Data‐driven iterative learning control using a uniform quantizer with an encoding–decoding mechanism

In this paper, a new iterative learning algorithm is proposed for repetitive nonlinear systems. The control system employs a combination of state feedback and iterative learning control (ILC) in which the coefficients of states are learned similar to ILC methods. The control system is in a closed loop format both in iteration domain (because of ILC) and in time domain (because of feedback control) which improves the robustness of the conventional ILC. The convergence of the control algorithm is also proved. Finally, simulation results for a 5-DOF manipulator have been presented to illustrate that the proposed algorithm is more robust than a first order P type ILC method at the presence of white Gaussian noise as a nonrepeating disturbance.

In iterative learning control (ILC), it is usually assumed that the disturbances, uncertainties and the desired trajectories are invariant with respect to the iteration number or iteration-independent. In practice, this may not be true. How to accommodate the iteration-dependent disturbances, uncertainties and the desired trajectories is practically important for any successful application of ILC. In practice, it is observed that the baseline performance of ILC is limited mainly by the nonrepetitiveness factors. In this paper, by the proposed two methods, it is shown that one can harness or make use of the nonrepetitiveness in ILC to reduce the baseline errors. When the pattern of the nonrepetitiveness is known, an internal model principle (IMP) in the iteration domain can be applied. When the pattern of the nonrepetitiveness is unknown in advance, a disturbance observer in the iteration domain is proposed. It is noted that to harness the nonrepetitiveness in ILC, usually, the ILC updating law has to be high-order in the iteration direction. To facilitate our discussion, a supervector notion is adopted in a fairly general setting. Simulation examples are provided to illustrate the fact that nonrepetitiveness in ILC, if properly handled, can be harnessed to achieve a better performance previously not achievable.

An iterative learning control algorithm within prescribed input-output subspace

Iteration dependent interval based open‐closed‐loop iterative learning control for time varying systems with vector relative degree

Since they were first introduced by Arimoto, iterative learning control (ILC) methods have received lots of attention because of their effectiveness and briefness. In this paper, an open-closed-loop PID-type ILC scheme with bounded learning matrixes for the control of nonlinear time-varying systems are studied. Under a few reasonable restrictions that are very common, as in other ILC research papers on the convergence problem, sufficient conditions for guaranteeing the convergence of ILC systems are given and then proved with linear operator theory. Both the system and the ILC scheme described have very general forms. It is shown that the convergence condition is weaker than some known results for a similar ILC scheme.

When applied to the consensus tracking of repetitive leader-follower multiagent systems (MASs), most of existing distributed iterative learning control (DILC) methods assume that the dynamics of agents are exactly known or up to the affine form. In this article, we study a more general case where the dynamics of agents are unknown, nonlinear, nonaffine, and heterogeneous, and the communication topologies can be iteration-varying. More specifically, we first apply the controller-based dynamic linearization method in the iteration domain to obtain a parametric learning controller using only the local input-output data collected from neighboring agents in a directed graph, and then propose a data-driven distributed adaptive iterative learning control (DAILC) method through the parameter-adaptive learning methods. We show that for each time instant, the tracking error is ultimately bounded in the iteration domain for both of the cases with iteration-invariant and iteration-varying communication topologies. The simulation results show that the proposed DAILC method has faster convergence speed, higher tracking accuracy, and more robust learning and tracking in comparison with a typical DAILC method.

This paper reconsiders the iterative learning control (ILC) problem for variable trial lengths via compensating output data by using an auxiliary predictive model when the controlled process does not reach the desired trial length. Moreover, this paper aims to propose a general and data-driven ILC method without requiring any explicit mechanistic model information. Specifically, an iterative difference with state transition expression is performed at first over the desired trial length in iteration domain to build an auxiliary predictive model for the iterative input-output dynamics of the linear discrete-time system. Then, an auxiliary predictive compensation-based ILC (APC-ILC) method is presented by defining an expanded output variable in which the predictive output is incorporated to compensate the unavailable output data due to the shorter operation length. The learning gain is iteration-time-varying and is updated using real-time data to adapt to system changes. Furthermore, the proposed learning control law contains additional input information to further improve the control performance. Theoretical analysis and simulations further verify the effectiveness of the proposed APC-ILC.

This article investigates the iterative learning control problem for a class of nonlinear heterogeneous multi-agent systems. The main contribution of this article is to apply iterative learning control algorithm to the multi-agent systems with multiple leaders, and solve the containment control problem of multi-agent systems in the sense of iterative learning control stability. Based on the framework of communication topologies, distributed iterative learning controllers are designed. And when the iterative learning control laws are applied to the systems, the containment errors between the followers’ states and the convex hull spanned by the leaders’ states over a finite-time interval are bounded, and furthermore, the containment errors can converge to zero as the iteration index approaches to infinity in the absence of initial errors. A simulation example is finally constructed to verify the effectiveness of the theoretical method.

In this paper, a novel iterative learning control (ILC) algorithm is presented for a class of joint position constrained robot manipulator systems. Unlike the traditional ILC probelms, where the reference trajectory is iteration invariant, the reference trajectory in this work can be non-repetitive over the iteration domain. A tan-type time-varying Barrier Lyapunov Function (BLF) is proposed to deal with the constraint requirements which can be both time and iteration varying. We show that under the proposed ILC scheme, uniform convergence of the full state tracking error beyond a small time interval in each iteration can be guaranteed over the iteration domain, while the constraints on the joint position vector will not be violated during operation. An illustrative example is presented in the end to demonstrate the effectiveness of the proposed control scheme.

The repetitive processing and large quantity of single product represented by 3C products are urgently needed. However, for current processing operations, previous processing data have not been used in the optimization of control input. In order to utilize previous processing data to facilitate the next process and avoid adverse effects caused by repetitive disturbance and noise, the idea of iterative learning was introduced to improve the accuracy of machining. On the control level, since it is difficult to obtain high accuracy by traditional feedback control when faced with complex trajectories, an open-loop iterative learning controller and a position loop feedback controller were introduced, which worked fast with good convergence effects. Aiming at reducing the influence of accidental error, step type iterative learning was put forward. The iteration mechanism was stopped when the accuracy converged to the allowable range so as to reduce computational complexity, store the current iterative part of the control input, and make constant value compensation. However, in simulation and experiment, it was found that after superposition of the iterative learning controller, the phenomenon of partial divergence of the system tracking error occurred. Therefore, the speed and acceleration characteristics of input trajectories in time domain and frequency domain were analyzed. High-frequency noise was introduced in frequency domain, which was found to be the cause of the abovementioned phenomenon, and high-frequency components were filtered to solve the problem. To further improve the accuracy of convergence and avoid filtering effective high-frequency information in some area, a switchable filter based on the analysis of the frequency characteristics of input trajectory was proposed. Through SIMULINK simulation and dSPACE experimental verification, it was proved that the iterative learning controller of modifying controlled quantity and filter based iterative learning control method are effective.

In this paper, the uncertain model of the robotic system is decomposed into repetitive and non-repetitive parts, and the norm model of the system is taken into account. By using the Lyapunov method, an adaptive robust iterative learning control scheme is presented for the robotic system with both structured and unstructured uncertainty, and the overall stability of the system in the iteration domain is established. In the scheme the bound parameters estimated as well as the iterative learning control input are adjusted in the iteration domain. The validity of the scheme is illustrate through a simulation example.

In this article, we propose a data-driven iterative learning control (ILC) framework for unknown nonlinear nonaffine repetitive discrete-time single-input-single-output systems by applying the dynamic linearization (DL) technique. The ILC law is constructed based on the equivalent DL expression of an unknown ideal learning controller in the iteration and time domains. The learning control gain vector is adaptively updated by using a Newton-type optimization method. The monotonic convergence on the tracking errors of the controlled plant is theoretically guaranteed with respect to the 2-norm under some conditions. In the proposed ILC framework, existing proportional, integral, and derivative type ILC, and high-order ILC can be considered as special cases. The proposed ILC framework is a pure data-driven ILC, that is, the ILC law is independent of the physical dynamics of the controlled plant, and the learning control gain updating algorithm is formulated using only the measured input-output data of the nonlinear system. The proposed ILC framework is effectively verified by two illustrative examples on a complicated unknown nonlinear system and on a linear time-varying system.

In this paper, an adaptive iterative learning control (AILC) method combined with sliding mode technique is proposed to improve the force control performance for repeating tasks of fluidic muscle (FM) driven parallel manipulators. Different from the traditional iterative learning control method, the proposed AILC is to learn the controller time-varying parameters rather than to learn the control signals. Since the AILC is sensitive to non-repetitive disturbances, the sliding mode technique is introduced to enhance the robustness. Since no model information involved in the controller design, the proposed method is a complete data-driven method. Hence, the difficulty of obtaining accurate model is avoided. Simulation studies are performed on a two degrees of freedom FM driven parallel manipulator. Simulation results demonstrate that the proposed method can achieve high force tracking performance and robustness.

The paper analyze the mathematical model of ship steering system and propose a control algorithm of ship steering system based on iterative learning control. In the article, we describe the principle of iterative learning control, analyze the dynamic equation of ship steering system, and demonstrate the convergence of corresponding updating law. The numerical simulations show that iterative learning control overcomes the difficult to establish accurate mathematical model of the ship steering system, and improves learning control convergence and convergence rate, the algorithm is efficient and worthy.

This paper investigates the consensus tracking problem for the discrete multi-agent system (DMAS) with time-delay. By using iterative learning control (ILC) method and convergence in discrete system, the convergence properties for total system can be analyzed based on the time-domain analysis, frequency-domain analysis and matrix theory. The result shows that the proposed methods depend on each agent's self-delay time, the weights of the edges to each agent's neighbors, and the interconnection topology of the network. The iterative number of learning control relies on the sampling period and self-delay time for the discrete multi-agent system. Finally, numerical examples are presented to demonstrate the theoretical results.