An adaptive iterative learning algorithm for boundary control of a flexible manipulator

In this study, we consider the boundary control problem of a flexible manipulator in the presence of system parametric uncertainty and external disturbances. The dynamic behavior of the flexible manipulator is represented by partial differential equations (PDEs). Based on the Lyapunov method, we propose an adaptive iterative learning control scheme for trajectory tracking and vibration suppressing of a flexible manipulator. The proposed control scheme is designed using both a proportional‐derivative feedback structure and an iterative term. The learning convergence of iterative learning control is achieved through rigorous analysis without any simplification or discretization of the PDE dynamics. Finally, the results are illustrated using numerical simulations for control performance verification. Copyright © 2016 John Wiley & Sons, Ltd.     

Model reference adaptive iterative learning control for linear systems

In this paper, we propose a model reference adaptive control (MRAC) strategy for continuous‐time single‐input single‐output (SISO) linear time‐invariant (LTI) systems with unknown parameters, performing repetitive tasks. This is achieved through the introduction of a discrete‐type parametric adaptation law in the ‘iteration domain’, which is directly obtained from the continuous‐time parametric adaptation law used in standard MRAC schemes. In fact, at the first iteration, we apply a standard MRAC to the system under consideration, while for the subsequent iterations, the parameters are appropriately updated along the iteration‐axis, in order to enhance the tracking performance from iteration to iteration. This approach is referred to as the model reference adaptive iterative learning control (MRAILC). In the case of systems with relative degree one, we obtain a pointwise convergence of the tracking error to zero, over the whole finite time interval, when the number of iterations tends to infinity. In the general case, i.e. systems with arbitrary relative degree, we show that the tracking error converges to a prescribed small domain around zero, over the whole finite time interval, when the number of iterations tends to infinity. It is worth noting that this approach allows: (1) to extend existing MRAC schemes, in a straightforward manner, to repetitive systems; (2) to avoid the use of the output time derivatives, which are generally required in traditional iterative learning control (ILC) strategies dealing with systems with high relative degree; (3) to handle systems with multiple tracking objectives (i.e. the desired trajectory can be iteration‐varying). Finally, simulation results are carried out to support the theoretical development. Copyright © 2006 John Wiley & Sons, Ltd.     

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。     

Universal iterative learning control using adaptive high-gain feedback

Convergence theorems for adaptive (universal) iterative learning control systems provide a well-defined convergence criterion parametrized by a single adaptive gain parameter. The convergence is in the weak topology of L(0,T) with T finite and applies to both finite-dimensional systems and a class of infinite-dimensional systems.     

Dynamic modeling and adaptive robust boundary control of a flexible robotic arm with 2‐dimensional rigid body rotation

This paper investigates the control of a single‐link flexible robot manipulator with a tip payload appointed to rotate about 2 perpendicular axes in space. The control objective is to regulate the rigid body rotation of the manipulator with guaranteeing the stability of its vibration in the presence of exogenous disturbances. To achieve this, a Lyapunov‐based control design procedure is used and accomplished in some steps. First, the partial differential equation (PDE) dynamic model governing the rigid‐flexible hybrid motion of the arm is derived by applying Hamilton's principle. Next, based on the developed PDE model, an adaptive robust boundary control is established using the Lyapunov redesign approach. To this end, an adaptation mechanism is proposed so that the robust boundary control gains are dynamically updated online and there is no need for prior knowledge of disturbance upper bounds. The actuators and sensors are fully implemented at the arm boundary without using distributed actuators or sensors. Furthermore, in order to avoid control errors resulting from the spillover, control design is directly based on infinite‐dimensional PDE model without resorting to model truncation. Simulation results illustrate the efficacy of the considered method.     

Mapping filtered forwarding‐based robust adaptive control for uncertain nonlinear systems with input constraint

This work develops a robust adaptive control algorithm for uncertain nonlinear systems with parametric uncertainties and external disturbances satisfying an extended matching condition. This control method is implemented in the framework of a mapping filtered forwarding‐based technique. As an attractive alternative of the adaptive backstepping method, this bottom‐up strategy forms a virtual controller and a parameter updated law at each step of the design, where Lyapunov functions and the prior knowledge of system parameters are not required. The boundedness of all signals is guaranteed by using Barbalat's lemma. According to immersion relationship, a compliant behavior of systems behaves accordingly to the lower‐order target dynamics. Furthermore, input constraints are handled by estimating a saturated scaling. A spring, mass, and damper system is used to demonstrate the controller performances via simulation results.     

Distributed adaptive iterative learning control for nonlinear multiagent systems with state constraints

This paper addresses the consensus problem of nonlinear multiagent system with state constraints. A novel γ‐type barrier Lyapunov function is adopted to handle with the bounded constraints. The iterative learning control strategy is introduced to estimate the unknown parameter and basic control signal. Five control schemes are designed, in turn, to address the consensus problem comprehensively from both theoretical and practical viewpoints. These schemes include the original adaptive scheme, projection‐based scheme, smooth function‐based scheme and its alternative, and dead‐zone–like scheme. The consensus convergence and constraints guarantee are strictly proved for each control scheme by using the barrier composite energy function approach. Illustrative simulations verify the theoretical analysis.     

Adaptive constraint control for flexible manipulator systems modeled by partial differential equations with dead-zone input

In this article, based on partial differential equations (PDEs), the flexible manipulator system with both dead-zone input and state constraints is studied. The dynamic model of the flexible manipulator system is described by PDEs. The parameters of the dead-zone input are unknown, and the state constraint problem is also considered. An adaptive approach is proposed to offset the effects caused by dead-zone input. Thus, to guarantee that all states remain within their respective constraint regions, the boundary control law based on the barrier Lyapunov function is given, and an adaptive controller is designed. According to the Lyapunov analysis method, the control method is given to ensure that all signals of the closed-loop system are bounded and all states satisfy the constraint conditions. Finally, simulation results show the effectiveness of the proposed control method in this article.     

掘进机截割臂运动轨迹的迭代学习控制

悬臂式掘进机截割臂系统受参数不确定、非线性、时变和负载干扰等因素的影响,使截割头不能精确按照预定的轨迹截割,导致超挖或欠挖的现象发生,断面成形质量差。为了实现断面精确成形,采用自适应迭代学习控制算法对截割头运行轨迹进行跟踪控制。建立掘进机截割臂的动力学模型,设计相应自适应迭代学习控制算法。仿真结果表明随着学习次数的增加截割臂横向摆角误差趋近于零,纵向摆角误差小于0.0007rad且逐渐趋于零,满足实际现场的精度要求,验证了该控制方法对截割轨迹跟踪的有效性,为掘进机器人断面自动截割成形的研究奠定理论基础。     

Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

Without using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete‐time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well‐known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discrete‐time varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed‐loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Fuzzy adaptive two-bits-triggered control for nonlinear uncertain system with input saturation and output constraint

In this work, a fuzzy adaptive two-bits-triggered control is investigated for the nonlinear uncertain systems with input saturation and output constraint. The considered systems are more widespread. Without sufficient transmission resources, how to resolve the constraint issues while guarantee the control performance is difficult and challenging. Then, hyperbolic tangent function and barrier Lyapunov function are integrated with the designed auxiliary system to solve input saturation and output constraint. Meanwhile, faced with the transmission resources limitation, this work both considers the triggering condition and the control signal transmission bits. A two-bits-triggered control is proposed to economize the transmission resources. Furthermore, improved fuzzy logic systems are established to further promote the control performance. It combines with the time-varying approximation error for processing. The boundedness of all the system signals can be proved. Simulation results illustrate the validity of the proposed approach.     

Composite learning adaptive backstepping control using neural networks with compact supports

The ability to learn is crucial for neural network (NN) control as it is able to enhance the overall stability and robustness of control systems. In this study, a composite learning control strategy is proposed for a class of strict‐feedback nonlinear systems with mismatched uncertainties, where raised‐cosine radial basis function NNs with compact supports are applied to approximate system uncertainties. Both online historical data and instantaneous data are utilized to update NN weights. Practical exponential stability of the closed‐loop system is established under a weak excitation condition termed interval excitation. The proposed approach ensures fast parameter convergence, implying an exact estimation of plant uncertainties, without the trajectory of NN inputs being recurrent and the time derivation of plant states. The raised‐cosine radial basis function NNs applied not only reduces computational cost but also facilitates the exact determination of a subregressor activated along any trajectory of NN inputs so that the interval excitation condition is verifiable. Numerical results have verified validity and superiority of the proposed approach.     

输入受限下非完整轮式移动机器人迭代学习跟踪控制

为了解决输入受限下非完整轮式移动机器人的跟踪控制问题,考虑迭代学习控制方法,设计了一种迭代学习控制律,这里所设计的迭代学习控制律结合了系统的跟踪误差和约束下的上一代控制律.通过应用范数分析理论,对跟踪误差的收敛性进行了理论分析,验证了设计的控制律的有效性.最后,给出了一个仿真实例以证明理论分析结果的正确性,仿真结果表明...     

Model and experience‐based initial input construction for iterative learning control

The initial choice of input in iterative learning control (ILC) generally has a significant effect on the error incurred over subsequent trials. In this paper, techniques are developed that use experimental data gathered over previous applications of ILC in order to generate an initial input signal for the tracking of a new reference trajectory. A model‐based approach is then incorporated to overcome the limitation of insufficient previous experimental data, and a robust design procedure is developed. Experimental evaluation results are obtained using a gantry robot facility. Copyright © 2010 John Wiley & Sons, Ltd.     

Distributed adaptive control for multiple nonholonomic systems with nonlinearly parameterized uncertainties

This paper investigates the distributed adaptive control problem for multiple nonholonomic systems with nonlinearly parameterized uncertainties. Under the assumption that the graph topology is directed and the leader is globally reachable, distributed adaptive controllers are designed recursively by using backstepping technique and algebra graph theory. It is shown that all the followers' outputs will exponentially converge to the reference output signal while all the signals of the closed‐loop system are bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the control scheme.     

Global adaptive learning control of robotic manipulators by output error feedback

This paper addresses the problem of designing a global, output error feedback based, adaptive learning control for robotic manipulators with revolute joints and uncertain dynamics. The reference signals to be tracked are assumed to be smooth and periodic with known period. By developing in Fourier series expansion the input reference signals of every joint, an adaptive, output error feedback, learning control is designed, which ‘learns’ the input reference signals by identifying their Fourier coefficients: global asymptotic and local exponential stability of the tracking error dynamics are obtained when the Fourier series expansion of each input reference signal is finite, while arbitrary small tracking errors are achieved otherwise. The resulting control is not model based and depends only on the period of the reference signals and on some constant bounds on the robot dynamics. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust adaptive tracking control for nontriangular time-delay nonlinear systems with input dead-zone and multiple uncertainties

This article studies the robust adaptive tracking control problem of nontriangular nonlinear systems that are affected by multiple state delays rather than the input-delay. Different from the related studies, the considered systems involve input dead-zone and various uncertainties arising in the control coefficients, structure parameters, time delays, and disturbances. A new adaptive control strategy is presented by introducing a dynamic-gain-based Lyapunov-Krasovskii functional and by generalizing the tuning function method in the framework of time-delay system theory. All the states of the closed-loop system are bounded and the tracking error can be adjusted sufficiently small. In the simulation, the delayed chemical system is studied to demonstrate the validity of the strategy.     

Transfer learning for high‐precision trajectory tracking through adaptive feedback and iterative learning

Robust and adaptive control strategies are needed when robots or automated systems are introduced to unknown and dynamic environments where they are required to cope with disturbances, unmodeled dynamics, and parametric uncertainties. In this paper, we demonstrate the capabilities of a combined adaptive control and iterative learning control (ILC) framework to achieve high‐precision trajectory tracking in the presence of unknown and changing disturbances. The adaptive controller makes the system behave close to a reference model; however, it does not guarantee that perfect trajectory tracking is achieved, while ILC improves trajectory tracking performance based on previous iterations. The combined framework in this paper uses adaptive control as an underlying controller that achieves a robust and repeatable behavior, while the ILC acts as a high‐level adaptation scheme that mainly compensates for systematic tracking errors. We illustrate that this framework enables transfer learning between dynamically different systems, where learned experience of one system can be shown to be beneficial for another different system. Experimental results with two different quadrotors show the superior performance of the combined ‐ILC framework compared with approaches using ILC with an underlying proportional‐derivative controller or proportional‐integral‐derivative controller. Results highlight that our ‐ILC framework can achieve high‐precision trajectory tracking when unknown and changing disturbances are present and can achieve transfer of learned experience between dynamically different systems. Moreover, our approach is able to achieve precise trajectory tracking in the first attempt when the initial input is generated based on the reference model of the adaptive controller.     

Distributed output estimation error observer-based adaptive fault-tolerant consensus tracking control of multi-agent systems

The purpose of this study is to discuss the fully distributed design of output estimation error observer and fault-tolerant consensus tracking control for a class of multi-agent systems with Lipschitz nonlinear dynamics and actuator faults. Firstly, based on the relative output measurements of neighboring agents, the distributed output estimation error observer is developed to adaptively estimate the state and fault information of each agent, and further overcome the difficulties of online updating the adaptive estimations of unknown hyper-parameters. Secondly, to achieve the state consensus tracking goal and compensate for the negative effects of actuator faults, the distributed fault-tolerant consensus tracking control scheme is proposed on the basis of the state estimation and adaptive fault estimation information, and has excellent robustness and consensus tracking control performance. Moreover, sufficient criteria can ensure that consensus tracking error of each agent converges to a small set near the origin. Finally, numerical simulations are provided to show the effectiveness of the proposed fully distributed algorithm.     

Attitude control of reusable launch vehicle in reentry phase with input constraint via robust adaptive backstepping control

The paper presents an attitude control problem of reusable launch vehicles in reentry phase. The controller is designed based on synthesizing robust adaptive control into backstepping control procedure in the presence of input constraint, model uncertainty, and external disturbance. In view of the coupling between the states of translational motion and the states of attitude motion, the control‐oriented model is developed, where the uncertainties do not satisfy linear parameterization assumption. The time derivative of the virtual control input is viewed as a part of uncertain term to facilitate the analytic computations and avoid the ‘explosion of terms’ problem. The robust adaptive backstepping control scheme is first proposed to overcome the uncertainty and external disturbance. The robust adaptive law is employed to estimate the unknown bound of the uncertain term. Furthermore, the attitude control problem subjects to input constraint is studied, and the constrained robust adaptive backstepping control strategy is proposed. Within the Lyapunov theory framework, the stability analysis of the closed‐loop system is carried out, and the tracking error converges to a random neighborhood around origin. Six‐degree‐of‐freedom reusable launch vehicle simulation results are presented to show the effectiveness of the proposed control strategy. Copyright © 2015 John Wiley & Sons, Ltd.