Zuliani, Riccardo, Balta, Efe C., Rupenyan, Alisa et al. · ArXiv.org · 2025
Iterative learning control (ILC) improves the performance of a repetitive system by learning from previous trials. ILC can be combined with Model Predictive Control (MPC) to mitigate non-repetitive disturbances, thus improving overall system performance. However, existing approaches either assume perfect model knowledge or fail to actively learn system uncertainties, leading to conservativeness. To address these limitations we propose a binary mixed-integer ILC scheme, combined with a convex MPC scheme, that ensures robust constraint satisfaction, non-increasing nominal cost, and convergence to optimal performance. Our scheme is designed for uncertain nonlinear systems subject to both bounded additive stochastic noise and additive uncertain components. We showcase the benefits of our scheme in simulation.
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Lecture notes in control and information sciences · 2007
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Kirti D. Mishra, K. Srinivasan · 2020
Abstract Many forms of system uncertainty result in interval description of linear systems, and numerically efficient design methods for the computation of robust iterative learning controllers with good learning transients for these systems are lacking. Using a Lyapunov framework, two design procedures that ensure robust convergence of the tracking error to zero with good learning transients are described in this study. Both methods are validated numerically for an application of position control, and robust and monotonic convergence of the tracking error to zero is demonstrated.
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Meiyu Zhang, Panpan Gu, Senping Tian · International Journal of Systems Science · 2024
In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method.
Cited by 4
Farah Bouakrif · 2010
This paper presents an iterative learning control D-type for linear system to follow a reference model (also called desired system). This desired system doesn't have dependence with the model of the real system. In addition, the initial states of the two systems must not be necessarily equal. The λ-norm is adopted as the topological measure in our proof of the asymptotic stability of this control scheme, over the whole finite time-interval, when the iteration number tends to infinity. Simulation results are presented to illustrate the effectiveness of the proposed control scheme.
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이진수 · Open Access System for Information Sharing (Pohang University of Science and Technology) · 2018
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Merid Lješnjanin, Ying Tan, Denny Oetomo et al. · 2017
This paper proposes a novel Iterative Learning Control (ILC) framework for spatial tracking. Spatial tracking means that the temporal component is not fixed which violates the standing assumption on time intervals in traditional ILC. The proposed framework allows for the length of the time interval to change with each iteration. To relate the spatial information from the past to the present iteration, the concept of spatial projection is proposed. A class of nonlinear uncertain systems with input saturation is chosen for demonstration. An a appropriate ILC control law, exploiting the spatial projection idea, is proposed and the corresponding convergence analysis, based on the Composite Energy Function, is carried out. It is shown that spatial tracking is achieved under appropriate assumptions related to spatial projection and provided that the desired trajectory is realizable within the saturation bound. Finally, simulation results illustrate the predicted convergence.
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A. Hock, Angela P. Schoellig · Autonomous Robots · 2019
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Sven Pfeiffer, Gerwald Lichtenberg · IFAC Proceedings Volumes · 2013
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Na Lin, Ronghu Chi, Biao Huang · IEEE Transactions on Systems Man and Cybernetics Systems · 2024
This work aims at improving the control performance of the iterative learning control through set-point learning along iteration direction. A double-layered learning control mechanism is designed for both the control input and the set-point, respectively. The learning control of the input is regarded as a local controller in the inner layer, and the learning control of the set-point is designed as an auxiliary controller in the outer layer whose design is a main challenge since no any priori knowledge is available to describe the relationship between the set-point and the control performance. To solve this issue, an ideal nonlinear nonaffine set-point learning optimization (SPLO) algorithm is designed by taking the set-point and the tracking error as the arguments. Then, an iterative dynamic linearization (iDL) is introduced to formulate the ideal SPLO algorithm as a linear parametric one whose unknown parameter is estimated by designing a parameter updating algorithm. Further, since a strongly nonlinear and nonaffine system is considered without any model information available, the iDL is also used to derive its equivalent linear data model which is then updated by the input and output data to make the linear parametric SPLO realizable. Finally, a double-layered iterative learning control (DLILC) is proposed under the data-driven framework for tracking an iteration-varying trajectory. Convergence analysis and extensive simulations are included to demonstrate the effectiveness of the presented DLILC.
Cited by 6
Chen, Bin · ePrints Soton (University of Southampton) · 2022
Networked dynamical systems have found increasingly more applications during the last<br/>few decades, thanks to the significant reduction in the cost of sensing, computing and actuating technologies. Among them, there exists a class of networked dynamical systems<br/>working in a repetitive manner and requiring high control performance. As an example,<br/>next generation advanced manufacturing contains a large number of subsystems working<br/>together to perform a variety of manufacturing tasks repeatedly with high performance<br/>requirements. For such systems, traditional control methods have significant difficulties<br/>meeting the high performance requirements: centralised design does not scale well, while<br/>distributed methods mainly focus on asymptotic behaviour. In addition, they all require<br/>a highly accurate model which can be difficult/expensive to obtain in practice.<br/>Recently, iterative learning control (ILC), which ‘learns’ from the input and error information of the previous attempts of the same task without requiring an accurate model<br/>to generate the input, has been proposed as an alternative solution. However, most of<br/>the existing ILC design for networked dynamical systems have poor scalability, limited<br/>convergence performance, and also lack of the ability to deal with system constraints<br/>and more general task, e.g., point-to-point (P2P) task. To address these limitations, this<br/>thesis proposes novel distributed/decentralised optimisation-based ILC design methods.<br/>This thesis considers three design problems for networked dynamical systems, i.e., consensus tracking, formation control and collaborative tracking. We propose optimisation<br/>based ILC design methods using the idea of norm optimal ILC, and the proposed ILC<br/>methods show appealing convergence properties and certain degree of robustness to<br/>model uncertainties. Using the alternating direction method of multipliers (ADMM),<br/>all the designs can be implemented in the distributed/decentralised manner such that<br/>only local information is needed, allowing the proposed algorithms to be applied to large<br/>scale networked dynamical systems and have great scalability for dynamically growing<br/>network. These algorithms can also be extended to solve two unexplored problems in<br/>ILC design for networked dynamical systems, namely, constraint handling and P2P task.<br/>Numerical examples are given to illustrate the performance of the proposed algorithms
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Xiaoming Jiang, Yan Wang, Xin Li et al. · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2013
This paper presents a dual iterative learning control strategy for a dual stroke actuator system in the lithography scanner. The motion control strategy is employed, in which the trajectory of a short stroke stage is followed by one of a long stroke stage. A short stroke stage is used for improving the system response performance while a long stroke stage is introduced for the purpose of long motion stroke of the system. Combining the dynamic model of the system, the coupling effects between two actuators are analyzed, and the system model is simplified. This model is used for the design of a dual iterative learning control strategy and decoupling controllers. As a result, the heavy proportion of the recurrent coupling force on the long stroke stage is eliminated by the decoupling feedforward action from the output of the short stroke stage in the scanning process. The rest of the coupling force is removed by the first iterative learning control between two subsystems. The impact on the short stroke stage from the long stroke stage is weakened, and the short stroke stage is then designed independently by the two degree of freedom control strategy combining feedback control with the second iterative learning control. The convergence of the iterative learning control system is shown, and the effectiveness of the combined method is verified by a simulated wafer stage.
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Fang Zhong · 2001
A sampled data iterative learning control algorithm is proposed for continuous time systems with state delay. A condition under which the algorithm is exponential convergence is presented. The conclusion is proven by induction. It is shown that exponential convergence is achieved not only at every sampling instant but the entire time span. A numerical example shows the effectiveness of the proposed algorithm.
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Zhaoqiang Ge · 2025
Convergence of iterative learning control (ILC) algorithm for stochastic generalized systems is studied in the sense of integral solution in separable Hilbert spaces. It is proved with stochastic equation theory and GE-semigroup theory that the convergence of input error and tracking error is bounded in the mean square sense, respectively.
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Mouhacine Benosman, Amir‐massoud Farahmand, Meng Xia · International Journal of Adaptive Control and Signal Processing · 2018
Summary In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach : we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model . We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller . We show the efficiency of this approach on a two‐link robot manipulator numerical example.
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Abdelhamid Tayebi · International Journal of Adaptive Control and Signal Processing · 2006
Abstract 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.
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Jian‐Xin Xu · International Journal of Control · 2011
In this article we review the recent advances in iterative learning control (ILC) for nonlinear dynamic systems. In the research field of ILC, two categories of system nonlinearities are considered, namely, the global Lipschitz continuous (GLC) functions and local Lipschitz continuous (LLC) functions. ILC for GLC systems is widely studied and analysed using contraction mapping approach, and the focus of recent exploration moves to application problems, though a number of theoretical issues remain open. ILC for LLC systems is currently a hot area and the recent research focuses on ILC design and analysis by means of Lyapunov approach. The objectives of this article are to introduce recent development and advances in nonlinear ILC schemes, highlight their effectiveness and limitations, as well as discuss the directions for further exploration of nonlinear ILC.
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Cong Wang, Zining Wang, Cheng Peng et al. · 2015
Industrial servo systems usually have high gear ratio reducers, which introduce flexibility and transmission errors. The consequential vibrations and compliance bring difficulties to many demanding applications. For applications in which the servos move repetitively, iterative learning control (ILC) is a powerful tool to improve performance. An intuitive implementation of ILC for flexibility compensation involves combining a torque ILC with a motor reference ILC. This paper explains why such a direct combination does not work well. A systematic synthesis method is introduced to address the coupling between torque learning and reference learning. In addition, a robust control method is proposed to address system uncertainties. The proposed method is demonstrated using a servo control example.
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Dahui Luo, JinRong Wang, Dong Shen et al. · Journal of the Franklin Institute · 2019
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Cao Wei, Ming Sun · Acta Physica Sinica · 2014
Aiming at the problem of trajectory tracking in a class of discrete time-varying switched system with arbitrary sequence, in this paper we propose a discrete iterative learning control algorithm. Under the precondition that the switched sequence does not change along the iterative axis but it does along the time axis, this algorithm divides the whole finite time region into several finite subintervals, and uses -norm to prove the convergence strictly, and provides the sufficient convergent condition of the algorithm in the norm form. This method not only realizes the complete tracking for a discrete time-varying switched system within a limited time, but also has a simple structure easy to be realized in engineering. Simulation results verify the validity of the method.
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