controller derived from such switching surface is nonsingular and it can stabilize the chaotic systems in a finite time. Besides the second-order system and the triangular system, the proposed method can also be applied to a general class of uncertain nonlinear system. Finally, simulation results are presented to illustrate the effectiveness of the design.     

不确定电液位置伺服系统的自适应终端滑模控制

为了解决非线性、不确定电液伺服系统的位置跟踪控制问题,提出了一种基于反步法的自适应终端滑模控制方法.该方法将自适应控制和终端滑模方法结合在一起,一方面,提出的自适应控制律可以对电液伺服系统中的不确定性参数进行有效在线估计和补偿;另一方面,通过引入误差吸引子到滑模趋近律中得到变系数趋近律,设计的终端滑模控制律不仅能够消除普通终端滑模控制律中的非奇异项,还大大降低了滑模面的抖震.最终,根据Lyapunov稳定性理论,位置跟踪误差的有限时间稳定性得以严格证明.将该方法与积分反步滑模控制和线性滑模控制方法进行了对比研究,仿真结果验证了该方法在电液伺服系统位置跟踪控制方面良好的鲁棒性和跟踪精度.     

Finite-time disturbance observer-based trajectory tracking control for quadrotor unmanned aerial vehicle with obstacle avoidance

This paper investigates the problem of trajectory tracking control for quadrotor unmanned aerial vehicle (UAV) in the presence of dynamic obstacles and external disturbance forces/torques. More specifically, two new sliding mode disturbance observers are firstly designed to estimate the external disturbances, in which the observation errors can converge to zero in finite time. Furthermore, utilizing the observation information, a new sliding mode surface-like variable-based position tracking control scheme and a novel nonsingular terminal sliding mode-based attitude synchronization control scheme are developed to drive the UAV tracking the reference trajectory with obstacle avoiding. Moreover, the tracking errors of the close-loop control system can converge to zero within finite time by the analyses of Lyapunov methodology. Finally, the numerical simulation results are presented to illustrate the effectiveness of the proposed control schemes.     

Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation

This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.     

Fractional terminal sliding mode control design for a class of dynamical systems with uncertainty

A novel type of control strategy combining the fractional calculus with terminal sliding mode control called fractional terminal sliding mode control is introduced for a class of dynamical systems subject to uncertainties. A fractional-order switching manifold is proposed and the corresponding control law is formulated based on the Lyapunov stability theory to guarantee the sliding condition. The proposed fractional-order terminal sliding mode controller ensures the finite time stability of the closed-loop system. Finally, numerical simulation results are presented and compared to illustrate the effectiveness of the proposed method.     

Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique

In this paper, the problem of finite-time chaos synchronization between two different chaotic systems with fully unknown parameters is investigated. First, a new nonsingular terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is proved. Then, appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Afterwards, based on the adaptive laws and finite-time control idea, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, some numerical simulations are presented to demonstrate the applicability and effectiveness of the proposed technique.     

Novel dynamics of a predator–prey system with harvesting of the predator guided by its population

A predator–prey model was extended to include nonlinear harvesting of the predator guided by its population, such that harvesting is only implemented if the predator population exceeds an economic threshold. The proposed model is a nonsmooth dynamic system with switches between the original predator-prey model (free subsystem) and a model with nonlinear harvesting (harvesting subsystem). We initially examine the dynamics of both the free and the harvesting subsystems, and then we investigate the dynamics of the switching system using theories of nonsmooth systems. Theoretical results showed that the harvesting subsystem undergoes multiple bifurcations, including saddle-node, supercritical Hopf, Bogdanov–Takens and homoclinic bifurcations. The switching system not only retains all of the complex dynamics of the harvesting system but also exhibits much richer dynamics such as a sliding equilibrium, sliding cycle, boundary node (saddle point) bifurcation, boundary saddle-node bifurcation and buckling bifurcation. Both theoretical and numerical results showed that, by implementing predator population guided harvesting, the predator and prey population could coexist in more scenarios than those in which the predator may go extinct for the continuous harvesting regime. They could either stabilize at an equilibrium or oscillate periodically depending on the value of the economic threshold and the initial value of the system.     

Simplex sliding mode control for nonlinear uncertain systems via chaos optimization

As an emerging effective approach to nonlinear robust control, simplex sliding mode control demonstrates some attractive features not possessed by the conventional sliding mode control method, from both theoretical and practical points of view. However, no systematic approach is currently available for computing the simplex control vectors in nonlinear sliding mode control. In this paper, chaos-based optimization is exploited so as to develop a systematic approach to seeking the simplex control vectors; particularly, the flexibility of simplex control is enhanced by making the simplex control vectors dependent on the Euclidean norm of the sliding vector rather than being constant, which result in both reduction of the chattering and speedup of the convergence. Computer simulation on a nonlinear uncertain system is given to illustrate the effectiveness of the proposed control method.     

Fast terminal sliding mode controller design for nonlinear second‐order systems with time‐varying uncertainties

This article investigates a novel fast terminal sliding mode control approach combined with global sliding surface structure for the robust tracking control of nonlinear second‐order systems with time‐varying uncertainties. The suggested control technique is formulated based on the Lyapunov stability theory and guarantees the existence of the sliding mode around the sliding surface in a finite time. Using the new form of switching surface, the reaching phase elimination and the robustness improvement of the whole system are satisfied. Simulation results demonstrate the efficiency of the proposed technique. © 2014 Wiley Periodicals, Inc. Complexity 21: 239–244, 2015     

线性滞后广义系统的二阶滑模控制方法

讨论了时滞广义系统在不同条件下的变结构控制,根据终端滑模控制的特点,提出了一种由线性滑模与终端滑模构成的二阶终端滑模及相应控制策略.研究结果表明,该方法能够有效地清除系统的高频抖振,同时保证闭环系统的渐近稳定,实现滑模运动.举例说明了设计的合理性和有效性.     

An efficient parallel processing optimal control scheme for a class of nonlinear composite systems

This article presents an efficient parallel processing approach for solving the optimal control problem of nonlinear composite systems. In this approach, the original high-order coupled nonlinear two-point boundary value problem (TPBVP) derived from the Pontryagin's maximum principle is first transformed into a sequence of lower-order decoupled linear time-invariant TPBVPs. Then, an optimal control law which consists of both feedback and forward terms is achieved by using the modal series method for the derived sequence. The feedback term specified by local states of each subsystem is determined by solving a matrix Riccati differential equation. The forward term for each subsystem derived from its local information is an infinite sum of adjoint vectors. The convergence analysis and parallel processing capability of the proposed approach are also provided. To achieve an accurate feedforward-feedback suboptimal control, we apply a fast iterative algorithm with low computational effort. Finally, some comparative results are included to illustrate the effectiveness of the proposed approach.     

Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems

In this paper, a novel direct adaptive interval type-2 fuzzy-neural tracking control equipped with sliding mode and Lyapunov synthesis approach is proposed to handle the training data corrupted by noise or rule uncertainties for nonlinear SISO nonlinear systems involving external disturbances. By employing adaptive fuzzy-neural control theory, the update laws will be derived for approximating the uncertain nonlinear dynamical system. In the meantime, the sliding mode control method and the Lyapunov stability criterion are incorporated into the adaptive fuzzy-neural control scheme such that the derived controller is robust with respect to unmodeled dynamics, external disturbance and approximation errors. In comparison with conventional methods, the advocated approach not only guarantees closed-loop stability but also the output tracking error of the overall system will converge to zero asymptotically without prior knowledge on the upper bound of the lumped uncertainty. Furthermore, chattering effect of the control input will be substantially reduced by the proposed technique. To illustrate the performance of the proposed method, finally simulation example will be given.     

Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems

This study is concerned with the design of a disturbance-observer-based fuzzy terminal sliding mode controller (FTSMC) for multi-input multi-output (MIMO) uncertain nonlinear systems by considering unknown non-symmetric input saturation and control singularity. The disturbance observer is proposed for the unmeasured external disturbance and guarantees the convergence of the disturbance estimation error to zero in a finite time. The terminal sliding mode controller (TSMC) is designed for MIMO uncertain nonlinear systems by utilizing the output of the proposed disturbance observer. This control scheme combines the disturbance-observer-based TSMC with a fuzzy logic system in the presence of unknown non-symmetric input saturation and control singularity in order to reduce chattering phenomena. Finite time asymptotic stability, convergence of the disturbance observer, and convergence of the closed-loop system are proved via Lyapunov stability theorem. In addition, a five-rotor unmanned aerial vehicle (UAV) is employed in the numerical simulations to demonstrate the effectiveness and performance of the proposed control scheme. Disturbance observer estimates the payload and flight endurance of the five-rotor UAV. Genetic algorithm (GA) optimization is used to specify the parameters of the disturbance-observer-based TSMC (GATSMC) to decrease chattering. Finally, the superior performance of FTSMC is investigated over TSMC and GATSMC.     

Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros

Under the existence of system uncertainties, external disturbances, and input nonlinearity, complete synchronization and anti-synchronization between two chaotic gyros are achieved by introducing a novel adaptive terminal sliding mode (ATSM) controller. In the literature, by taking account of input nonlinearity, the magnitudes of bounded nonlinear dynamics of synchronous error system were required in the designed sliding mode controller. In this study, the proposed ATSM controller associated with time-varying feedback gains can tackle nonlinear dynamics according to the novel adaptive rules. These feedback gains are not necessary to be determined in advance but updated by the adaptive rules without known the magnitudes of bounded nonlinear dynamics, system uncertainties, and external disturbances. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem, and the numerical simulations are performed to verify the effectiveness of presented schemes.     

基于谱变换的奇异二阶系统解耦研究

针对奇异二阶系统的解耦问题,提出了一种基于谱变换的解耦方法.首先分析了质量矩阵非奇异的解耦条件,提出一种非奇异二阶同谱对角系统的构造解耦方法,然后引入谱变换将首系数转换为非奇异的,利用非奇异的构造方法来构造同谱对角系统,最后对解耦系统进行还原,从而实现奇异二阶系统的解耦.数值试验证明该方法确实有效.     

Suboptimal Integral Sliding Mode Controller Design for a Class of Affine Systems

This paper proposes an nth-order suboptimal integral sliding mode controller for a class of nonlinear affine systems. First, a general form of integral sliding mode is given. An extended Theta-D method is developed for the optimal control problems characterized by a quadratic cost function with a cross term. Then the extended Theta-D method is employed to determine a suboptimal integral sliding mode. Rigorous proof shows that the controller guarantees semi-global asymptotical stability of affine systems. To verify the accuracy of the extended Theta-D method, a numerical example is provided. To verify the effectiveness of the proposed suboptimal integral sliding mode controller, a numerical example and an application example of an overhead crane system are provided.     

非线性转子系统稳定性量化分析方法

转子轴承系统是一类多自由度非线性动力系统,广泛应用于工程实际．设计观念和维修体制的变革提出了稳定性量化分析的要求．本文利用轨线保稳降维方法提出了转子系统稳定性的量化分析方法．首先,对高维非线性非自治转子系统进行数值积分,将n维空间的轨线映射为一系列一维的映象轨线,并将各自由度的运动方程中除该自由度外的所有状态变量用积分结果代换,得到n个互相解耦,含有多个时变参数的单自由度方程．然后,在一维观察空间的外力位移扩展相平面上定义了动态中心点,研究转子系统中常见的几种运动的动态中心点动能差序列的特点,给出了上述典型运动形式的轨线稳定裕度的定量评估指标,应用灵敏度分析技术快速有效地预测周期运动的倍周期分岔点和Hopf分岔点．以一个具有非线性支承的滑动轴承柔性转子模型为例,证明了该方法的有效性．     

Unidirectional synchronization for Hindmarsh–Rose neurons via robust adaptive sliding mode control

This paper presents an adaptive neural network (NN) based sliding mode control for unidirectional synchronization of Hindmarsh–Rose (HR) neurons in a master–slave configuration. We first give the dynamics of single HR neuron which may exhibit spike-burst chaotic behaviors. Then we formulate the problem of unidirectional synchronization control of two HR neurons and propose a NN based sliding mode controller. The controller consists of two simple radial basis function (RBF) NNs which are used to approximate the desired sliding mode controller and the uncertain nonlinear part of the error dynamical system, respectively. The control scheme is robust to the uncertainties such as approximate errors, ionic channel noise and external disturbances. The simulation results demonstrate the validity of the proposed control method.     

Nonlinear modelling and control of a common rail injection system for diesel engines

Modern trends in designing mechatronic systems call for a synergic design of the separated subsystems (mechanic, electronic parts, control modules, etc.) concurring to the overall performance. Following this point of view, this paper presents a control oriented model and a nonlinear control design for a Common Rail injection system. First a model is developed, which is tuned in a virtual simulation environment, representing the injection system in details in a reliable replication of reality. Then a sliding mode control is developed. Both the model of the injection process and of the control law are validated by a virtual detailed simulation environment. The prediction capability of the model and the control efficiency are clearly shown.