基于神经网络的机器人二阶滑模控制

本文提出了一种基于神经网络与二阶滑模控制融合的控制策略用于非线性机器人控制,设计了一种新颖简易的二阶滑模控制方法,有效地避免了常规变结构控制的抖震问题,并采用神经网络辨识未知的机器人的非线性模型,通过Lyapunov直接法设计网络的权值更新率,确保了系统闭环全局渐近稳定性。最后,通过仿真验证了算法的有效性。     

受约束空间机器人降阶自适应神经网络滑模控制

为了实现受约束空间机器人的高精度控制,提出了一种基于U-K(Udwadia-Kalaba)方程的降阶自适应神经网络滑模控制算法;基于U-K方程,同时考虑受约束空间机器人各个关节的理想约束力与非理想约束力,推导得到详细的动力学方程;考虑到非理想约束力具有不确定性且单独采用滑模控制会出现抖振现象,提出了自适应神经网络滑模控制算法,实现各关节角度、角速度以及非理想约束力的高精度跟踪;针对系统受约束模型,对动力学方程和滑模控制器进行了降阶求解,减少了变量并简化了计算过程;为了验证所提算法的正确性与合理性,以2自由度受约束空间机器人为例进行了仿真验证;仿真结果表明：受约束空间机器人的各关节角度、角速度以及非理想约束力的跟踪误差均低于10^-4量级。     

Finite‐Time Consensus Tracking for Second‐Order Multiagent Systems

In this paper, the finite‐time consensus tracking problem is investigated for second‐order multi‐agent systems. A novel distributed consensus algorithm based on the sliding mode control (SMC) is designed, and the tracking time is estimated analytically.     

基于分数阶滤波器的高泛化性神经网络建模

为了显著提高神经网络建模的泛化性,提出了激活函数是分数阶滤波器的神经网络.分数阶滤波器涵盖了Butterworth和Chebyshev滤波器的性能.滤波器集对样本信号进行频率分解,既提升了信息的致密性,也保证了遍历性,更有助于提高神经网络的泛化性.各滤波器参数由盲动粒子群优化算法寻优.神经网络解算时,既采用了线性回归求解神经网络输出层权重,又在有限频段上用线性传递函数模拟替代分数阶传递函数,这两种措施缩短了解算时间.仿真结果表明,线性系统的泛化性精度可达亿分之几,非线性系统可达万分之几,可以离线应用.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control (AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance. To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control (ILC), a new boundary layer function is proposed by employing Mittag-Leffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function (CEF) containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

Robust Adaptive Fractional‐Order Terminal Sliding Mode Control for Lower‐Limb Exoskeleton

This paper introduces a robust adaptive fractional‐order non‐singular fast terminal sliding mode control (RFO‐TSM) for a lower‐limb exoskeleton system subject to unknown external disturbances and uncertainties. The referred RFO‐TSM is developed in consideration of the advantages of fractional‐order and non‐singular fast terminal sliding mode control (FONTSM): fractional‐order is used to obtain good tracking performance, while the non‐singular fast TSM is employed to achieve fast finite‐time convergence, non‐singularity and reducing chattering phenomenon in control input. In particular, an adaptive scheme is formulated with FONTSM to deal with uncertain dynamics of exoskeleton under unknown external disturbances, which makes the system robust. Moreover, an asymptotical stability analysis of the closed‐loop system is validated by Lyapunov proposition, which guarantees the sliding condition. Lastly, the efficacy of the proposed method is verified through numerical simulations in comparison with advanced and classical methods.     

集成神经网络与自适应算法的分数阶滑模控制

针对被控对象的参数时变和外部扰动问题,本文融合神经网络的万能逼近能力和自适应控制技术,并结合分数阶微积分理论,提出了基于神经网络和自适应控制算法的分数阶滑模控制策略.本文采用等效控制的方法设计滑模控制律,并利用神经网络的万能逼近能力估测控制律的变化,结合自适应控制算法和分数阶微积分理论抑制传统滑模控制系统的抖震,同时根据Lyapunov稳定性理论分析了系统的稳定性,最后给出了实验结果.实验结果表明,本文提出的基于神经网络和自适应控制算法的分数阶滑模控制系统,能保持滑模控制器对系统外部扰动和参数变化鲁棒性的同时,也能有效地抑制抖震,使得系统获得较高的控制性能.     

Reduced‐order design of high‐order sliding mode control system

To design an rth (r>2) order sliding mode control system, a sliding variable and its derivatives of up to (r ? 1) are in general required for the control implementation. This paper proposes a reduced‐order design algorithm using only the sliding variable and its derivatives of up to (r ? 2) as the extension of the second‐order asymptotic sliding mode control. For a linear time‐invariant continuous‐time system with disturbances, it is found that a high‐order sliding mode can be reached locally and asymptotically by a reduced‐order sliding mode control law if the sum of the system poles is less than the sum of the system zeros. The robust stability of the reduced‐order high‐order sliding mode control system, including the convergence to the high‐order sliding mode and the convergence to the origin is proved by two Lyapunov functions. Simulation results show the effectiveness of the proposed control algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

基于积分滑动流形的高阶滑模控制器设计

滑模变结构控制方法因其易实现,鲁棒性强等优点广泛应用于实际控制系统中,讨论了具有积分滑动流形的高阶滑模控制器的设计方法.通过设计含积分滑动流形的高阶滑模面,使系统状态在一阶乃至高阶滑模面上均能达到滑动模态.同时利用高阶滑模面为状态变量设计新的状态空间系统,将原先促使系统状态接近并停留在滑模面上的控制目标,拓展为使高阶滑模状态变量趋近于零的控制目标,并结合最优控制方法来设计等效控制量,利用积分流形设计切换控制的切换面,通过严格证明来证实控制器设计的稳定性.在仿真验证部分采用了一阶倒立摆模型,通过比较常规趋近律滑模控制方法和本文方法的仿真结果,可以得出本文方法在减小系统控制量抖振方面的重要作用和优异效果.     

Robust nonovershooting tracking control for fractional‐order systems

A robust tracking control is proposed for the fractional‐order systems (FOSs) to achieve a tracking response with no overshoot, even in the presence of a class of disturbances. The control proposed makes use of a newly designed integral sliding mode technique for FOSs, which is capable of rejecting the bounded disturbances acting through the input channel. The proposed integral sliding mode control design has two components: a nominal control component and a discontinuous control component. The overshoot in the system response is avoided by the nominal control designed with the use of Moore's eigenstructure assignment algorithm. The sliding mode technique is used for the design of discontinuous part of the control that imparts the desired robustness properties.     

Real-time torque control using discrete-time recurrent high-order neural networks

This paper presents a discrete-time direct current (DC) motor torque tracking controller, based on a recurrent high-order neural network to identify the plant model. In order to train the neural identifier, the extended Kalman filter (EKF) based training algorithm is used. The neural identifier is in series-parallel configuration that constitutes a well approximation method of the real plant by the neural identifier. Using the neural identifier structure that is in the nonlinear controllable form, the block control (BC) combined with sliding modes (SM) control techniques in discrete-time are applied. The BC technique is used to design a nonlinear sliding manifold such that the resulting sliding mode dynamics are described by a desired linear system. For the SM control technique, the equivalent control law is used in order to the plant output tracks a reference signal. For reducing the effect of unknown terms, it is proposed a specific desired dynamics for the sliding variables. The control problem is solved by the indirect approach, where an appropriate neural network (NN) identification model is selected; the NN parameters (synaptic weights) are adjusted according to a specific adaptive law (EKF), such that the response of the NN identifier approximates the response of the real plant for the same input. Then, based on the designed NN identifier a stabilizing or reference tracking controller is proposed (BC combined with SM). The proposed neural identifier and control applicability are illustrated by torque trajectory tracking for a DC motor with separate winding excitation via real-time implementation.     

Combined backstepping and HOSM control design for a class of nonlinear MIMO systems

This paper presents a control design algorithm that combines backstepping and high‐order sliding modes. It is known that backstepping can achieve asymptotic stability for nonlinear systems in strict‐feedback form in spite of parametric uncertainties. Nevertheless, when external perturbations are also present, only practical stability can be ensured. For the same aforementioned perturbed conditions, the combined design presented in this paper can achieve finite‐time exact tracking/regulation. At the same time, the semi‐global or global stability obtained through backstepping is preserved, and the gains of the high‐order sliding modes controller can be reduced with respect to its direct application. The design is based on recently reported combined designs that are based on the idea of virtual controls, which can contain terms based on high‐order sliding modes algorithms. The proposal also extends previous results to the multiple‐input–multiple‐output case. Copyright © 2016 John Wiley & Sons, Ltd.     

Output‐feedback tracking in causal nonminimum‐phase nonlinear systems using higher‐order sliding modes

Asymptotic output‐feedback tracking in a class of causal nonminimum phase uncertain nonlinear systems is addressed via sliding mode techniques. Sliding mode control is proposed for robust stabilization of the output tracking error in the presence of a bounded disturbance. The output reference profile and the unknown input/disturbance are supposed to be described by unknown linear exogenous systems of a given order. Local asymptotic stability of the output tracking error dynamics along with the boundedness of the internal states are proven. The unstable internal states are estimated asymptotically via the proposed multistage observer that is based on the method of extended system center. A higher‐order sliding mode observer/differentiator is used for the exact estimation of the input–output states in a finite time. The bounded disturbance is reconstructed asymptotically. A numerical example illustrates the efficiency of the proposed output‐feedback tracking approach developed for causal nonminimum phase nonlinear systems. Copyright © 2009 John Wiley & Sons, Ltd.     

Distributed finite‐time formation control for multiple quadrotors via local communications

This paper investigates finite‐time formation tracking control problem for multiple quadrotors with external disturbance. The states of the virtual leader are not available to all the followers and the network topology is described by a directed graph. The model of each quadrotor is divided into position subsystem and attitude subsystem. Firstly, novel distributed finite‐time state observers are designed to estimate the relative state errors between followers and the virtual leader. Secondly, the values of these observers are used to design controllers that achieve finite‐time robust coordinated tracking in the position subsystem. Thirdly, the terminal sliding mode disturbance observers and finite‐time attitude tracking controllers are proposed, respectively, in the attitude subsystem to estimate the external disturbance and achieve attitude tracking control. The finite‐time stability analysis of the control algorithms is carried out using the Lyapunov theory and the homogeneous technique. Finally, the efficiency of the proposed algorithm is illustrated by numerical simulations.     

基于RBF神经网络滑模控制的车辆横向控制研究

针对车辆横向控制系统中滑模控制器存在的抖振现象对转向机械结构带来的损耗问题,提出了一种基于RBF神经网络的滑模控制算法。利用RBF神经网络较强的自学习能力实时在线调节滑模控制器的切换项增益参数,增强系统的抗干扰能力与动态性能。将车辆实际参数代入仿真数学模型中,在Simulink仿真环境中进行对比仿真实验,仿真结果表明:该控制算法跟踪性能好,能够有效降低滑模控制器的抖振,满足车辆横向控制要求。     

神经网络自适应滑模控制的不确定机器人轨迹跟踪控制

提出一种针对机器人跟踪控制的神经网络自适应滑模控制策略。该控制方案将神经网络的非线性映射能力与滑模变结构和自适应控制相结合。对于机器人中不确定项,通过RBF网络分别进行自适应补偿,并通过滑模变结构控制器和自适应控制器消除逼近误差。同时基于Lyapunov理论保证机器手轨迹跟踪误差渐进收敛于零。仿真结果表明了该方法的优越性和有效性。     

Integrated 3‐D Flight Trajectory Tracking Control with Aerodynamic Constraints on Attitude and control Surfaces

In this paper, a new 3‐D trajectory tracking problem for an uncertain high fidelity six‐degree‐of‐freedom (6‐DOF) aerodynamic system is considered. Instead of designing controllers for each subsystem separately, an integrated trajectory tracking control algorithm is proposed to exploit beneficial relationships among interacting subsystems. The high‐order aerodynamic model is first transformed into a quasi‐strict‐feedback form. Then, backstepping technique is utilized to resolve the coupling effect problem of three control channels resulting from the bank‐to‐turn (BTT) control mode. In addition, command filters are introduced to handle state and actuator constraints caused by the physical limitations and the coordinated turn requirement. Furthermore, the uncertain aerodynamic force and moment coefficients are reconstructed by using the B‐spline neural network approximation and adaptive learning approaches. With Lyapunov stability analysis, all the states in the closed‐loop system are shown to be semi‐globally uniformly ultimately bounded (SUUB), and the tracking errors will asymptotically converge into a small compact set around zero by properly adjusting the control parameters. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed algorithm.     

A Neuro-Sliding Mode Control Scheme for Constrained Robots with Uncertain Jacobian

The joint robot control requires to map desired cartesian tasks into desired joint trajectories, by using the ill-posed inverse kinematics mapping. In order to avoid inverse kinematics, the control problem is formulated directly in task space to gives rise to cartesian robot control. In addition, when the robot is constrained due to its kinematic mappings yields a stiff system and an additional complexity arises to implement cartesian control for constrained robots. In this paper, an alternative approach is proposed to guarantee global convergence of force and position cartesian tracking errors under the assumption that the jacobian is not exactly known. A neuro-sliding mode controller is presented, where a small size adaptive neural network compensates approximately for the inverse dynamics and an inner control loop induces second order sliding modes to guarantee tracking. The sliding mode variable tunes the online adaptation of the weights. A passivity analysis yields the energy Lyapunov function to prove boundedness of all closed-loop signals and variable structure control theory is used to finally conclude convergence of position and force tracking errors. Experimental results are provided to visualize the expected performance.     

Robust Tracking Control For A Wheeled Mobile Manipulator With Dual Arms Using Hybrid Sliding‐Mode Neural Network

In this paper, a robust tracking controller is proposed for the trajectory tracking problem of a dual‐arm wheeled mobile manipulator subject to some modeling uncertainties and external disturbances. Based on backstepping techniques, the design procedure is divided into two levels. In the kinematic level, the auxiliary velocity commands for each subsystem are first presented. A sliding‐mode equivalent controller, composed of neural network control, robust scheme and proportional control, is constructed in the dynamic level to deal with the dynamic effect. To deal with inadequate modeling and parameter uncertainties, the neural network controller is used to mimic the sliding‐mode equivalent control law; the robust controller is designed to compensate for the approximation error and to incorporate the system dynamics into the sliding manifold. The proportional controller is added to improve the system's transient performance, which may be degraded by the neural network's random initialization. All the parameter adjustment rules for the proposed controller are derived from the Lyapunov stability theory and e‐modification such that uniform ultimate boundedness (UUB) can be assured. A comparative simulation study with different controllers is included to illustrate the effectiveness of the proposed method.