Iterative Learning Control Problem Research Articles

Iterative learning control for non-normal and biased measured targets

In the original iterative learning control (ILC) algorithm, it is commonly assumed that the target signal remains constant throughout iterations. However, this assumption may not be satisfied in practical industrial applications. Therefore, this paper proposes a novel ILC approach for non-normal and biased measured targets, in which the target is not predetermined by a fixed curve or formula but generated from the generation system. The iterative learning control problem is first formulated, followed by algorithm implementation through mechanism analysis, process determination, and assessments for feasibility and convergence. The proposed algorithm is simulated subsequently. Results demonstrate that application of this algorithm can effectively minimize expected error between non-normal and biased measured targets and output. After a sufficient number of iterations, the tracking error will originate solely from the trajectory itself.

Robust data‐driven iterative learning control for nonlinear cyber‐physical systems

AbstractThis article mainly studies the problem of the robust security iterative learning control for nonlinear cyber‐physical systems, which suffer from external disturbances and denial‐of‐service (DoS) attacks. First, the nonlinear system can be transformed into an iterative linear data model, which is only used for the controller parameter design and the stability analysis without the physical meaning. Then, an extended state observer is introduced to estimate external disturbances along the iteration axis. At the same time, considering the influence of DoS attacks, an attack compensation mechanism is designed for DoS attacks along the iteration axis. In addition, an iterative‐varying penalty is designed to accelerate the convergence of the tracking error. Further, the mathematical induction is used to decouple the control input from the tracking error and the compression mapping principle is utilized to prove that the tracking error is ultimately bounded under the influence of disturbances and DoS attacks. Finally, the main results are verified by the motor simulation.

Extension of iterative learning control design for batch processes with time-delay in the input subject to random cycle-varying uncertainties

For uncertain time-delay batch processes with repetitive nature, this work deals with an unresolved problem of robust iterative learning control (ILC) design, in which we simultaneously remove the conventional assumptions of cycle-invariant uncertainties in reference trajectories, initial states, external disturbances, process dynamics, and time-delay. Moreover, we consider the variation of all existing uncertainties from a random point of view. Based on the idea of the internal model control (IMC) and indirect ILC, a novel IMC-based ILC structure is proposed. Then, we derive the practical convergence conditions, which have two design functions. By introducing a simple method for adjusting these functions, not only can we ensure that the expected tracking error converges monotonically to zero-neighborhood (in the L2-norm sense) but we can also achieve an acceptable convergence rate. Moreover, it is shown that the satisfaction of derived convergence conditions can always be guaranteed for any process. Simulation tests are provided to demonstrate the effectiveness of the proposed design.

Alternating projection‐based iterative learning control for discrete‐time systems with non‐uniform trial lengths

AbstractThis article develops a novel framework for iterative learning control (ILC) design of discrete‐time systems with non‐uniform trial lengths by using the method of alternating projections. In contrast to existing results for the non‐uniform trial length problem, this article uses the Hilbert space setting and hence the linear discrete‐time system dynamics with non‐uniform trial lengths can be represented by multiple affine subspaces (or linear varieties). Motivated by the successive projection design between two closed convex sets, the considered ILC problem can be transformed into alternating projections between multiple sets, then the Hilbert space setting is used to establish key systems theoretic properties. Moreover, an optimal ILC design is developed for systems with non‐uniform trial lengths, which is also extended to the case of input constraints. A numerical case study is given to illustrate the applicability of the new design.

Emerging robust and data‐driven control methods for uncertain learning systems

Emerging robust and data‐driven control methods for uncertain learning systems

Robust convergence conditions of iterative learning control for time‐delay systems under random non‐repetitive uncertainties

Some of the most fundamental assumptions in the design of iterative learning control (ILC) for uncertain systems are the strict repetitiveness (i.e. iteration-independence) of uncertainties in all factors of plant dynamic, external disturbances, initial conditions, and reference trajectory, which may not always hold in practical applications. The simultaneous relaxation of all these assumptions is a challenging problem that has been addressed only for delay-free systems. This problem is still open for time-delay systems, especially when the time-delay factor also has non-repetitive (i.e. iteration-dependent/varying) uncertainty. Hence, this study extends the problem of robust ILC for a class of time-delay systems under nonrepetitive uncertainties in not only plant dynamic, external disturbances, initial conditions, and reference trajectory but also time-delay. By using the ILC scheme introduced in this work, and based on the frequency domain analysis, it is shown that both monotonic convergence and boundedness of the expected tracking error can be achieved (in the sense of L2-norm) when the non-repetitiveness (i.e. iteration-dependence) of all existing uncertainties from a random viewpoint are taken into account. The effectiveness of the proposed strategy is verified by two simulation examples.

Robust decentralized iterative learning control for large‐scale interconnected systems described by 2‐D Fornasini–Marchesini systems with iteration‐dependent uncertainties including boundary states, disturbances, and reference trajectory

SummaryThis article first investigates robust iterative learning control (ILC) problem of a class of large‐scale interconnected systems, which consist of many subsystems described by two‐dimensional linear discrete first Fornasini–Marchesini systems with iteration‐dependent uncertainties arising from not only boundary states, disturbances, but also reference trajectory. A decentralized P‐type ILC law without any information exchanges with other subsystems is proposed such that the ultimate ILC tracking error of each subsystem can converge to a bounded range, the bound of which depends continuously on the bounds of all iteration‐dependent uncertainties considered. Especially, if these iteration‐dependent uncertainties are convergent progressively along the iteration direction, perfect ILC tracking on 2‐D reference trajectory can be obtained. Additionally, a modified ILC law with compensation technique is used to a class of large‐scale interconnected systems composed of many subsystems represented by two‐dimensional linear discrete second Fornasini–Marchesini systems. Two simulation examples are used to demonstrate the effectiveness and validity of the obtained ILC results. Finally, some comparative discussions are given.

Event-Triggered Model-Free Adaptive Iterative Learning Control for a Class of Nonlinear Systems Over Fading Channels.

This article investigates the problem of event-triggered model-free adaptive iterative learning control (MFAILC) for a class of nonlinear systems over fading channels. The fading phenomenon existing in output channels is modeled as an independent Gaussian distribution with mathematical expectation and variance. An event-triggered condition along both iteration domain and time domain is constructed in order to save the communication resources in the iteration. The considered nonlinear system is converted into an equivalent linearization model and then the event-triggered MFAILC independent of the system model is constructed with the faded outputs. Rigorous analysis and convergence proof are developed to verify the ultimately boundedness of the tracking error by using the Lyapunov function. Finally, the effectiveness of the presented algorithm is demonstrated with a numerical example and a velocity tracking control example of wheeled mobile robots (WMRs).

A Fuzzy System Based Iterative Learning Control for Nonlinear Discrete-Time Systems with Iteration-Varying Uncertainties

In this paper, we consider an iterative learning control problem for a class of unknown discrete-time nonlinear systems with iteration-varying initial error, iteration-varying system parameters, iteration-varying external disturbance, iteration-varying desired output, and iteration-varying control direction. These iteration-varying uncertainties are not required to take any particular structure such as the high-order internal model and only need to satisfy certain boundedness conditions. We propose an iterative learning control law with an adaptive iteration-varying fuzzy system to overcome all the uncertainties and achieve the learning control objective. Furthermore, we present a sufficient condition for designing adaptive gains and prove the convergence of the learning error to a small value as the trial number is large enough. Finally, we use two simulation examples to demonstrate all the theoretical results.

Data-Based Security Fault Tolerant Iterative Learning Control under Denial-of-Service Attacks

This paper mainly studies the data-based security fault tolerant iterative learning control (SFTILC) problem of nonlinear networked control systems (NCSs) under sensor failures and denial-of-service (DoS) attacks. Firstly, the radial basis function neural network (RBFNN) is used to approximate the sensor failure function and a DoS attack compensation mechanism is proposed in the iterative domain to lessen the impact of DoS attacks. Then, using the dynamic linearization technology, the nonlinear system considering failures and network attacks is transformed into a linear data model. Further, based on the designed linearization model, a new data-based SFTILC algorithm is designed to ensure the satisfactory tracking performance of the system. This process only uses the input and output data of the system, and the stability of the system is proved by using the compression mapping principle. Finally, a digital simulation is used to demonstrate the effectiveness of the proposed SFTILC algorithm.

Adaptive iterative learning control for high-order nonlinear systems with random initial state shifts

Aiming at the tracking problem for a class of high-order nonlinear systems with arbitrary initial state, this paper proposes different initial state shifts rectifying schemes for systems with different orders from the perspective of solving differential equations to ensure that the systems achieve complete tracking over the specified interval. This method relaxes the requirement of initial positioning in iterative learning control, and solves the problem of iterative learning control for high-order nonlinear systems with arbitrary initial state error. The theoretical analysis shows that the proposed schemes can make all signals in the system bounded, and ensure that the tracking error in the preset interval tends to zero as the number of iterations increases. When designing the controller, the arctangent function is used to avoid flutter of the control signal and related variables. The final simulations verify the effectiveness of the proposed algorithms.

Iterative learning control for impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices

SummaryWe introduce an impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices whose solution is given by delayed perturbation of Mittag–Leffler type matrix function. The existence and uniqueness of the solution of the system is proved by using Banach contraction principle. The Ulam–Hyers stability of the given system below are demonstrated. Construct the iterative learning control (ILC) problem obtaining from the mentioned system. The conditions of convergence of ILC problem of each of P, D, and ‐types are presented and proved. A comprehensive example with three different original reference trajectories is given to illustrate some theoretical results. This article provides novel outcomes.

Iterative learning control for repetitive tasks with randomly varying trial lengths using successive projection

SummaryThis article proposes an effective iterative learning control (ILC) approach based on successive projection scheme for repetitive systems with randomly varying trial lengths. A modified ILC problem is formulated to extend the classical ILC task description to incorporate a randomly varying trial length, while its design objective considers the mathematical expectation of its tracking error to evaluate the task performance. To solve this problem, this article employs the successive projection framework to give an iterative input signal update law by defining the corresponding convex sets based on the design requirements. This update law further yields an ILC algorithm, whose convergence properties are proved to be held under mild conditions. In addition, the input signal constraint can be embedded into the design without violating the convergence properties to obtain an alternative algorithm. The performance of the proposed algorithms is verified using a numerical model to show the effectiveness at occasions with and without input constraints.

Barrier Adaptive Iterative Learning Control for Tank Gun Control Systems Under Nonzero Initial Error Condition

In this paper, a barrier adaptive iterative learning control scheme is proposed to solve the trajectory-tracking problem for tank gun control systems under nonzero initial error condition. A novel construction method of rectified reference trajectory is presented for dealing with the initial position problem of iterative learning control for tank gun control systems. With a quadratic form barrier Lyapunov function adopted to controller design, the quadratic form of system error is constrained within the preset range during each iteration. Adaptive iterative learning control technique and robust control technique are jointly used to compensate for the parametric/nonparametric uncertainties and nonsymmetric deadzone nonlinearity. As the iteration number increases, the system state of tank gun control systems may accurately track the rectified reference trajectory, which leads to a excellent tracking performance during the part operation interval of tank gun control systems. Simulation results are presented to verify the effectiveness of the proposed barrier adaptive iterative control scheme.

Filtering-Error Constrained Angle Tracking Adaptive Learning Fuzzy Control for Pneumatic Artificial Muscle Systems Under Nonzero Initial Errors

In this paper, a filtering-error constrained adaptive iterative learning control scheme is proposed to solve the angle tracking problem for a pneumatic artificial muscle-actuated mechanism. The adaptive learning controller is designed by a novel barrier Lyapunov function, and the filtering error of pneumatic artificial muscle system is ensured to be constrained during each iteration. The initial position problem of iterative learning control is solved by utilizing time-varying boundary layer method. Fuzzy logic system is applied to approximate the unknown nonparametric uncertainties in the pneumatic artificial muscle system, whose optimal weight is estimated by using difference learning approach. The approximation error of fuzzy logic system is tackled by robust control strategy. Simulation results show the effectiveness of the propose angle tracking adaptive learning fuzzy control scheme.

Consensus-based iterative learning of heterogeneous agents with application to distributed optimization

This paper deals with the distributed iterative learning control (ILC) problem of leaderless consensus in a network of heterogeneous nonlinear agents. For a general case that the topology graph is dynamically changing with respect to both iteration and time axes, an ILC-based consensus protocol is designed for each agent by utilizing its control input and neighboring information from the last iteration. It is shown that under a basic joint spanning tree condition, the states of all agents can exponentially agree on a common trajectory along the iteration axis. Interestingly, by the appropriate design of the agents’ dynamics, it is found that the consensus trajectory and the network state can approach the unique optimal point of a convex optimization problem as the time evolves. Simulations demonstrate the validity of the proposed algorithms and theoretical analysis.

ILC for Non-Linear Hyperbolic Partial Difference Systems

This paper discusses the iterative learning control problem for a class of non-linear partial difference system hyperbolic types. The proposed algorithm is the PD-type iterative learning control algorithm with initial state learning. Initially, we introduced the hyperbolic system and the control law used. Subsequently, we presented some dilemmas. Then, sufficient conditions for monotone convergence of the tracking error are established under the convenient assumption. Furthermore, we give a detailed convergence analysis based on previously given lemmas and the discrete Gronwall’s inequality for the system. Finally, we illustrate the effectiveness of the method using a numerical example.

Robust high-order iterative learning control approach for two-dimensional linear discrete time-varying Fornasini–Marchesini systems with iteration-dependent reference trajectory

This paper first investigates robust tracking problem of a high-order iterative learning control (HOILC) algorithm for two classes of two-dimensional linear discrete time-varying Fornasini–Marchesini systems (2-D LDTVFMS) and 2-D LDTVFMS with input delays with iteration-dependent reference trajectory described by a high-order internal model (HOIM) operator, boundary states and disturbances. An extended high-order linear discrete inequality is proposed to guarantee the ILC tracking error of 2-D LDTVFMS converge robustly to a bounded range, the bound of which is relied on iteration-dependent uncertainties from reference trajectory, boundary states and disturbances. A simulation example on a practical thermal process is used to validate the effectiveness and feasibility of the proposed HOILC law. Additionally, it is verified by theory analysis and simulation that no matter how the ILC controller gain is selected, the convergence condition in Theorem 2 of Wan and Li [(2021). High-order internal model based iterative learning control for 2-D linear FMMI systems with iteration-varying trajectory tracking. IEEE Transactions on Systems Man and Cybernetics: Systems, 51, 1462–1472] is not satisfied. Using the proposed HOILC law, perfect tracking result in Theorem 2 of Wan and Li (2021) can be obtained.

Robust ILC of Nonlinearly Parametric Time-Delay Systems with Input Deadzone

The trajectory tracking problem for a class of nonlinearly parametric systems with input deadzone and time-delay is studied in this work. An adaptive iterative learning control (ILC) scheme is developed by using Lyapunov synthesis. The alignment condition is applied to solve the initial position problem of ILC. Robust control and ILC are used to deal with input deadzone, delay and nonlinearly parametric uncertainties, together. As the iteration learning cycle increases, the system state may precisely track the reference signal over the whole interval. A numerical simulation is presented to verify the efficacy of the proposed adaptive iterative learning control method.

Iterative learning control of air pressure variation inside a high-speed train under the excitation of the tunnel pressure wave with a fixed-morphologic form

Based on the characteristics that the tunnel pressure wave has a fixed-morphologic form when the same train passes through the same tunnel, an applicational approach based on the iterative learning control (ILC) is developed, aiming at overcoming the drawbacks of the traditional strategy for controlling the air pressure variation inside a high-speed train carriage. To achieve the goal, the control system is mathematically modelled. Then, the problem is formulated. The task of suppressing the influence of the tunnel pressure wave on the air pressure inside the carriages is shifted as an ILC problem of tracking the comfort index with varying trial length. The algorithm of refreshing the control signal from trial to trial is determined and the process of ILC control is designed. Next, the convergence of the newly-developed applicational ILC algorithm is discussed and the algorithm is simulated by the simulation signal and field-test signal. Results show that the applicational ILC algorithm be more adaptable in handling the control of the air pressure inside carriage under the excitation of varying-amplitude, varying-scale and varying-initial-states tunnel pressure wave. Meanwhile, the matching with tunnel pressure wave makes the applicational ILC algorithm will take both the riding comfort and fresh air into consideration, which upgrades the performances when the high-speed train passing through long tunnels.