Repetitive process based design and experimental verification of a dynamic iterative learning control law

This paper gives new results on iterative learning control (ILC) design and experimental verification using the stability theory of linear repetitive processes. Using this theory a control law can be designed in one step to force error convergence and produce acceptable transient dynamics. Previous research developed algorithms for the design of a static control law with supporting experimental verification. Should a static law not give the required levels of performance one option is to allow the control law to have internal dynamics. This paper develops a procedure for the design of such a control law with supporting experimental verification on a gantry robot, including a comparative performance against a static law applied to the same robot. The resulting ILC design is an efficient combination of linear matrix inequalities and optimization algorithms.     

Predictive iterative learning control with experimental validation

This paper develops an iterative learning control law that exploits recent results in the area of predictive repetitive control where a priori information about the characteristics of the reference signal is embedded in the control law using the internal model principle. The control law is based on receding horizon control and Laguerre functions can be used to parameterize the future control trajectory if required. Error convergence of the resulting controlled system is analyzed. To evaluate the performance of the design, including comparative aspects, simulation results from a chemical process control problem and supporting experimental results from application to a robot with two inputs and two outputs are given.     

Constrained data-driven optimal iterative learning control

A constrained optimal ILC for a class of nonlinear and non-affine systems, without requiring any explicit model information except for the input and output data, is proposed in this work. In order to address the nonlinearities, an iterative dynamic linearization method without omitting any information of the original plant is introduced in the iteration direction. The derived linearized data model is equivalent to the original nonlinear system and reflects the real-time dynamics of the controlled plant, rather than a static approximate model. By transferring all the constraints on the system output, control input, and the change rate of input signals into a linear matrix inequality, a novel constrained data-driven optimal ILC is developed by minimizing a predesigned objective function. The optimal learning gain is unfixed and updated iteratively according to the input and output measurements, which enhances the flexibility regarding modifications and expansions of the controlled plant. The results are further extended to the point-to-point control tasks where the exact tracking performance is required only at certain points and a constrained data-driven optimal point-to-point ILC is proposed by only utilizing the error measurements at the specified points only.     

Robust finite frequency range iterative learning control design and experimental verification

Iterative learning control is an application for two-dimensional control systems analysis where it is possible to simultaneously address error convergence and transient response specifications but there is a requirement to enforce frequency attenuation of the error between the output and reference over the complete spectrum. In common with other control algorithm design methods, this can be a very difficult specification to meet but often the control of physical/industrial systems is only required over a finite frequency range. This paper uses the generalized Kalman–Yakubovich–Popov lemma to develop a two-dimensional systems based iterative learning control law design algorithm where frequency attenuation is only imposed over a finite frequency range to be determined from knowledge of the application and its operation. An extension to robust control law design in the presence of norm-bounded uncertainty is also given and its applicability relative to alternative settings for design discussed. The resulting designs are experimentally tested on a gantry robot used for the same purpose with other iterative learning control algorithms.     

Analysis of two particular iterative learning control schemes in frequency and time domains

This paper deals with iterative learning control design for multiple-input multiple-output (MIMO), linear time-invariant (LTI) systems. Two particular ILC schemes are considered and analyzed in both frequency and time domains. Some remarks on the convergence, implementation, robustness with respect to disturbances and reinitialization errors, as well as positive realness issues related to both schemes are provided.     

On the equivalence of causal LTI iterative learning control and feedback control

The goal of iterative learning control (ILC) is to improve the accuracy of a system that repeatedly follows a reference trajectory. This paper proves that for each causal linear time-invariant ILC, there is an equivalent feedback that achieves the ultimate ILC error with no iterations. Remarkably, this equivalent feedback depends only on the ILC operators and hence requires no plant knowledge. This equivalence is obtained whether or not the ILC includes current-cycle feedback. If the ILC system is internally stable and converges to zero error, there exists an internally stabilizing feedback that approaches zero error at high gain. Since conventional feedback requires no iterations, there is no reason to use causal ILC.     

Estimation-based norm-optimal iterative learning control

The norm-optimal iterative learning control (ilc) algorithm for linear systems is extended to an estimation-based norm-optimal ilc  algorithm where the controlled variables are not directly available as measurements. A separation lemma is presented, stating that if a stationary Kalman filter is used for linear time-invariant systems then the ilc  design is independent of the dynamics in the Kalman filter. Furthermore, the objective function in the optimisation problem is modified to incorporate the full probability density function of the error. Utilising the Kullback–Leibler divergence leads to an automatic and intuitive way of tuning the ilc  algorithm. Finally, the concept is extended to non-linear state space models using linearisation techniques, where it is assumed that the full state vector is estimated and used in the ilc  algorithm. Stability and convergence properties for the proposed scheme are also derived.     

Experimentally verified generalized KYP Lemma based iterative learning control design

This paper considers iterative learning control law design for plants modeled by discrete linear dynamics using repetitive process stability theory. The resulting one step linear matrix inequality based design produces a stabilizing feedback controller in the time domain and a feedforward controller that guarantees convergence in the trial-to-trial domain. Additionally, application of the generalized Kalman–Yakubovich–Popov (KYP) lemma allows a direct treatment of differing finite frequency range performance specifications. The results are also extended to plants with relative degree greater than unity. To support the algorithm development, the results from an experimental implementation are given, where the performance requirements include specifications over various finite frequency ranges.     

Necessary and sufficient condition for convergence of iterative learning algorithm

This correspondence is concerned with an iterative learning algorithm for MIMO linear time-varying systems. We provide a necessary and sufficient condition for the existence of a convergent algorithm. The result extends the main result in Saab (IEEE Trans. Automat. Control 40(6) (1995) 1138).     

Networked iterative learning control approach for nonlinear systems with random communication delay

This paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.     

Adaptive iterative learning control for switched nonlinear continuous-time systems

In this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.     

Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval time-varying delays

A robust feedback integrated with iterative learning control (FILC) scheme for batch processes with uncertain perturbations and interval time-varying delay is developed. The batch process is modeled as a two-dimensional (2D) Rosser system with a delay varying in a range. The design of FILC scheme is transformed into a robust control problem of uncertain 2D system. New delay-range-dependent stability criteria and stabilization conditions are derived in terms of linear matrix inequalities (LMIs), which depend on not only the difference between the upper and lower delay bounds but also the upper delay bound of the interval time-varying delay. Parameterized characterizations for stabilizing the controller are given in terms of the feasibility solutions to the LMIs. Applications to injection velocity control show that the proposed FILC achieve the design objectives well.     

无人直升机的姿态增强学习控制设计与验证

针对小型无人直升机的姿态控制问题,考虑到现有基于模型的控制方法对直升机动力学模型的先验信息依赖较大,以及未建模动态系统的影响等问题,设计了一种基于增强学习(RL)的飞行控制算法.仅利用直升机的在线飞行数据,补偿了未建模不确定性的影响.同时为了抑制外界扰动,提高系统的鲁棒性,设计了一种基于误差符号函数积分的鲁棒(RISE)控制算法.将两种算法结合,并利用基于Lyapunov分析的方法,证明了无人机姿态控制误差的半全局渐近收敛.最后在无人直升机飞行控制实验平台上,进行了姿态控制的实时实验验证.实验结果表明,本文提出的控制方法具有良好的控制效果,对系统不确定性和外界风扰具有良好鲁棒性.     

Observer-based distributed adaptive iterative learning control for linear multi-agent systems

This paper investigates the consensus problem for linear multi-agent systems from the viewpoint of two-dimensional systems when the state information of each agent is not available. Observer-based fully distributed adaptive iterative learning protocol is designed in this paper. A local observer is designed for each agent and it is shown that without using any global information about the communication graph, all agents achieve consensus perfectly for all undirected connected communication graph when the number of iterations tends to infinity. The Lyapunov-like energy function is employed to facilitate the learning protocol design and property analysis. Finally, simulation example is given to illustrate the theoretical analysis.     

Adaptive iterative learning control for robot manipulators

In this paper, we propose some adaptive iterative learning control (ILC) schemes for trajectory tracking of rigid robot manipulators, with unknown parameters, performing repetitive tasks. The proposed control schemes are based upon the use of a proportional-derivative (PD) feedback structure, for which an iterative term is added to cope with the unknown parameters and disturbances. The control design is very simple in the sense that the only requirement on the PD and learning gains is the positive definiteness condition and the bounds of the robot parameters are not needed. In contrast to classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the second controller proposed in this paper uses just two iterative variables, which is an interesting fact from a practical point of view since it contributes considerably to memory space saving in real-time implementations. We also show that it is possible to use a single iterative variable in the control scheme if some bounds of the system parameters are known. Furthermore, the resetting condition is relaxed to a certain extent for a certain class of reference trajectories. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.     

Convex modifications to an iterative learning control law

In this paper, a predictive norm-optimal iterative learning control algorithm from Amann, Owens, and Rogers (Int. J. Control 69 (2) (1998) 203-226) is analyzed. The main new result of this is that any of the predictive inputs from the predictive algorithm can be used in the control of the plant. This results in a faster convergence rate than that obtained with the approach proposed by Amann, Owens, and Rogers. Furthermore, the nature of the convergence of this new scheme is analysed in detail in terms of the free parameters of the algorithm.     

高阶无模型自适应迭代学习控制

针对一类非线性非仿射离散时间系统,提出了高阶无模型自适应迭代学习控制方案.控制器的设计和分析仅依赖于系统的输入/输出(I/O)数据,不需要已知任何其他知识.该方法采用了高阶学习律,可利用更多以前重复过程中的控制信息提高系统收敛性,且学习增益可通过"拟伪偏导数"更新律迭代调节.仿真结果验证了所提出算法的有效性.