ON HYBRID POSITION/FORCE COORDINATED LEARNING CONTROL OF MULTIPLE MANIPULATORS

In this paper, coordinated control of multiple robot manipulators holding a rigid object is discussed. In consideration of inaccuracy of the dynamic model of a multiple manipulator system, the error equations on object position and internal force are derived. Then a hybrid position/force coordinated learning control scheme is presented and its convergence is proved. The scheme can improve the system performance by modifying the control input of the system after each iterative learning. Simulation results of two planar robot manipulators holding an object show the effectiveness of this control scheme.

Observer-based Iterative and Repetitive Learning Control for a Class of Nonlinear Systems

In this paper, both output-feedback iterative learning control(ILC) and repetitive learning control(RLC) schemes are proposed for trajectory tracking of nonlinear systems with state-dependent time-varying uncertainties. An iterative learning controller, together with a state observer and a fully-saturated learning mechanism, through Lyapunov-like synthesis, is designed to deal with time-varying parametric uncertainties. The estimations for outputs, instead of system outputs themselves, are applied to form the error equation, which helps to establish convergence of the system outputs to the desired ones. This method is then extended to repetitive learning controller design. The boundedness of all the signals in the closed-loop is guaranteed and asymptotic convergence of both the state estimation error and the tracking error is established in both cases of ILC and RLC. Numerical results are presented to verify the effectiveness of the proposed methods.

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.

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.

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.

Generalized projective synchronization of chaotic systems via adaptive learning control

In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.

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.

PD-type iterative learning control for nonlinear time-delay system with external disturbance

The PD-type iterative learning control design of a class of affine nonlinear time-delay systems with external disturbances is considered. Sufficient conditions guaranteeing the convergence of the n-norm of the tracking error are derived. It is shown that the system outputs can be guaranteed to converge to desired trajectories in the absence of external disturbances and output measurement noises. And in the presence of state disturbances and measurement noises, the tracking error will be bounded uniformly. A numerical simulation example is presented to validate the effectiveness of the proposed scheme.

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 With Incomplete Information： A Survey

Abstract--This paper conducts a survey on iterative learn- ing 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. Index Terms--Data dropout, data robustness, incomplete in- formation, iterative learning controi（ILC）, quantized control, sampled control, varying lengths.

An LMI Method to Robust Iterative Learning Fault-tolerant Guaranteed Cost Control for Batch Processes

Based on an equivalent two-dimensional Fornasini-Marchsini model for a batch process in industry, a closed-loop robust iterative learning fault-tolerant guaranteed cost control scheme is proposed for batch processes with actuator failures. This paper introduces relevant concepts of the fault-tolerant guaranteed cost control and formulates the robust iterative learning reliable guaranteed cost controller (ILRGCC). A significant advantage is that the proposed ILRGCC design method can be used for on-line optimization against batch-to-batch process uncertainties to realize robust tracking of set-point trajectory in time and batch-to-batch sequences. For the convenience of implementation, only measured output errors of current and previous cycles are used to design a synthetic controller for iterative learning control, consisting of dynamic output feedback plus feed-forward control. The proposed controller can not only guarantee the closed-loop convergency along time and cycle sequences but also satisfy the H∞performance level and a cost function with upper bounds for all admissible uncertainties and any actuator failures. Sufficient conditions for the controller solution are derived in terms of linear matrix inequalities (LMIs), and design procedures, which formulate a convex optimization problem with LMI constraints, are presented. An example of injection molding is given to illustrate the effectiveness and advantages of the ILRGCC design approach.

Optimal Iterative Learning Control for Batch Processes Based on Linear Time-varying Perturbation Model

A batch-to-batch optimal iterative learning control （ILC） strategy for the tracking control of product quality in batch processes is presented. The linear time-varying perturbation （LTVP） model is built for product quality around the nominal trajectories. To address problems of model-plant mismatches, model prediction errors in the previous batch run are added to the model predictions for the current batch run. Then tracking error transition models can be built, and the ILC law with direct error feedback is explicitly obtained, A rigorous theorem is proposed, to prove the convergence of tracking error under ILC, The proposed methodology is illustrated on a typical batch reactor and the results show that the performance of trajectory tracking is gradually improved by the ILC.

Observer-based Adaptive Iterative Learning Control for Nonlinear Systems with Time-varying Delays

An observer-based adaptive iterative learning control （AILC） scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality （LMI） method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative （PID） feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function （CEF）, we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.

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.

Iterative Learning Control Algorithm with a Fixed Step

Iterative Learning Control （ILC） captures interests of many scholars because of its capability of high precision control implement without identifying plant mathematical models, and it is widely applied in control engineering. Presently, most ILC algorithms still follow the original ideas of ARIMOTO, in which the iterative-learning-rate is composed by the control error with its derivative and integral values. This kind of algorithms will result in inevitable problems such as huge computation, big storage capacity for algorithm data, and also weak robust. In order to resolve these problems, an improved iterative learning control algorithm with fixed step is proposed here which breaks the primary thought of ARIMOTO. In this algorithm, the control step is set only according to the value of the control error, which could enormously reduce the computation and storage size demanded, also improve the robust of the algorithm by not using the differential coefficient of the iterative learning error. In this paper, the convergence conditions of this proposed fixed step iterative learning algorithm is theoretically analyzed and testified. Then the algorithm is tested through simulation researches on a time-variant object with randomly set disturbance through calculation of step threshold value, algorithm robustness testing,and evaluation of the relation between convergence speed and step size. Finally the algorithm is validated on a valve-serving-cylinder system of a joint robot with time-variant parameters. Experiment results demonstrate the stability of the algorithm and also the relationship between step value and convergence rate. Both simulation and experiment testify the feasibility and validity of the new algorithm proposed here. And it is worth to noticing that this algorithm is simple but with strong robust after improvements, which provides new ideas to the research of iterative learning control algorithms.

An Anticipatory Terminal Iterative Learning Control Approach with Applications to Constrained Batch Processes

This work presents an anticipatory terminal iterative learning control scheme for a class of batch proc- esses, where only the final system output is measurable and the control input is constant in each operations. The propgsed approach works well with input constraints provided that the desired control input with respect to the desired trajectory is within the samratiorl bound. The tracking error convergence is established with rigorous mathe- matical analysis. Simulation results .are provided to showthe effectiveness, of the proposed approach.

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 fluctuation caused by wireless channel noise through the analysis results for fluctuation boundary. The simulation results prove the proposed rule is correct.

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.

Filter-based iterative learning control for linear large-scale industrial processes

In the procedure of the steady-state hierarchical optimization with feedback for large-scale industrial processes, a sequence of set-point changes with different magnitudes is carried out on the optimization layer. To improve the dynamic performance of transient response driven by the set-point changes, a filter-based iterative learning control strategy is proposed. In the proposed updating law, a local-symmetric-integral operator is adopted for eliminating the measurement noise of output information,a set of desired trajectories are specified according to the set-point changes sequence, the current control input is iteratively achieved by utilizing smoothed output error to modify its control input at previous iteration, to which the amplified coefficients related to the different magnitudes of set-point changes are introduced. The convergence of the algorithm is conducted by incorporating frequency-domain technique into time-domain analysis. Numerical simulation demonstrates the effectiveness of the proposed strategy,