Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integralderivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

Adaptive Iterative Learning Control for Nonlinear Time-delay Systems with Periodic Disturbances Using FSE-neural Network

An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion （FSE） are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions （such as global Lipschitz condition） is relaxed. Furthermore, by using appropriate Lyapunov-Krasovskii functionals, all signs in the closed loop system are guaranteed to be semiglobally uniformly ultimately bounded, and the output of the system is proved to converge to the desired trajectory. A simulation example is provided to illustrate the effectiveness of the control scheme.

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 MittagLeffler 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.

Discounted Iterative Adaptive Critic Designs With Novel Stability Analysis for Tracking Control

The core task of tracking control is to make the controlled plant track a desired trajectory.The traditional performance index used in previous studies cannot eliminate completely the tracking error as the number of time steps increases.In this paper,a new cost function is introduced to develop the value-iteration-based adaptive critic framework to solve the tracking control problem.Unlike the regulator problem,the iterative value function of tracking control problem cannot be regarded as a Lyapunov function.A novel stability analysis method is developed to guarantee that the tracking error converges to zero.The discounted iterative scheme under the new cost function for the special case of linear systems is elaborated.Finally,the tracking performance of the present scheme is demonstrated by numerical results and compared with those of the traditional approaches.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.

Dual-stage Optimal Iterative Learning Control for Nonlinear Non-affine Discrete-time Systems

根据沿着重复轴的一种新动态 linearization 技术，双阶段的最佳的反复的学习控制为非线性、非仿射的分离时间的系统被介绍。双阶段显示二个最佳的学习阶段分别地被设计反复地改进控制输入顺序和学习获得。主要特征是控制器设计和集中分析仅仅取决于动态系统的 I/O 数据。换句话说，没有知道系统的任何另外的知识，我们能容易选择控制参数。模拟学习沿着重复轴说明介绍方法的几何集中，在哪个马路的一个例子控制为它的内在的工程重要性是引人注目的交通反复的学习。

Neural networks-based iterative learning control consensus for periodically time-varying multi-agent systems

In this paper,the problem of adaptive iterative learning based consensus control for periodically time-varying multi-agent systems is studied,in which the dynamics of each follower are driven by nonlinearly parameterized terms with periodic disturbances.Neural networks and Fourier base expansions are introduced to describe the periodically time-varying dynamic terms.On this basis,an adaptive learning parameter with a positively convergent series term is constructed,and a distributed control protocol based on local signals between agents is designed to ensure accurate consensus of the closed-loop systems.Furthermore,consensus algorithm is generalized to solve the formation control problem.Finally,simulation experiments are implemented through MATLAB to demonstrate the effectiveness of the method used.

Repetitive Learning Control for Time-varying Robotic Systems： A Hybrid Learning Scheme

重复学习控制为不明确的变化时间的机器的系统追踪的 finite-time-trajectory 被介绍。在时间函数以一个反复的学习方法被学习的地方，一个混合学习计划被给在系统动力学应付经常、变化时间的 unknowns，没有泰勒表示的帮助，当常规微分学习方法为估计经常的被建议时。介绍重复学习控制为在每个周期的开始的起始的重新定位避免要求，是不同的，并且变化时间的 unknowns 不是必要的周期。随混合学习的采纳，靠近环的系统的州的变量的固定被保证，追踪的错误被保证作为重复增加收敛到零，这被显示出。建议计划的有效性通过数字模拟被表明。

Adaptive Iterative Learning Control for Nonlinearly Parameterized Systems with Unknown Time-varying Delay and Unknown Control Direction

This paper proposes a new adaptive iterative learning control approach for a class of nonlinearly parameterized systems with unknown time-varying delay and unknown control direction.By employing the parameter separation technique and signal replacement mechanism,the approach can overcome unknown time-varying parameters and unknown time-varying delay of the nonlinear systems.By incorporating a Nussbaum-type function,the proposed approach can deal with the unknown control direction of the nonlinear systems.Based on a Lyapunov-Krasovskii-like composite energy function,the convergence of tracking error sequence is achieved in the iteration domain.Finally,two simulation examples are provided to illustrate the feasibility of the proposed control method.

Consensus control for heterogeneous uncertain multi-agent systems with hybrid nonlinear dynamics via iterative learning algorithm

In this study,We propose a compensated distributed adaptive learning algorithm for heterogeneous multi-agent systems with repetitive motion,where the leader's dynamics are unknown,and the controlled system's parameters are uncertain.The multiagent systems are considered a kind of hybrid order nonlinear systems,which relaxes the strict requirement that all agents are of the same order in some existing work.For theoretical analyses,we design a composite energy function with virtual gain parameters to reduce the restriction that the controller gain depends on global information.Considering the stability of the controller,we introduce a smooth continuous function to improve the piecewise controller to avoid possible chattering.Theoretical analyses prove the convergence of the presented algorithm,and simulation experiments verify the effectiveness of the algorithm.

Decentralized adaptive iterative learning control for interconnected systems with uncertainties

In many applications, the system dynamics allows the decomposition into lower dimensional subsystems with interconnections among them. This decomposition is motivated by the ease and flexibility of the controller design for each subsystem. In this paper, a decentralized model reference adaptive iterative learning control scheme is developed for interconnected systems with model uncertainties. The interconnections in the dynamic equations of each subsystem are considered with unknown boundaries. The proposed controller of each subsystem depends only on local state variables without any information exchange with other subsystems. The adaptive parameters are updated along iteration axis to com- pensate the interconnections among subsystems. It is shown that by using the proposed decentralized controller, the states of the subsystems can track the desired reference model states iteratively. Simulation results demonstrate that, utilizing the proposed adaptive controller, the tracking error for each subsystem converges along the iteration axis.

Observer-Based Adaptive Neural Iterative Learning Control for a Class of Time-Varying Nonlinear Systems

In this paper an adaptive iterative learning control scheme is presented for the output tracking of a class of nonlinear systems. An observer is designed to estimate the tracking errors. A mixed time domain and s-domain representation is constructed to derive an error model with relative degree one for our purpose. And time-varying radial basis function neural network is employed to deal with system uncertainty. A new signal is constructed by using a first-order filter, which removes the requirement of strict positive real(SPR) condition and identical initial condition of iterative learning control. Based on property of hyperbolic tangent function,the system tracing error is proved to converge to the origin as the iteration tends to infinity by constructing Lyapunov-like composite energy function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

A New Discrete-time Adaptive ILC for Nonlinear Systems with Time-varying Parametric Uncertainties

用在分离时间轴和反复的学习轴之间的类比，一条新分离时间的适应反复的学习控制(AILC ) 途径被开发与变化时间的参量的无常探讨非线性的系统的一个班。类似于适应控制，新 AILC 能合并一个设计算法，因此，学习获得能沿着学习的轴反复地被调节。当起始的状态是随机的，参考轨道是变化重复的时，新 AILC 能沿着反复的学习轴 asymptotically 在有限时间间隔上完成 pointwise 集中。

全状态约束下长行程混联机器人投影迭代鲁棒控制算法

针对全状态约束下的长行程混联机器人系统鲁棒性较差提出了基于自适应学习神经网络和等效误差函数的投影迭代鲁棒控制算法。基于自适应学习神经网络逼近未知的非线性项,提出投影迭代鲁棒控制算法,更新网络权值并估计逼近误差和随机外部扰动的未知上界;构造用于抵消初始时刻随机变化扩展误差的时变边界层,设计基于时变边界层和扩展误差的等效误差函数作为迭代控制器的主要控制变量以克服随机初始误差满足相同初始条件;在控制器设计中引入正切型障碍Lyapunov函数,确保系统状态在预定范围内。仿真实验结果证明了该方法的有效性,可在全状态约束下实现高精度强鲁棒性的轨迹跟踪。

基于自适应迭代学习的多智能体系统编队控制

针对带未知时变参数的非线性多智能体系统的编队问题,提出一种分布式自适应迭代学习控制策略。首先,通过傅里叶级数对系统的不确定参数进行展开,采用一个收敛级数序列处理傅里叶级数展开产生的截断误差,结合多智能体运行过程中的编队误差推导自适应迭代学习控制律和参数更新律;其次,针对领导者动态对大部分智能体都是未知的情况,设计新的辅助控制来补偿未知动态和避免未知有界干扰;然后,基于李亚普诺夫能量函数证明了在所设计控制律作用下多智能体系统编队误差随着迭代次数的增加在有限时间内趋于0;最后,将该控制策略运用到多无人机编队系统中,并通过搭建半物理实验平台,验证了控制方法的有效性。实验结果表明该控制方法可以确保多智能体快速形成所需编队,并且每个智能体在有限时间内可以精确跟踪期望轨迹。所提方法充分考虑了多智能体系统的参数不确定性以及抗干扰的能力,为实际应用中复杂多智能体系统的精确控制提供了有效的方法。

基于自适应终端滑模的高速列车迭代学习速度控制

针对高速列车的速度追踪控制问题,充分利用列车运行的重复性,考虑工程应用中迭代初始状态不同和复杂的外部环境,提出一种基于线性扩张状态观测器(LESO)的自适应非奇异终端滑模迭代学习控制算法,使系统在任意迭代初值时均能保证追踪精度。提出一种时变非奇异终端滑模面以抑制初态误差影响,采用LESO估计并补偿列车扰动,设计自适应迭代更新律估计LESO的观测误差,设计全饱和自适应迭代控制律计算输入并将其约束于允许范围内。建立类Lyapunov的复合能量函数,通过严格的数学分析证明其迭代域的差分负定性和有界性,证明所设计的时变滑模面可实现渐进收敛,并证明追踪误差在滑模面内可在有限时间内收敛至平衡点。将本文提出的算法与滑模控制、变增益迭代学习控制、自抗扰控制等算法进行比较。仿真结果表明:无论是否存在迭代初始误差,在相同的条件下,本文提出的算法较其他算法具有更强的抗干扰能力,速度追踪精度提高90%及以上,停车误差可迭代收敛至001 m。

Neural Network State Learning Based Adaptive Terminal ILC for Tracking Iteration-varying Target Points

Terminal iterative learning control(TILC) is developed to reduce the error between system output and a fixed desired point at the terminal end of operation interval over iterations under strictly identical initial conditions. In this work, the initial states are not required to be identical further but can be varying from iteration to iteration. In addition, the desired terminal point is not fixed any more but is allowed to change run-to-run. Consequently, a new adaptive TILC is proposed with a neural network initial state learning mechanism to achieve the learning objective over iterations. The neural network is used to approximate the effect of iteration-varying initial states on the terminal output and the neural network weights are identified iteratively along the iteration axis.A dead-zone scheme is developed such that both learning and adaptation are performed only if the terminal tracking error is outside a designated error bound. It is shown that the proposed approach is able to track run-varying terminal desired points fast with a specified tracking accuracy beyond the initial state variance.

基于无模型自适应迭代学习的液压锚杆钻机转速控制

针对存在参数不确定、非线性约束液压锚杆钻机回转系统的转速高精度控制问题,利用钻机作业的重复性,提出了一种基于无模型自适应迭代学习的液压锚杆钻机回转系统转速控制方案。首先,搭建钻机回转控制系统关于转速的状态空间模型。其次,利用动态线性化技术,构造钻机回转系统液压马达与伺服阀电流在迭代域的等价线性映射关系,并根据系统采集的历史伺服阀电流输入、液压马达转角输出数据,提出无模型自适应迭代学习转速控制设计方法。然后在理论上给出液压锚杆钻机回转系统转速跟踪误差沿数据方向以及重复作业方向的渐近收敛性。最后,利用MATLAB软件和AMEsim平台联合仿真验证算法的有效性。结果表明,相比于传统PID算法和迭代学习控制算法,所提出的算法在不需要已知锚杆钻机系统模型的情况下,能够仅利用可测数据实现钻机转速的高精度控制,并且在面对突加外部干扰、油温波动情况下仍具备良好的自适应、抗干扰能力。