Composite adaptive control for Euler-Lagrange systems with additive disturbances

In a typical adaptive update law, the rate of adaptation is generally a function of the state feedback error. Ideally, the adaptive update law would also include some feedback of the parameter estimation error. The desire to include some measurable form of the parameter estimation error in the adaptation law resulted in the development of composite adaptive update laws that are functions of a prediction error and the state feedback. In all previous composite adaptive controllers, the formulation of the prediction error is predicated on the critical assumption that the system uncertainty is linear in the uncertain parameters (LP uncertainty). The presence of additive disturbances that are not LP would destroy the prediction error formulation and stability analysis arguments in previous results. In this paper, a new prediction error formulation is constructed through the use of a recently developed Robust Integral of the Sign of the Error (RISE) technique. The contribution of this design and associated stability analysis is that the prediction error can be developed even with disturbances that do not satisfy the LP assumption (e.g., additive bounded disturbances). A composite adaptive controller is developed for a general MIMO Euler-Lagrange system with mixed structured (i.e., LP) and unstructured uncertainties. A Lyapunov-based stability analysis is used to derive sufficient gain conditions under which the proposed controller yields semi-global asymptotic tracking. Experimental results are presented to illustrate the approach.     

Adaptive neural control with fast approximation for uncertain nonlinear systems: A novel composite learning approach

In existing adaptive neural control approaches, only when the regressor satisfies the persistent excitation (PE) or interval excitation (IE) conditions, the constant optimal weights of neural network (NN) can be identified, which can be used to establish uncertainties in nonlinear systems. This paper proposes a novel composite learning approach based on adaptive neural control. The focus of this approach is to make the NN approximate uncertainties in nonlinear systems quickly and accurately without identifying the constant optimal weights of the NN. Hence, the regressor does not need to satisfy the PE or IE conditions. In this paper, regressor filtering scheme is adopted to generate prediction error, and then the prediction error and tracking error simultaneously drive the update of NN weights. Under the framework of Lyapulov theory, the proposed composite learning approach can ensure that approximation error of the uncertainty and tracking error of the system states converge to an arbitrarily small neighborhood of zero exponentially. The simulation results verify the effectiveness and advantages of the proposed approach in terms of fast approximation.     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Type-2 fuzzy sliding mode control without reaching phase for nonlinear system

A new sliding mode control (SMC) algorithm for the nth order nonlinear system suffering from parameters uncertainty and subjected to an external perturbation is proposed. The algorithm employs a time-varying switching plane. At the initial time t=t₀, the plane passes through the point determined by the system initial conditions in the error state space. Afterwards, the plane moves to the origin of the state space. Since the nonlinear system is sensible to the perturbations and uncertainties during the reaching phase, the elimination of such phase yields in a considerable amelioration of system robustness. Switching plane is chosen such that: (1) the reaching phase is eliminated, (2) the nonlinear system is insensitive to the external disturbance and the model uncertainty from the initial time (3) the convergence of the tracking error to zero. Furthermore, a Type-2 fuzzy system is used to approximate system dynamics (assumed to be unknown) and to construct the equivalent controller such that: (1) all signals of closed-loop system are uniformly ultimately bounded, (2) the problems related to adaptive fuzzy controllers like singularity and constraints on the control gain are resolved. To ensure the robustness of the overall closed-loop system, analytical demonstration using Lyapunov theorem is considered. Finally, a robot manipulator is considered as a real time system in order to confirm the efficiency of the proposed approach. The experimentation is done for both regulation and tracking control problems.     

Adaptive finite‐time neural backstepping control for multi‐input and multi‐output state‐constrained nonlinear systems using tangent‐type nonlinear mapping

This article focuses on the problem of adaptive finite‐time neural backstepping control for multi‐input and multi‐output nonlinear systems with time‐varying full‐state constraints and uncertainties. A tan‐type nonlinear mapping function is first proposed to convert the strict‐feedback system into a new pure‐feedback one without constraints. Neural networks are utilized to cope with unknown functions. To improve learning performance, a composite adaptive law is designed using tracking error and approximate error. A finite‐time convergent differentiator is adopted to avoid the problem of “explosion of complexity.” By theoretical analysis, all the signals of system are proved to be bounded, the outputs can track the desired signals in a finite time, and full‐state constraints are not transgressed. Finally, comparative simulations are offered to confirm the validity of the proposed control scheme.     

Bi-Objective Optimal Control Modification Adaptive Control for Systems with Input Uncertainty

This paper presents a new model-reference adaptive control method based on a bi-objective optimal control formulation for systems with input uncertainty. A parallel predictor model is constructed to relate the predictor error to the estimation error of the control effectiveness matrix. In this work, we develop an optimal control modification adaptive control approach that seeks to minimize a bi-objective linear quadratic cost function of both the tracking error norm and the predictor error norm simultaneously. The resulting adaptive laws for the parametric uncertainty and control effectiveness uncertainty are dependent on both the tracking error and the predictor error, while the adaptive laws for the feedback gain and command feedforward gain are only dependent on the tracking error. The optimal control modification term provides robustness to the adaptive laws naturally from the optimal control framework. Simulations demonstrate the effectiveness of the proposed adaptive control approach.      

Robust Adaptive Terminal Sliding Mode Control of an Omnidirectional Mobile Robot for Aircraft Skin Inspection

In this paper, an adaptive terminal sliding mode control scheme for an omnidirectional mobile robot is proposed as a robust solution to the trajectory tracking control problem. The omnidirectional mobile robot has a double-frame structure, which adsorbes on the aircraft surface by suction cups. The major difficulties lie in the existence of nonholonomic constraints, system uncertainty and external disturbance. To overcome these difficulties, the kinematic model is established, the dynamic model is derived by using Lagrange method. Then, a robust adaptive terminal sliding mode (RATSM) control scheme is proposed to solve the problem of state stabilization and trajectory tracking. In order to enhance the robustness of the system, an adaptive online estimation law is designed to overcome the total uncertainty. Subsequently, the asymptotic stability of the system without total uncertainty is proved with basis on Lyapunov theory, and the system considering total uncertainty can converge to the domain containing the origin. Simulation results are given to show the verification and validation of the proposed control scheme.

     

Adaptive Neural Network-Based Control for a Class of Nonlinear Pure-Feedback Systems With Time-Varying Full State Constraints

In this paper, an adaptive neural network (NN) control approach is proposed for nonlinear pure-feedback systems with time-varying full state constraints. The pure-feedback systems of this paper are assumed to possess nonlinear function uncertainties. By using the mean value theorem, pure-feedback systems can be transformed into strict feedback forms. For the newly generated systems, NNs are employed to approximate unknown items. Based on the adaptive control scheme and backstepping algorithm, an intelligent controller is designed. At the same time, time-varying Barrier Lyapunov functions (BLFs) with error variables are adopted to avoid violating full state constraints in every step of the backstepping design. All closedloop signals are uniformly ultimately bounded and the output tracking error converges to the neighborhood of zero, which can be verified by using the Lyapunov stability theorem. Two simulation examples reveal the performance of the adaptive NN control approach.      

Command Filter Based Robust Nonlinear Control of Hypersonic Aircraft with Magnitude Constraints on States and Actuators

The command filter based robust nonlinear controller is designed for the longitudinal dynamics of a generic hypersonic aircraft in presence of parametric model uncertainty and magnitude constraints on the states and actuators. The functional subsystems are transformed into the linearly parameterized form and the controller is proposed based on dynamic inversion and adaptive gain. Since the dynamics are with cascade structure, the states are considered as virtual control and the signal is filtered to produce the limited command signal and its derivative. To eliminate the effect of the constraint, the auxiliary error compensation design is employed and the parameter projection estimation is proposed based on the compensated tracking error. The uniformly ultimately boundedness is guaranteed for the closed-loop control system. Simulation results show that the proposed approach achieves good tracking performance.     

Robust output tracking of nonlinear systems with mismatched uncertainties

The problem of robust output tracking for a class of uncertain nonlinear systems which do not satisfy the conventional matching condition is considered. The main assumption on the uncertainty is that the triangularity condition is satisfied. Based on backstepping method and input/output linearization approach, we propose a class of non-adaptive state feedback controllers which can guarantee exponential stability of the tracking error for the uncertain nonlinear systems first. Next, adaptive control laws are developed so that no prior knowledge of the bounds on the uncertainties is required. By updating these upper bounds, we design a class of adaptive robust controllers. It is shown that under the proposed adaptive robust control the tracking error of the controlled system converges to zero as time approaches infinity.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.     

电液伺服系统的多滑模鲁棒自适应控制

针对一类参数与外负载非匹配不确定的非线性高阶系统,提出了一种基于逐步递推方法的多滑模鲁棒自适应控制策略.应用逐步递推的多滑模控制方法简化了高阶系统的控制问题,同时在自适应控制中加入鲁棒控制的方法,以消除不确定性对控制性能的影响.首先利用逐步递推方法与状态反馈精确线性化理论,得出确定系统的多滑模控制器设计方法;然后基于Lyapunov稳定性分析方法,给出不确定系统的参数自适应律,及鲁棒自适应控制器的设计方法.本文把该控制策略应用到电液伺服系统的位置跟踪控制中,仿真结果显示,该控制方法具有较强的鲁棒性及良好的跟踪效果.     

基于自适应模糊控制器和非线性扰动观测器的永磁直线同步电机反馈线性化控制

由于永磁直线同步电机(PMLSM)伺服系统应用于一些高精密场合,因此克服系统存在的负载扰动、参数变化等不确定性影响是提高系统性能的关键.针对不确定性问题,采用一种基于自适应模糊控制器(AFC)和非线性扰动观测器(NDO)的反馈线性化控制方法.首先设计反馈线性化控制器(FLC)实现系统的线性化,便于位置跟踪;其次采用NDO估计并补偿系统的不确定性,提高跟踪精度.但在实际运行过程中观测器增益较难选取,极易产生较大的观测误差,为此,采用AFC方法逼近NDO的观测误差,通过自适应律动态调整模糊规则,改善模糊控制器的学习能力,增强系统的鲁棒性,并用李雅普诺夫定理保证系统闭环稳定性.实验结果表明,与基于DOB和NDO的反馈线性化位置控制相比,该方法能够明显提高系统的跟踪性和鲁棒性.     

基于ESO的船舶航向鲁棒自适应控制

针对具有内部未建模动态和外部不确定扰动的水面船舶设计一种鲁棒自适应航向控制器,并同时解决转向过程中的漂角补偿问题.基于二阶非线性Nomoto模型和一阶漂角模型,建立非积分链结构的漂角-航向非线性状态空间模型,将航向控制系统未建模动态与外部不确定扰动合并为复合扰动,应用扩张状态观测器估计模型中的未测量状态和系统复合扰动.基于Lyapunov稳定性理论和自适应反步法设计航向状态反馈控制规律,为避免反步法控制过程中的微分爆炸问题,采用动态面控制技术获取虚拟控制信号的近似导数.所提出的扩张状态观测器和航向控制算法能够保证闭环系统内所有误差信号一致最终有界,提高航向保持和转向过程中的航向跟踪精度.仿真结果验证了所提出的航向控制规律的有效性.     

An uncertainty compensator for robust control of wheeled mobile robots

This paper proposes an uncertainty compensator to design a novel robust control for mobile robots with dynamic and kinematic uncertainties. A novel gradient-based adaptive fuzzy estimator is developed to compensate uncertainties with minimum required feedback signals. As a novelty, the proposed approach uses the tracking error and its first time derivative to form the estimation error of uncertainty, and guarantees that both the estimation error and tracking error converge asymmetrically to ignorable value. Advantages of the proposed robust control are simplicity in design, robustness against uncertainties, guaranteed stability, and good control performance. The control approach is verified by stability analysis. Simulation results and experimental results illustrate the effectiveness of the proposed control. Experimental evaluation of the proposed controller is expressed for two different low-cost nonholonomic wheeled mobile robots. The proposed control design is compared with an adaptive control approach to confirm the superiority of the proposed approach in terms of precision, simplicity of design, and computations.     

板球系统的间接模糊自适应控制

针对具有强耦合、不确定摩擦力的多变量非线性板球系统,利用Lyapunov稳定理论,设计一种间接模糊自适应控制器。该控制器可以在确保系统变量在有限范围内变动的同时保持收敛性,并且在系统的增益矩阵不可逆时,使得板球系统稳定并跟踪误差收敛到零邻域内。控制器是由监督、间接模糊自适应和自适应补偿3种控制算法结合的。仿真实验表明,所提出的控制方法能够确保板球系统跟踪控制的稳定性和收敛性。     

A performance oriented multi-loop constrained adaptive robust tracking control of one-degree-of-freedom mechanical systems: Theory and experiments

A performance oriented multi-loop approach to the adaptive robust tracking control of one-degree-of-freedom mechanical systems with input saturation, state constraints, parametric uncertainties and input disturbances is presented. The control system contains three loops. In the outer loop, constrained optimization algorithms are developed to generate a replanned trajectory on-line at a low sampling rate so that the converging speed of the overall system response to the desired target is maximized while not causing input saturation and the violation of state constraints. In the inner loop, a constrained adaptive robust control (ARC) law is synthesized and implemented at high sampling rate to achieve the required robust tracking performances with respect to the replanned trajectory even with various types of uncertainties and input saturation. In the middle loop, a set-membership identification (SMI) algorithm is implemented to obtain a tighter estimate of the upper bound of the inertia so that more aggressive replanned trajectory could be used to further improve the overall system response speed. Interaction of the three loops is explicitly characterized by a set of inequalities that the design variables of each loop have to satisfy. It is theoretically shown that the resulting closed-loop system can track feasible desired trajectories with a guaranteed converging time and steady-state tracking accuracy without violating the state constraints. Experiments have been carried out on a linear motor driven industrial positioning system to compare the proposed multi-loop constrained ARC algorithm with some of the traditional control algorithms. Comparative experimental results obtained confirm the superior performance of the proposed algorithm over existing ones.     

含模型不确定性移动机器人路径跟踪的分层模糊控制

对受非完整约束且含模型不确定性的移动机器人基于分层模糊系统设计了跟踪期望几何路径的鲁棒间接自适应控制方案.此方法除实现路径跟踪外,还可避免控制器的奇异性并保证跟踪方向.由于控制结构中使用了分层模糊系统,大大减少了模糊规则数目;并用鲁棒控制项对模糊系统逼近误差进行补偿,减少了其对跟踪精度的影响.证明了闭环系统跟踪误差收敛到原点的小邻域内,且可通过适当增大鲁棒控制项的设计参数使跟踪误差进一步减小.最后用实验结果验证了方法的有效性.     

基于神经网络观测器的船舶轨迹跟踪递归滑模 动态面输出反馈控制

针对三自由度全驱动船舶速度向量不可测问题,考虑船舶模型参数和外部环境扰动均未知的情况,提出一种基于神经网络观测器的船舶轨迹跟踪递归滑模动态面输出反馈控制方法.该方法设计神经网络自适应观测器估计船舶速度向量,且利用神经网络逼近模型参数不确定项,综合考虑船舶位置和速度误差之间关系构造递归滑模面,再采用动态面控制技术设计轨迹跟踪控制律和参数自适应律,并引入低频增益学习方法消除外界扰动导致的高频振荡控制信号.选取李雅普诺夫函数证明了该控制律能够保证轨迹跟踪闭环系统内所有信号的一致最终有界性.最后,基于一艘供给船进行仿真验证,结果表明,船舶轨迹跟踪响应速度快,所设计控制器对系统模型参数摄动及外界扰动具有较强的鲁棒性.