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.

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。

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.

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。

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.

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.

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。

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.

高速列车受限自适应有限次迭代学习容错控制

为研究高速列车(High-Speed Train, HST)自动运行系统在执行器故障和速度受限下的速度控制问题,本文提出一种有限次运行收敛的受限自适应迭代学习容错控制(Finite-Iteration Constrained Adaptive Iterative Learning Fault-Tolerant Control, FI-CAILFTC)方法。首先,基于障碍组合能量函数(Barrier Composite Energy Function, BCEF)构建沿迭代域方向有限次运行收敛条件,并且利用所期望任意跟踪精度计算所需运行次数,同时,指导控制器参数选择,以保证HST有限次运行收敛性;其次,设计具有自适应容错能力的迭代学习控制算法,对未知时变且迭代变化的执行器故障进行自适应估计和补偿;再次,针对HST运行过程中超速问题,在所设计容错控制器基础上,加入超速防护机制,保证HST实际运行速度始终满足速度约束,保障列车安全运行;最后,以CRH-3型高速动车组列车作为研究对象,对设计的控制方法进行仿真研究。仿真结果表明:FI-CAILFTC方法下,HST速度跟踪误差在预先计算出的第17次迭代后达到期望控制精度0.2,相较于对比算法,控制精度分别提高了90.70%和90.22%;FI-CAILFTC有更快的收敛速度和更好的自适应容错能力;HST实际运行速度始终主动满足速度受限。

迭代学习控制器参数的数据驱动自适应整定方法

针对PID型迭代学习控制(iterative learning control,ILC)方法,提出了两种数据驱动自适应整定(data-driven adaptive tuning,DDAT)方法。首先采用紧格式迭代动态线性化(compact form iterative dynamic linearization,CFIDL)方法将原始的非线性系统转化为等价的线性数据模型,设计了一个目标函数来动态地调整PID型ILC的学习增益。其次,通过对设计的目标函数进行优化,提出了一种基于CFIDL的DDAT方法。该方法只使用实际的I/O数据,而不需要任何机理模型信息。进一步,引入偏格式迭代动态线性化(partial form iterative dynamic linearization,PFIDL)方法对结果进行扩展,提出了一种基于PFIDL的DDAT方法。所提出的两种DDAT方法都可以提高PID型ILC对不确定性的鲁棒性。最后,通过仿真验证了两种方法的有效性。

膝-踝-趾动力型假肢解耦控制研究

针对膝-踝-趾动力型假肢系统的强耦合性,导致系统控制效果不理想等问题,本文设计控制法则分解法解耦器对系统进行解耦,降低耦合度,提高控制效果。利用拉格朗日方程建立了膝-踝-趾动力型假肢系统支撑末期的动力学模型,此模型的耦合度为1.22,耦合性较强,需要进行解耦;基于控制法则分解法设计模型解耦器,以此简化假肢系统,将耦合度强的系统简化为膝、踝、趾独立控制的模型;基于自适应迭代学习设计控制器,对解耦前后三自由度假肢系统的各关节进行控制。结果表明:此解耦器可以将假肢模型简化为3个单输入、单输出的系统,同时降低关节间的耦合度,加快系统的收敛速度,与解耦前的控制效果相比,解耦后系统收敛误差明显减小。本文为多关节假肢系统提供了模型简化方法,为实物样机控制提供理论验证。

基于数据驱动的凸轮磨削轮廓误差补偿

针对数控凸轮磨削机床在加工过程中存在的周期性、重复性轮廓误差和不易建模等问题,提出一种基于数据驱动的轮廓误差补偿策略。在数控凸轮磨削机床的单轴伺服跟踪系统中加入无模型自适应迭代学习控制,该方法沿迭代轴引入伪偏导数,将复杂的非线性系统动态线性化处理。针对两轴之间由于伺服跟踪误差不同导致的滞后量不同,利用交叉耦合迭代学习控制,将补偿量按照交叉耦合系数反馈到单轴伺服控制系统中,实现对凸轮磨削轮廓误差的补偿。最后通过仿真实验验证了提出的轮廓误差补偿策略可以有效减小凸轮的轮廓误差,提高了数控凸轮磨削机床的加工精度。