Iterative Learning Control Scheme Research Articles

Robust adaptive learning for attitude control of rigid bodies with initial alignment errors

In the attitude tracking control tasks of rigid-body systems, initial alignment errors are recognized as one of the main factors that hinder the effective controller design and thus the control accuracy improvement. To overcome this difficulty, we develop a novel adaptive iterative learning control (ILC) scheme to achieve the attitude tracking control tasks with high precision for rigid bodies. Owing to the newly employed deadzone mechanism in the parametric updating law, the proposed adaptive ILC scheme is able to deal with initial alignment errors properly without imposing extra requirements to the system dynamics. Moreover, by utilizing the quaternion-based description in the system dynamics, various uncertainties, including external iteration-varying disturbances and unknown system parameters, can be addressed together by a single scalar estimation scheme. The convergence of the proposed adaptive ILC scheme is analyzed rigorously with a Lyapunov-like theory by virtue of newly introducing a modified composite energy function. In addition, to demonstrate its effectiveness, the proposed adaptive ILC method is applied to the attitude tracking of a spacecraft, which shows excellent control performances despite various uncertainties.

Equivalence and convergence of two iterative learning control schemes with state feedback

AbstractThis article considers the equivalence and convergence of two iterative learning control (ILC) schemes with state feedback for a class of multi‐input‐multi‐output discrete‐time nonlinear systems in which each desired trajectory corresponds to a unique desired input or an infinite number of desired inputs. First, we strictly prove that the two ILC schemes are equivalent if they have the identical initial system inputs. Moreover, by the input space transformation method and mathematical induction we establish the necessary and sufficient criterion for the convergence of system output, input and state sequences. It is shown that the (locally Lipschitz) continuity is enough to guarantee the (exponential) convergence. Generally, the learned desired input depends on the values of the initial signals, the learning gain matrix and the state feedback item. By designing them with appropriate structures, the dependence is disappeared. Third, we show how to leverage the available information of system dynamics to design the learning gain matrix and state feedback for better tracking performance. Finally, we provide an example to illustrate the usefulness of our findings, in which we introduce the energy of learnable desired input to evaluate the learning performance.

Event-triggered iterative learning control for linear time-varying systems

In this paper, an event-triggered P-type iterative learning control (ILC) scheme is developed, where the control input update only occurs in the event-triggered iterations. The event-triggered iterations are determined by a pre-defined event-triggering condition, which is composed of two parts, one is the threshold condition to ensure convergence, the other is derived from the Lyapunov stability principle to ensure stability. The convergence analysis theorem is deduced mathematically. Further, using similar steps, event-triggered PD-type ILC and event-triggered PID-type ILC are proposed. Finally, the simulation results illustrate that the presented algorithms can ensure that the error converges and make the control input update less frequently, so as to realise the goal of saving resources.

Iterative learning control for consensus of second-order multi-agent systems with interval uncertain topologies

Abstract This paper is devoted to the robust consensus tracking problem of second-order nonlinear multi-agent systems (MASs) with the interval uncertain topologies. For the second-order MASs including one leader agent and multiple follower agents, a control protocol is proposed by combining the iterative learning control scheme with the sliding mode control method. By analyzing the convergence of sliding mode variables, the consensus conditions including the unknown eigenvalues and the undetermined weight coefficient are obtained. In order to deal with the difficulties of weight coefficient design caused by the unknown eigenvalues of graphs, a min-max optimization problem is formulated based on the fastest convergence of the λ-norm of sliding mode variables, then the optimal weight coefficient is obtained by solving the min-max optimization problem. Moreover, for the undirected and directed interval uncertain graphs, two algorithms about the optimal weight coefficients are proposed, respectively. Finally, three numerical simulation examples are presented to demonstrate the effectiveness of the proposed methods.

Robust finite‐iteration tracking of discrete‐time systems in repetitive process setting via ILC scheme

AbstractIn this work, based on the robust iterative learning control (ILC) scheme, the finite‐iteration tracking control is investigated for discrete‐time linear systems in repetitive process setting with external disturbances. First, the concept of finite‐iteration tracking is defined. Then by utilizing the lifted‐vector‐matrix technique, the discrete‐time linear system can be reformulated as an input–output transmission equation. Moreover, a P‐type ILC scheme is employed, and then the finite‐iteration tracking of the resultant system is guaranteed with the designed iterative learning controller. Meanwhile, the settling iteration can be explicitly obtained. Particularly, the case of data loss occurred during information transmission is also studied, and sufficient conditions are presented such that the finite‐iteration tracking can be achieved in a finite interval. Lastly, the effectiveness and applicability of the presented method are validated via a numerical simulation.

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.

Analysis of PD‐type iterative learning control for discrete‐time singular system

It is eminent that iterative learning control algorithm is of high significance due to its speciality of tracking control for systems developed from real‐world phenomena that occurs repeatedly. Singular systems are well‐known for their applications in network analysis, biological systems, economic systems, social systems, engineering systems, time‐series analysis, and many other areas of science and technology. In this article, we investigate and analyze the convergence characteristic of PD‐type iterative learning control (ILC) scheme for linear discrete‐time singular system. We reformulate the discrete‐time singular system as a kind of algebraic input‐output transmission based on the lifted vector technique. The monotonic convergence has been deduced in the sense of 2‐norm for the first‐order as well as second‐order PD‐type ILC scheme. It is shown that the second‐order PD‐type ILC algorithm has good tracking performance than the first‐order on the whole time interval. Finally, we perform comparative analysis to validate the results numerically.

Quantisation compensated data-driven iterative learning control for nonlinear systems

This work presents a quantisation compensation-based data-driven iterative learning control (QC-DDILC) scheme by incorporating a uniform quantiser and an encoding–decoding mechanism (E-DM) to deal with the problem of limited communication resources in a networked control system. Since it is directly aimed at a nonlinear nonaffine system, an iterative dynamic linearisation method is employed to transfer it to a linear data model. Then, the QC-DDILC method is developed by the use of optimisation technique for the learning control law and the parameter updating law, respectively, where the quantised output from the E-DM is used. Since the direct output measurement of the system is unavailable, the linear data model is also acted as an iterative predictive model to estimate the system outputs utilised as the compensator in the consequent QC-DDILC. The proposed QC-DDILC is a data-driven method without relying on any explicit mechanism model information. The convergence analysis is conducted by using the mathematical tools of contraction mapping and induction. Simulations verify the theoretical results.

Adaptive Iterative Learning Control for High-Speed Train: A Multi-Agent Approach

The precise tracking control of high-speed train is an essential prerequisite to ensure the safety and comfort of the train. In this paper, an adaptive iterative learning control (ILC) scheme for the velocity and displacement tracking of high-speed train is proposed to handle the unknown time-varying parameters and lumped uncertainties. The composite energy function (CEF) method is used to analyze the stability of closed-loop system. Since the train usually runs on the same railway periodically, such as the same tunnels, slopes, bridges, etc., ILC is an inherent method for designing the tracking controller that is able to improve the operation performance of train iteratively. To the best of our knowledge, it is the first time that the multi-agent framework and ILC methodology are considered simultaneously in a single train, which can better reveal the coupled characteristic of adjacent cars and impose the repetitive operation pattern of train. The results of numerical simulations show that the tracking performance of the train toward the reference trajectory is significantly improved along with the increase of the number of operations.

Monotone convergence rate of norm‐optimal‐gain‐arguable iterative learning control for LDTI systems

AbstractFor a class of repetitive linear discrete‐time‐invariant (LDTI) systems, this paper exploits a norm‐optimal‐gain‐arguable iterative learning control (NOGAILC) scheme. For the scheme, the sequential performance index is additive quadratic norms of the tracking error vector and the incremental input vector, while the argument is the iteration‐time‐variable learning‐gain vector. To balance the importance of the incremental input vector and the tracking error vector, the sequential tuning factors are concerned. By means of matrix theory, the learning‐gain vector and the convergence rate are explicated that indicate that both the tracking error and the optimal performance index are linearly monotonically convergent and the NOGAILC with a smaller tuning factor delivers a faster convergence. Further, for the system parameters existing uncertainties, a quasi‐NOGAILC profile is established and the time‐domain rigorous derivation conveys that the quasi‐scheme is linearly monotonically convergent for the parameters uncertainties within a wider range. Numerical simulations testify the validity and the effectiveness.

Norm Optimal Iterative Learning Control for Non-Repetitive Trajectory Tracking of Servo System

This paper presents a novel control scheme that augments the Norm Optimal Iterative Learning Control (NOILC) with the Proportional Velocity (PV) feedback control in order to improve the non-repetitive trajectory tracking performance of servo system. According to Bode’s sensitivity integral, the performance of feedback controller is always limited due to the trade-off between the low frequency tracking and high frequency disturbance rejection. Hence, in order to address this so called “waterbed effect” and improve the transient and steady state performance of the motion control system, an optimal iterative learning control scheme based on the current cycle configuration is synthesized. For satisfying the performance objectives, which are formulated as a quadratic cost function with weighted norms, the monotonic convergence of the tracking error using the maximum singular value condition is discussed. Moreover, the asymptotic stability of the PV augmented NOILC is proved using the spectral norm condition. The efficacy of the proposed control scheme is experimentally validated on a rotary servo system using Hardware In Loop (HIL) testing. The experimental results of the proposed control scheme compared with the ones of the conventional feedback and ILC schemes highlight the improvement in trajectory tracking and robustness of the NOILC augmented PV control scheme.

Neural-Network-Based Iterative Learning Control for Hysteresis in a Magnetic Shape Memory Alloy Actuator

The typical characteristic of a magnetic shape memory alloy (MSMA)-based actuator is rate-dependent and stress-dependent hysteresis. In addition, the hysteresis in an MSMA-based actuator includes memory, multivalued mapping, and asymmetry properties, which seriously degrade the positioning accuracy. In this article, a feedforward neural network (FNN)-based nonlinear autoregressive moving average with exogenous inputs (NARMAX) model is employed to describe the hysteresis in an MSMA-based actuator. Through a Taylor expansion, it is revealed how the FNN constructs the nonlinear function of the NARMAX model. For the controller implementation, an FNN-based iterative learning control (ILC) strategy is proposed to achieve the desired tracking performance. The contributions of this study include exploring the update rule of the FNN-based ILC and analyzing the convergence properties of the proposed controller when the initial state of the system varies. To verify the effectiveness of the proposed method, experiments on an MSMA-based actuator were conducted. The results illustrate that the proposed modeling and control methods achieve an excellent performance and that the theoretical results are correct.

Iterative learning sliding mode control for output-constrained upper-limb exoskeleton with non-repetitive tasks

This paper investigates an iterative learning control scheme for a 5 degrees of freedom upper-limb exoskeleton with time-varying constraints. No priori knowledge of nonlinear dynamic parameters is needed in the modeling process by applying the iterative recursive method, thereby the time-consumption modelling work can be averted. Unlike most iterative learning algorithms that require identical initial condition between different iterations, the estimation errors of learning part in our work can be arbitrary small along the iterations under random initial status. To further improve the safety of human-robot system, a tan-type barrier Lyapunov function is utilized in convergence analysis to guarantee the constraint requirements of tracking errors between human body and robot. Furthermore, in order to handle the nonparametric uncertainties and external disturbances, sliding mode control strategy is constructed where the chattering phenomenon in control torques is suppressed by adaptive method. The stability over the time domain and convergence over the iterative domain are proved by composite energy function. Finally, comparative study and co-simulation results of Matlab/Simulink and ADAMS are presented to verify the advantages and effectiveness of proposed algorithm.

Iterative learning control of dispatchable grid-connected distributed energy resources for compensation of grid current harmonic distortions

This paper proposes a power regulation scheme for dispatchable grid-connected distributed energy resource (DER) units based on the iterative learning control (ILC) strategy. The proposed control provides fast and stable control of the real and reactive powers that the DER unit delivers to the grid. In addition, it compensates the harmonic distortion of the grid current caused by the local nonlinear loads and delivers a high quality power to the grid. To this end, the paper presents the mathematical model on which the proposed control is based, as well as the control design methodology. A new MIMO iterative learning control with perfect power tracking and harmonic rejection performance as well as minor measurement requirements is proposed. The performance of the proposed ILC strategy is demonstrated through time-domain simulation of a grid-connected DER unit under various operating scenarios, and it is compared with the performance of the conventional control based on the instantaneous power theory (IPT).

Data‐driven urban traffic model‐free adaptive iterative learning control with traffic data dropout compensation

In this paper, to fully utilize the urban traffic flow characteristics of similarity and repeatability without using a mathematical traffic model, a data-driven urban traffic control strategy based on model-free adaptive iterative learning control (MFAILC) scheme is put forward. Firstly, by dynamically linearizing the urban traffic dynamics along the iteration axis, the traffic network system is transformed into a MFAILC data model with the help of repetitive pattern of urban traffic flow. Then, the traffic controller is designed based on the derived MFAILC data model only using the I/O data of the traffic network. Finally, a traffic data compensation method is proposed to deal with data dropout problem. Simulation study verifies the feasibility and effectiveness of the proposed control method.

Iterative Learning Control for Multiphase Batch Processes With Asynchronous Switching

Asynchronous switching between the controller and the active subsystems in multiphase batch processes may cause the systems to be unstable around the switching instants. In view of this, an average dwell-time method-based iterative learning control (ILC) scheme is proposed in this paper. First, the multiphase process is represented as an equivalent closed-loop two-dimensional (2-D) switched system composed of stable and unstable subsystems, based on which new relevant concepts on the stability of the switched system are given. Second, using an average dwell-time method, the ILC law is designed to guarantee the system exponentially stable. Minimum running time for the stable subsystems and maximum running time for the unstable ones are obtained. Lastly, depending on the maximum time for the unstable subsystems, the idea of putting the controller switching step forward is proposed. In this way, the asynchronous switching is removed such that the unstable subsystem can be avoided. The case study on an injection molding process demonstrates the effectiveness and superiority of the proposed method in comparison with the existing 2D-MPC and one-dimensional traditional control methods.

Linearly monotonic convergence of nonlinear parameter‐optimal iterative learning control to linear discrete‐time‐invariant systems

AbstractIn this paper, a parameter‐optimal iterative learning control (POILC) scheme is developed for linear discrete‐time‐invariant systems with Markov parameters available. For the scheme the iteration‐time‐variable learning‐gain vector is assigned as the argument while the sequential performance index is consisting of the quadratic tracking error energy plus quadratic learning effort intensity weighed by the iteration‐varying tuning factor. By making use of matrix theory, the learning‐gain vector and the convergence rate are explicated which conveys that the POILC is a nonlinear scheme and is linearly monotonously convergent with the smaller tuning factors delivering the faster convergence. In particular, the linearly monotone convergences are respectively exploited for the extreme case when the tuning‐factor sequence is identically nullity and for the optimal performance index. Further, a quasi POILC is established which considers additive systematic parameters uncertainties in composing of the learning‐gain vector. Rigorous analysis indicates that the quasi POILC is linearly monotonically convergent within a wider uncertainty range which conveys that the POILC is robust to the system parameters uncertainties. Numerical simulations testify the validity and the effectiveness.

Data-Driven Iterative Learning Control for Nonlinear Discrete-Time MIMO Systems.

This article considers the tracking control of unknown nonlinear nonaffine repetitive discrete-time multi-input multi-output systems. Two data-driven iterative learning control (ILC) schemes are designed based on two equivalent dynamic linearization data models of an unknown ideal learning controller, which exists theoretically in the iteration domain. The two control schemes provide ways of selecting learning controllers based on the complexity of the controlled nonlinear systems. The learning control gain matrixes of the two learning controllers are optimized through the steepest descent method using only the measured input-output data of the nonlinear systems. The proposed ILC approaches are pure data-driven since no model information of the controlled systems is involved. The stability and convergence of the proposed ILC approaches are rigorously analyzed under reasonable conditions. Numerical simulation and an experiment based on a Gantry-type linear motor drive system are conducted to verify the effectiveness of the proposed data-driven ILC approaches.

Dual-Loop Iterative Learning Control of Robot Manipulator for Human-Robot cooperation

This paper proposed a dual-loop iterative learning control strategy for robot manipulator in the situation of repetitive human-robot interaction. By utilizing the contact force between the human and the manipulator, a force-based loop is first conducted to produce the unknown desired trajectory of the manipulator. According to Lyapunov’s method and using the back-stepping technique, an adaptive iterative learning controller is presented to fulfill the trajectory tracking task of the robot manipulator, in spite of the model uncertainties and the unknown disturbances. The proposed control scheme is verified by numerical simulation on a robot manipulator with two degrees-of-freedom.

Performance‐enhanced iterative learning control using a model‐free disturbance observer

This paper proposes a novel performance-enhanced iterative learning control (ILC) scheme using a model-free disturbance observer (DOB) to achieve high performance for precision motion systems that encounter non-repetitive disturbances. As is well known, the performance of the standard ILC (SILC) is severely degraded by the non-repetitive disturbances. By introducing DOB into SILC, this paper improves the robustness of the ILC system against non-repetitive disturbances. In the proposed enhanced ILC (EILC), SILC aims at learning the feedforward signals for a specific reference, while DOB is to compensate for external disturbances. Little or no plant model knowledge is required for SILC. To maintain this advantage after introducing DOB, a model-free design method for DOB is proposed to release the need for the plant model. Based only on a specific reference and the corresponding feedforward signals learned by SILC, the filter of DOB is optimized via an instrumental-variable estimate method. Numerical simulation is performed to illustrate the effectiveness and enhanced performance of the proposed control approach.