Noise-Tolerant ZNN-Based Data-Driven Iterative Learning Control for Discrete Nonaffine Nonlinear MIMO Repetitive Systems

Aiming at the tracking problem of a class of discrete nonaffine nonlinear multi-input multi-output(MIMO) repetitive systems subjected to separable and nonseparable disturbances, a novel data-driven iterative learning control(ILC) scheme based on the zeroing neural networks(ZNNs) is proposed. First, the equivalent dynamic linearization data model is obtained by means of dynamic linearization technology, which exists theoretically in the iteration domain. Then, the iterative extended state observer(IESO) is developed to estimate the disturbance and the coupling between systems, and the decoupled dynamic linearization model is obtained for the purpose of controller synthesis. To solve the zero-seeking tracking problem with inherent tolerance of noise,an ILC based on noise-tolerant modified ZNN is proposed. The strict assumptions imposed on the initialization conditions of each iteration in the existing ILC methods can be absolutely removed with our method. In addition, theoretical analysis indicates that the modified ZNN can converge to the exact solution of the zero-seeking tracking problem. Finally, a generalized example and an application-oriented example are presented to verify the effectiveness and superiority of the proposed process.

A Modified Iterative Learning Control Approach for the Active Suppression of Rotor Vibration Induced by Coupled Unbalance and Misalignment

This paper proposes a modified iterative learning control(MILC)periodical feedback-feedforward algorithm to reduce the vibration of a rotor caused by coupled unbalance and parallel misalignment.The control of the vibration of the rotor is provided by an active magnetic actuator(AMA).The iterative gain of the MILC algorithm here presented has a self-adjustment based on the magnitude of the vibration.Notch filters are adopted to extract the synchronous(1×Ω)and twice rotational frequency(2×Ω)components of the rotor vibration.Both the notch frequency of the filter and the size of feedforward storage used during the experiment have a real-time adaptation to the rotational speed.The method proposed in this work can provide effective suppression of the vibration of the rotor in case of sudden changes or fluctuations of the rotor speed.Simulations and experiments using the MILC algorithm proposed here are carried out and give evidence to the feasibility and robustness of the technique proposed.

Data-Driven Learning Control Algorithms for Unachievable Tracking Problems

For unachievable tracking problems, where the system output cannot precisely track a given reference, achieving the best possible approximation for the reference trajectory becomes the objective. This study aims to investigate solutions using the Ptype learning control scheme. Initially, we demonstrate the necessity of gradient information for achieving the best approximation.Subsequently, we propose an input-output-driven learning gain design to handle the imprecise gradients of a class of uncertain systems. However, it is discovered that the desired performance may not be attainable when faced with incomplete information.To address this issue, an extended iterative learning control scheme is introduced. In this scheme, the tracking errors are modified through output data sampling, which incorporates lowmemory footprints and offers flexibility in learning gain design.The input sequence is shown to converge towards the desired input, resulting in an output that is closest to the given reference in the least square sense. Numerical simulations are provided to validate the theoretical findings.

Adaptive state-constrained/model-free iterative sliding mode control for aerial robot trajectory tracking

This paper develops a novel hierarchical control strategy for improving the trajectory tracking capability of aerial robots under parameter uncertainties.The hierarchical control strategy is composed of an adaptive sliding mode controller and a model-free iterative sliding mode controller(MFISMC).A position controller is designed based on adaptive sliding mode control(SMC)to safely drive the aerial robot and ensure fast state convergence under external disturbances.Additionally,the MFISMC acts as an attitude controller to estimate the unmodeled dynamics without detailed knowledge of aerial robots.Then,the adaption laws are derived with the Lyapunov theory to guarantee the asymptotic tracking of the system state.Finally,to demonstrate the performance and robustness of the proposed control strategy,numerical simulations are carried out,which are also compared with other conventional strategies,such as proportional-integralderivative(PID),backstepping(BS),and SMC.The simulation results indicate that the proposed hierarchical control strategy can fulfill zero steady-state error and achieve faster convergence compared with conventional strategies.

Fundamental Trackability Problems for Iterative Learning Control

Generally, the classic iterative learning control(ILC)methods focus on finding design conditions for repetitive systems to achieve the perfect tracking of any specified trajectory,whereas they ignore a fundamental problem of ILC: whether the specified trajectory is trackable, or equivalently, whether there exist some inputs for the repetitive systems under consideration to generate the specified trajectory? The current paper contributes to dealing with this problem. Not only is a concept of trackability introduced formally for any specified trajectory in ILC, but also some related trackability criteria are established. Further, the relation between the trackability and the perfect tracking tasks for ILC is bridged, based on which a new convergence analysis approach is developed for ILC by leveraging properties of a functional Cauchy sequence(FCS). Simulation examples are given to verify the effectiveness of the presented trackability criteria and FCS-induced convergence analysis method for ILC.

Iterative Learning Control for Discrete-time Stochastic Systems with Quantized Information

An iterative learning control(ILC) algorithm using quantized error information is given in this paper for both linear and nonlinear discrete-time systems with stochastic noises. A logarithmic quantizer is used to guarantee an adaptive improvement in tracking performance. A decreasing learning gain is introduced into the algorithm to suppress the effects of stochastic noises and quantization errors. The input sequence is proved to converge strictly to the optimal input under the given index. Illustrative simulations are given to verify the theoretical analysis.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.

Stochastic Iterative Learning Control With Faded Signals

Stochastic iterative learning control(ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists.Illustrative examples are provided to verify the effectiveness of the proposed schemes.

Stability of Iterative Learning Control with Data Dropouts via Asynchronous Dynamical System

In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control (ILC) system with data dropouts can be modeled as an asynchronous dynamical system with rate constraints on events in the iteration domain. The stability condition is provided in the form of linear matrix inequalities (LMIS) depending on the stability of asynchronous dynamical systems. The analysis is supported by simulations.

Iterative Learning Control for a Class of Linear Discrete-time Switched Systems

在这份报纸，反复的学习控制(ILC ) 与任意的切换的信号为线性分离时间的交换系统的一个类被考虑。交换系统重复地在有限时间间隔期间被操作，这被假定，然后第一个顺序 P 类型 ILC 计划能被用来完成完美的追踪在上自始至终间隔。由超级向量途径，为在重复领域的如此的 ILC 系统的一个集中条件能被给。理论分析被模拟支持。

Iterative Learning Control for homing guidance design of missiles

This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is appreciated with respect to a previous published base controller for comparison, this strategy, which is simple to realize, is able to reduce the time to reach the head-on condition to target destruction. This fact is important to minimize the missile lateral force-level to fulfill engaging in hyper-sonic target persecutions.

Robust iterative learning control for nonlinear systems with measurement disturbances

The iterative learning control (ILC) has been demon-strated to be capable of considerably improving the tracking perfor-mance of systems which are affected by the iteration-independent disturbance. However, the achievable performance is greatly degraded when iteration-dependent, stochastic disturbances are pre-sented. This paper considers the robustness of the ILC algorithm for the nonlinear system in presence of stochastic measurement disturbances. The robust convergence of the P-type ILC algorithm is firstly addressed, and then an improved ILC algorithm with a decreasing gain is proposed. Theoretical analyses show that the proposed algorithm can guarantee that the tracking error of the nonlinear system tends to zero in presence of measurement dis-turbances. The analysis is also supported by a numerical example.

Compensation of hysteresis in piezoelectric actuator with iterative learning control

This paper presents the application of iterative learning control (ILC) to compensate hysteresis in a piezoelectric actuator. The proposed controller is a hybrid of proportional-integral-differential (PID) control, whose main function is for trajectory tracking, and a chatter-based ILC, whose main function is for hysteresis compensation. Stability analysis of the proposed ILC is presented, with the PID included in the dynamic of the piezoelectric actuator. The performance of the proposed controller is analysed through simulation and verified with experiment with a piezoelectric actuator.

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Iterative Learning Control for Distributed Parameter Systems Based on Non-Collocated Sensors and Actuators

In this paper, an open-loop PD-type iterative learning control(ILC) scheme is first proposed for two kinds of distributed parameter systems(DPSs) which are described by parabolic partial differential equations using non-collocated sensors and actuators. Then, a closed-loop PD-type ILC algorithm is extended to a class of distributed parameter systems with a non-collocated single sensor and m actuators when the initial states of the system exist some errors. Under some given assumptions, the convergence conditions of output errors for the systems can be obtained. Finally, one numerical example for a distributed parameter system with a single sensor and two actuators is presented to illustrate the effectiveness of the proposed ILC schemes.

Iterative Learning Control With Incomplete Information： A Survey

This paper conducts a survey on iterative learning control(ILC) with incomplete information and associated control system design, which is a frontier of the ILC field.The incomplete information, including passive and active types,can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection,storage, transmission, and processing, such as data dropouts,delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects:the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory.

Error analysis for remote nonlinear iterative learning control system with wireless channel noise

In this paper, the iterative learning control problem is considered for a class of remote control system over wireless network communication channel. The control performance of remote iterative learning control (R-ILC) system is analyzed and an error boundary of the stable output of the R-ILC system is obtained for the boundary stochastic noise channel. Finally, we obtain some rules to reduce the ?uctuation caused by wireless channel noise through the analysis results for ?uctuation boundary. The simulation results prove the proposed rule is correct.

2D multi-model general predictive iterative learning control for semi-batch reactor with multiple reactions

Batch to batch temperature control of a semi-batch chemical reactor with heating/cooling system was discussed in this study. Without extensive modeling investigations, a two-dimensional(2D) general predictive iterative learning control(2D-MGPILC) strategy based on the multi-model with time-varying weights was introduced for optimizing the tracking performance of desired temperature profile. This strategy was modeled based on an iterative learning control(ILC) algorithm for a 2D system and designed in the generalized predictive control(GPC) framework. Firstly, a multi-model structure with time-varying weights was developed to describe the complex operation of a general semi-batch reactor. Secondly, the 2 D-MGPILC algorithm was proposed to optimize simultaneously the dynamic performance along the time and batch axes. Finally, simulation for the controller design of a semi-batch reactor with multiple reactions was involved to demonstrate that the satisfactory performance could be achieved despite of the repetitive or non-repetitive disturbances.

Fuzzy iterative learning control of electro-hydraulic servo system for SRM direct-drive volume control hydraulic press

A new kind of volume control hydraulic press that combines the advantages of both hydraulic and SRM(switched reluctance motor) driving technology is developed.Considering that the serious dead zone and time-variant nonlinearity exist in the volume control electro-hydraulic servo system,the ILC(iterative learning control) method is applied to tracking the displacement curve of the hydraulic press slider.In order to improve the convergence speed and precision of ILC,a fuzzy ILC algorithm that utilizes the fuzzy strategy to adaptively adjust the iterative learning gains is put forward.The simulation and experimental researches are carried out to investigate the convergence speed and precision of the fuzzy ILC for hydraulic press slider position tracking.The results show that the fuzzy ILC can raise the iterative learning speed enormously,and realize the tracking control of slider displacement curve with rapid response speed and high control precision.In experiment,the maximum tracking error 0.02 V is achieved through 12 iterations only.