Iterative Dynamic Linearization Research Articles

Dynamic Neural Network Predictive Compensation-Based Point-to-Point Iterative Learning Control With Nonuniform Batch Length.

This article discusses the problem of nonuniform running length in incomplete tracking control, which often occurs in industrial processes due to artificial or environmental changes, such as chemical engineering. It affects the design and application of iterative learning control (ILC) that relies on the strictly repetitive property. Therefore, a dynamic neural network (NN) predictive compensation strategy is proposed under the point-to-point ILC framework. To handle the difficulty of establishing an accurate mechanism model for real process control, the data-driven approach is also introduced. First, applying the iterative dynamic linearization (IDL) technique and radial basis function NN (RBFNN) to construct the iterative dynamic predictive data model (IDPDM) relies on input-output (I/O) signal, and the extended variable is defined by a predictive model to compensate for the incomplete operation length. Then, a learning algorithm based on multiple iteration errors is proposed using an objective function. This learning gain is constantly updated through the NN to adapt to changes in the system. In addition, the composite energy function (CEF) and compression mapping prove that the system is convergent. Finally, two numerical simulation examples are given.

Data-Driven Indirect Iterative Learning Control.

In this work, a data-driven indirect iterative learning control (DD-iILC) is presented for a repetitive nonlinear system by taking a proportional-integral-derivative (PID) feedback control in the inner loop. A linear parametric iterative tuning algorithm for the set-point is developed from an ideal nonlinear learning function that exists in theory by utilizing an iterative dynamic linearization (IDL) technique. Then, an adaptive iterative updating strategy of the parameter in the linear parametric set-point iterative tuning law is presented by optimizing an objective function for the controlled system. Since the system considered is nonlinear and nonaffine with no available model information, the IDL technique is also used along with a strategy similar to the parameter adaptive iterative learning law. Finally, the entire DD-iILC scheme is completed by incorporating the local PID controller. The convergence is proved by applying contraction mapping and mathematical induction. The theoretical results are verified by simulations on a numerical example and a permanent magnet linear motor example.

Data-driven set-point learning control with ESO and RBFNN for nonlinear batch processes subject to nonrepetitive uncertainties

This paper proposes an extended state observer (ESO) based data-driven set-point learning control (DDSPLC) scheme for a class of nonlinear batch processes with a priori P-type feedback control structure subject to nonrepetitive uncertainties, by only using the process input and output data available in practice. Firstly, the unknown process dynamics is equivalently transformed into an iterative dynamic linearization data model (IDLDM) with a residual term. A radial basis function neural network is adopted to estimate the pseudo partial derivative information related to IDLDM, and meanwhile, a data-driven iterative ESO is constructed to estimate the unknown residual term along the batch direction. Then, an adaptive set-point learning control law is designed to merely regulate the set-point command of the closed-loop control structure for realizing batch optimization. Robust convergence of the output tracking error along the batch direction is rigorously analyzed by using the contraction mapping approach and mathematical induction. Finally, two illustrative examples from the literature are used to validate the effectiveness and advantage of the proposed design.

Data-Driven Internal Model Learning Control for Nonlinear Systems.

A novel data-driven internal model learning control (DIMLC) strategy is developed for a nonlinear nonaffine system subject to unknown nonrepetitive uncertainties. At first, an iterative dynamic linearization (IDL) approach is employed for reformulating the nonlinear plant to an iterative linear data model (iLDM). Then, the nominal form of the IDL-based iLDM is used as an internal model of the nonlinear plant whose parameters are estimated by an iterative adaptive updating mechanism using only input-output (I/O) data. The equivalent feedback-principle-based internal model inversion is further applied to the subsequent controller design and analysis. The proposed DIMLC contains two parts. One is a nominal controller designed by the inversion of the internal model which achieves a perfect tracking of the target output; the other is a compensatory controller which offsets the uncertainties. The novel DIMLC is data-driven and does not require an explicit model. It can deal with model-plant mismatch and disturbances, enhancing the robustness against uncertainties. The theoretical results are verified by simulation study.

Data-Driven Spatial Adaptive Terminal Iterative Learning Predictive Control for Automatic Stop Control of Subway Train With Actuator Saturation

A data-driven spatial adaptive terminal iterative learning predictive control (SATILPC) scheme with actuator saturation is proposed for automatic stop control of the subway train. Considering the outstanding repetitive operation pattern and the unavailable accurate model of a subway train, the unknown train dynamics is firstly transformed into a nonlinear discrete form in spatial domain via the spatial differential operator. Since the train automatic stop control (TASC) only concentrates on the tracking performances of the terminal position and terminal speed, an iterative dynamic linearization approach considering the terminal operation point is devised to formulate the relationship of the train input and output (I/O) into a linear affine form. Then, a terminal iterative learning prediction mechanism is introduced to reconstruct the developed train data model to forecast the future train behaviors through rolling optimization process. As a result, by removing the constraints on the unimportant points, the optimal control input (braking force) can be obtained by minimizing the objective function through terminal I/O data. Further, actuator saturation is considered to address the passenger comfort and the reliable operation of the train. The proposed SATILPC approach is a pure data-driven iterative learning control scheme and no model information is involved in the whole design processes. By utilizing a newly space-based contraction mapping method, the convergence of the proposed approach is strictly proved. Finally, the simulation results further demonstrate the feasibility of the proposed algorithm.

ESO-Based Model-Free Adaptive Iterative Learning Energy-Efficient Control for Subway Train With Disturbances and Over-Speed Protection

An extended state observer based model-free adaptive iterative learning energy-efficient control (ESO-based MFAILEEC) scheme for subway train speed tracking with external disturbances and over-speed protection under the constraint on traction/braking force is proposed. Firstly, the continuous-time train motion dynamics is formulated into a discrete-time data model with consideration of external disturbances by applying the iterative dynamic linearization. Meanwhile, the external disturbances and the unknown nonlinear uncertainties of the train are transformed into a new state, which is estimated by an ESO designed in the iteration domain. Then, the ESO-based energy-efficient controller with learning ability is designed, which enables the train to achieve the purpose of energy efficiency by reducing the input force. Further, over-speed protection with trigger mechanism is developed to ensure the train operates within safe speed range. All the control strategies are designed under the constraint on traction/braking force by considering the practical limitation of the train system. No model information is involved in the whole design processes and it is a pure data-driven iterative learning approach. Rigorous mathematical analysis proves the feasibility and the robustness of the proposed method, which can guarantee the train operates safely and reliably. Finally, the simulation results further demonstrate the effectiveness of the proposed algorithm.

Data-Driven Virtual Reference Set-Point Learning of PD Control and Applications to Permanent Magnet Linear Motors

In this work, a data-driven virtual reference setting learning (DDVRSL) method is proposed to enhance the proportional-derivative (PD) feedback controller of the repetitive nonlinear system. First, an ideal nonlinear virtual reference setting learning law is presented in the outer loop of the control system to tune the reference setting. Such an ideal nonlinear learning law exists theoretically and is transferred to a linear parametric DDVRSL via iterative dynamic linearization (IDL). Next, an iterative adaptation law is proposed for the estimation of the parameters in the DDVRSL law subject to the nonlinear system which is also transferred into a linear form by using the IDL method. The iterative adaptation algorithm tunes the learning gains of DDVRSL law using input and output measurements, therefore improving the robust ability against uncertainties. The proposed DDVRSL-based PD control method does not require any exact mechanistic model knowledge. The convergence is proved via the contraction mapping principle, mathematical induction, and time-weighted norm. Further, the theoretical results are verified through simulations.

Double Dynamic Linearization-Based Higher Order Indirect Adaptive Iterative Learning Control.

In this article, a higher order indirect adaptive iterative learning control (HO-iAILC) scheme is developed for nonlinear nonaffine systems. The inner loop adopts a P -type controller whose set-point is updated iteratively by learning from the iterations. To this end, an ideal nonlinear learning control law is designed in the outer loop. It is then transferred to a linear parametric-learning controller with a corresponding parameter estimation law by introducing an iterative dynamic linearization (IDL) method. This IDL method is also used to gain an iterative linear data model of the nonlinear system. A parameter iterative updating algorithm is utilized for estimating the unknown parameters of the obtained linear data model. Finally, the HO-iAILC is presented that utilizes additional error information to improve the control performance and employs two iterative adaptive mechanisms to deal with uncertainties. The convergence of the proposed HO-iAILC scheme is proved by using two basic mathematical tools, namely: 1) contraction mapping and 2) mathematical induction. Simulation studies are conducted for the verification of the theoretical results.

A Discrete-time Integral Sliding Mode Predictive Control Using Iterative Dynamic Linearization Data Model

A Discrete-time Integral Sliding Mode Predictive Control Using Iterative Dynamic Linearization Data Model

Enhanced P-Type Control: Indirect Adaptive Learning From Set-Point Updates

In this article, an indirect adaptive iterative learning control (iAILC) scheme is proposed for both linear and nonlinear systems to enhance the P-type controller by learning from set points. An adaptive mechanism is included in the iAILC method to regulate the learning gain using input–output measurements in real time. An iAILC method is first designed for linear systems to improve control performance by fully utilizing model information if such a linear model is known exactly. Then, an iterative dynamic linearization (IDL)-based iAILC is proposed for a nonlinear nonaffine system, whose model is completely unknown. The IDL technique is employed to deal with the strong nonlinearity and nonaffine structure of the systems such that a linear data model can be attained consequently for the algorithm design and performance analysis. The convergence of the developed iAILC schemes is proved rigorously, where contraction mapping, two-dimensional (2-D) Roesser’s system theory, and mathematical induction are employed as the basic analysis tools. Simulation studies are provided to verify the developed theoretical results.

Iterative learning control for UAVs formation based on point-to-point trajectory update tracking

For the problem of trajectory tracking in UAVs formation system, an adaptive iterative learning control strategy based on point-to-point trajectory update tracking is proposed. The nonlinear discrete system after iterative dynamic linearization approximation is combined with the UAVs formation system, and the time-varying parameters are introduced for trajectory tracking. According to the iterative linear dynamic condition and the global Lipschitz condition, the system tracking error is analyzed under the iterative learning control based on point-to-point trajectory tracking. The proposed control method not only uses the freedom degree of the tracking points to analyze the convergence and robustness for the UAVs formation, but also introduces error prediction to improve the anti-disturbance ability for the system. Finally, the simulation study for the UAV formation system is carried out to verify the effectiveness of the proposed method.

Data-Driven Iterative Learning Predictive Control for Power Converters

This letter proposes a data-driven iterative learning predictive control architecture for power converters. The main objectives of this letter are to enhance the robustness and remain the high performance of finite control-set model predictive control (FCS-MPC) under unmodeled dynamics and parameter mismatch conditions. More specifically, an iterative dynamic linearization technique is utilized to equivalently reformulate the nonlinear power converter system at each operating point. Based on this, a model-free adaptive control scheme is presented to iteratively determine the optimal control actions. Due to the incorporation of iterative learning control and data-driven concept into the FCS-MPC framework, the effect of parameter perturbations can be alleviated in the proposed method, while creating a positive effect on the tracking error. Finally, a convergence analysis is provided and experimental investigations on a three-level neutral-point-clamped (NPC) converter confirm the effectiveness of the proposed method.

Data-driven adaptive tuning of iterative learning control

In this paper, we propose two data-driven adaptive tuning (DDAT) approaches of iterative learning control (ILC) for nonlinear non-affine systems. First, a compact-form iterative dynamic linearization (CFIDL) method is introduced to transfer the original nonlinear system into a linear data model. Then, we design an objective function for the tuning of the learning gains of a PD-type ILC law. By optimizing the designed cost function subjected to the linear data model, a CFIDL-based DDAT method is proposed, where only the real I/O data are used without requiring any mechanistic model information. Furthermore, the results are extended by introducing a partial-form iterative dynamic linearization (PFIDL) method for the purpose of utilizing more additional control information. Following the similar steps, a PFIDL-based DDAT method is developed for learning gain tuning of the PD-type ILC scheme. Both the proposed DDAT methods can help the PD-type ILC have a better robustness against to the uncertainties since they can use the real I/O data to iteratively tune the learning gains. The convergence of the DDAT-based PD-type ILC methods has been proved rigorously. The effectiveness of the two proposed DDAT-based ILC methods are further verified through simulations.

Model-Free Adaptive Iterative Learning Control Method for the Czochralski Silicon Monocrystalline Batch Process

Model-based control methods do not produce satisfactory control results with the batch process control of Czochralski (CZ) silicon monocrystalline with complex nonlinearity, large delay, and time-varying dynamics. Therefore, this paper proposes a data-driven model-free adaptive iterative learning control method (MFAILC) to achieve precision control of the batch process. Firstly, to improve the accuracy of the data-driven model, a novel deep learning model for crystal growth process is established by combining a stacked autoencoder (SAE) and a long short-term memory network (LSTM) to extract the working condition information and the dynamic timing features in process data. Traditional model-based control methods are limited by the difficulties in modeling and by the unmodeled dynamics. So, to overcome this problem, the heater controller and the crystal puller controller are designed, based on the iterative dynamic linearization technology, to ensure that the silicon monocrystalline batch manufacturing process always maintains precision control. Also, the discrete-time extended state observer (ESO) is introduced to compensate for the influence of disturbances, to improve the robustness of the control system. Finally, the efficacy of the proposed method is verified by applying it for the predictive modeling and batch control of thermal field temperature and crystal diameter during crystal growth.

Multi-lagged-input information enhancing quantized iterative learning control

Quantization is a significant technique in network control to save limited bandwidth. In this work, two new multi-lagged-input-based quantized iterative learning control (MLI-QILC) methods are proposed by using output quantization and error quantization, respectively. The multi-lagged-input iterative dynamic linearization method (MLI-IDL) is introduced to build a linear data model of nonlinear systems using additional control inputs in lagged time instants and multiple parameters where the condition of nonzero input change is not required any longer. The MLI-QILC is proposed by designing two new objective functions utilizing the quantized data of the system outputs and tracking errors, respectively. With rigorous analysis, it is shown that the proposed MLI-QILC with output quantization guarantees that the tracking error converges to a bound which is related to the quantization density and the bound of the desired trajectory. Furthermore, an asymptotic convergence can be achieved for the proposed MLI-QILC method with error quantization. The theoretical results are verified by simulations.

Distributed iterative learning temperature control for multi-zone HVAC system

By taking the dynamic features of the multi-zone heating ventilation air conditioning (HVAC) system into consideration, a distributed iterative learning temperature control (DILTC) method is proposed for building rooms where the exact values of the thermal capacitances, as the key parameters of the HVAC system, are unavailable. At first, an iterative dynamic linearization is applied to reformulate the HVAC system into an all-purposed linear incremental form virtually to facilitate the controller design without relying on model information. On this basis, a data-driven DILTC method is proposed with rigorous convergence analysis where the topology among rooms is considered via a thermal resistance matrix. Under the developed convergence conditions, the tracking error is guaranteed to be iteratively decreased to a small bound with nonrepetitive disturbances. If the disturbances are completely repeatable, a perfect tracking performance can be achieved. The results have also been extended to the HVAC systems subjected to I/O constraints to address the limited heating and cooling capacities. Through extensive simulations, we confirm the good efficiency and applicability of the proposed methods.

Iterative dynamic linearization and identification of a nonlinear learning controller: A data-driven approach

In this article, a nonlinear iterative learning controller (NILC) is developed using an iterative dynamic linearization (IDL) and a parameter iterative learning identification technique. First, the ideal NILC is transformed into a linear parameterized form by using a controller-oriented compact form IDL (controller-CFIDL) technique. Then an iterative learning identification approach is presented for tuning the parameters of the proposed controller using real-time I/O data. For the sake of analysis, a linear data model of the nonlinear plant is obtained by using the system-oriented IDL technology and a corresponding system parameter identification algorithm is developed in iteration domain. The convergence analysis is provided for the dynamically linearized nonlinear and nonaffine discrete-time system. The results are further extended by using a controller-oriented partial form iterative dynamic linearization (controller-PFIDL) method to gain a higher-order NILC utilizing additional control information from previous iterations. Simulations of two examples show the effectiveness of the proposed methods.

Extended State Observer-Based Data-Driven Iterative Learning Control for Permanent Magnet Linear Motor With Initial Shifts and Disturbances

In this paper, an extended state observer-based data-driven iterative learning control [extended state observer (ESO)-based DDILC] is developed for a permanent magnet linear motor (PMLM). The PMLM is formulated mathematically by using a general nonlinear discrete-time system with consideration of exogenous disturbances. Then, a new iterative dynamic linearization (IDL) is proposed to equivalently reformulate the nonlinear PMLM system with a linear input-output incremental form involving iteration-varying initial states and disturbances. The concept of ESO is introduced into iteration direction to iteratively estimate the random initial states and disturbances as well as their corresponding partial derivatives by considering all of them as a whole extended state. The proposed ESO-based DDILC scheme contains a learning control algorithm and a gradient parameter updating algorithm obtained from two distinct objective functions, respectively. Moreover, the proposed method is data-driven and no explicit model is involved. Theoretical analysis shows the robustness of the proposed method in the presence of iteration-varying initial shifts and disturbances. The simulation on PMLM is conducted to confirm the validity and applicability of the ESO-based DDILC.

A forgetting-factor based data-driven optimal terminal iterative learning control with applications to product concentration control of ethanol fermentation processes

Ethanol fermentation process (EFP) is characterized as a repetitive batch process with strong nonlinear behavior, changing operational conditions and exogenous disturbances which causes huge cost and hard difficulties in modeling an EFP. In this work, a forgetting-factor based data-driven optimal terminal iterative learning control (FF-DDOTILC) is proposed for the product concentration control of an EFP, which is regarded as an unknown nonlinear and nonaffine discrete-time system in general. An iterative dynamic linearization method is introduced to transfer the nonlinear system equivalently into a linear parametric incremental input-output form. The learning control law is derived by iteratively optimizing the proposed new objective function with a forgetting-factor. Meanwhile, a project parameter updating law is designed to estimate the unknown parameters in the linear input-output data model. By introducing a forgetting-factor, the proposed method becomes more flexible and efficient with a better control performance. The proposed FF-DDOTILC only depends on the I/O data for the design and analysis where the convergence of tracking error is guaranteed mathematically. The proposed method is applicable and effective in the product concentration control of the ethanol fermentation process verified through detail simulations.

Data-Driven Stochastic Optimal Iterative Learning Control for Nonlinear Non-Affine Systems With Measurement Data Loss

In this paper, the measurement data loss is considered and two data-driven stochastic optimal iterative learning control (DDSOILC) methods are presented directly for nonlinear network systems. Specifically, an iterative dynamic linearization (IDL) is adopted to construct the linear incremental input output relationship of the repetitive nonlinear network system between two consecutive iterations. In the sequel, a lifted IDL is obtained by defining two super vectors of inputs and outputs over the entire finite time interval. Then, a lifted IDL-based DDSOILC scheme is proposed where the random data loss is described by a Bernoulli distribution of random variable. The results are extended by using a non-lifted IDL where the input-output relationship is described pointwisely. The learning gains of the proposed two methods are iteration-time-variant and can be iteratively estimated using real-time data. The proposed two methods do not depend on any explicit model. Moreover, the proposed non-lifted IDL-based DDSOILC can use more control information than the proposed lifted IDL-based one, and thus it can achieve a better control performance. Both theoretical analysis and simulations verify the efficiency and applicability of the two proposed methods.