Ronghu Chi

A New Discrete-time Adaptive ILC for Nonlinear Systems with Time-varying Parametric Uncertainties

Abstract Using the analogy between the discrete time axis and the iterative learning axis, a new discrete-time adaptive iterative learning control (AILC) approach is developed to address a class of nonlinear systems with time-varying parametric uncertainties. Analogous to adaptive control, the new AILC can incorporate a projection algorithm, thus the learning gain can be tuned iteratively along the learning axis. When the initial states are random and the reference trajectory is iteration-varying, the new AILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis.

A Data-Driven Iterative Feedback Tuning Approach of ALINEA for Freeway Traffic Ramp Metering With PARAMICS Simulations

In this work, a new iterative feedback tuning approach is proposed to tune ALINEAs controller gain automatically when there is not enough prior information available to select a proper feedback gain of ALINEA. It is a data-driven method and the ALINEA controller is auto-tuned only depending on the input and output data collected from closed-loop experiments. To mimic a real traffic environment, a simulator is built on the PARAMICS platform. The flow-based ALINEA controller is also considered to illustrate the good tuning performance of IFT comprehensively. The effectiveness of the proposed methods is verified through PARAMICS based simulations.

Discrete-time adaptive iterative learning control for permanent magnet linear motor

A discrete-time adaptive iterative learning control approach (DAILC) is presented for improving the permanent magnet linear motor velocity tracking performance. The learning gain can be updated iteratively along the learning axis and pointwisely along the time axis. When the initial states are random and the reference trajectory and disturbance are iteration-varying, the DAILC can achieve the pointwise convergence over a finite time interval asymptotically along the iterative learning axis. The theoretical analysis and simulation results further verify the effectiveness of the proposed approach.

An Overview of Dynamic-Linearization-Based Data-Driven Control and Applications

A brief overview on the model-based control and data-driven control methods is presented. The data-driven equivalent dynamic linearization, as a foundational analysis tool of data-driven control methods for discrete-time nonlinear systems, is introduced in detail with motivations and distinct features. The prototype model-free adaptive control schemes by using the dynamic linearization to an unknown nonlinear plant model, as well as the alternative model-free adaptive control methods by using the dynamic linearization to an unknown ideal nonlinear controller, are discussed. Furthermore, the extensions of the dynamic linearization to unknown nonlinear repetitive systems and the corresponding model-free adaptive iterative learning control methods are also overviewed and summarized. This work highlights the characteristics and comments of the different model-free adaptive control schemes in detail to facilitate the understanding of the readers. Finally, some perspectives on data-driven control methods in information-rich age are given.

Adaptive iterative learning control for nonlinearly parameterised systems with unknown time-varying delays and input saturations

In this work, an adaptive iterative learning control (AILC) scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time-varying delays and input saturations. By incorporating a saturation function, a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain, which is used to estimate the unknown time-varying system uncertainty. A new time-weighted Lyapunov–Krasovskii-like composite energy function (LKL-CEF) is designed for the convergence analysis where time-weighted inputs, states and estimates of system uncertainty are all considered. Despite the existence of time-varying parametric uncertainties, time-varying delays, input saturations and local Lipschitz nonlinearities, the learning convergence is guaranteed with rigorous mathematical analysis. Simulation results verify the correctness and effectiveness of the proposed method further.

Enhanced Data-Driven Optimal Terminal ILC Using Current Iteration Control Knowledge

In this paper, an enhanced data-driven optimal terminal iterative learning control (E-DDOTILC) is proposed for a class of nonlinear and nonaffine discrete-time systems. A dynamical linearization approach is first developed with iterative operation points to formulate the relationship of system output and input into a linear affine form. Then, an ILC law is constructed with a nonlinear learning gain, which is a function about the system partial derivative with respect to the time-varying control input. In addition, a parameter updating law is designed to estimate the unknown partial derivatives iteratively. The input signals of the proposed E-DDOTILC are time-varying and updated utilizing not only the terminal tracking error of the previous run but also the input signals of the previous time instants in the current iteration. The proposed approach is a data-driven control strategy and only the I/O data are required for the controller design and analysis. The monotonic convergence and effectiveness of the proposed approach is further verified by both the rigorous mathematical analysis and the simulation results.

A data-driven adaptive ILC for a class of nonlinear discrete-time systems with random initial states and iteration-varying target trajectory

Abstract This paper presents a new data-driven adaptive ILC (DDAILC) for a class of nonlinear discrete-time systems by introducing a pointwise dynamical linearization approach in the iteration direction. For the nonlinear systems, which cannot be linearly parameterized, the proposed DDAILC is capable of achieving a perfect performance without requiring any identical conditions exposed both on the initial state and on the reference trajectory. It is a data-driven control approach since only the I/O data is required for the control system design and analysis. The parameter updating law is constructed to estimate the inverse values of the system׳s unknown partial derivatives of the nonlinear system with respect to the control inputs, which are utilized to compute the learning gain of control law further. The control input is updated by using both the information of reference trajectory of the current operation as a feedback term and the input signals in previous operations as a feedforward term. Extension results to MIMO nonlinear discrete-time systems are provided further. Both theoretical analysis and simulation results verify the effectiveness of the proposed data-driven AILC approach.

Freeway Traffic Density and On-Ramp Queue Control via ILC Approach

A new queue length information fused iterative learning control approach (QLIF-ILC) is presented for freeway traffic ramp metering to achieve a better performance by utilizing the error information of the on-ramp queue length. The QLIF-ILC consists of two parts, where the iterative feedforward part updates the control input signal by learning from the past control data in previous trials, and the current feedback part utilizes the tracking error of the current learning iteration to stabilize the controlled plant. These two parts are combined in a complementary manner to enhance the robustness of the proposed QLIF-ILC. A systematic approach is developed to analyze the convergence and robustness of the proposed learning scheme. The simulation results are further given to demonstrate the effectiveness of the proposed QLIF-ILC.

A Novel Data-Driven Terminal Iterative Learning Control with Iteration Prediction Algorithm for a Class of Discrete-Time Nonlinear Systems

A data-driven predictive terminal iterative learning control (DDPTILC) approach is proposed for discrete-time nonlinear systems with terminal tracking tasks, where only the terminal output tracking error instead of entire output trajectory tracking error is available. The proposed DDPTILC scheme consists of an iterative learning control law, an iterative parameter estimation law, and an iterative parameter prediction law. If the partial derivative of the controlled system with respect to control input is bounded, then the proposed control approach guarantees the terminal tracking error convergence. Furthermore, the control performance is improved by using more information of predictive terminal outputs, which are predicted along the iteration axis and used to update the control law and estimation law. Rigorous analysis shows the monotonic convergence and bounded input and bounded output (BIBO) stability of the DDPTILC. In addition, extensive simulations are provided to show the applicability and effectiveness of the proposed approach.

A Fuzzy-Neural Adaptive Terminal Iterative Learning Control for Fed-Batch Fermentation Processes

A fuzzy-neural adaptive terminal iterative learning controller is proposed in this paper for uncertain fed-batch fermentation processes with iteration-varying initial states. In order to derive a terminal output tracking error model, a technique of sampled-data transformation for differentiation is firstly utilized to transform the fed-batch fermentation process into a sampled-data system. An input and output algebraic function is then derived based on the sampled-data formulation of fed-batch fermentation process as well as the differential mean value theorem. According to the derived terminal output tracking error model, a fuzzy neural network is applied to approximate the unknown terminal desired input. In order to overcome a lumped uncertainty from the error induced by fuzzy-neural function approximation and the unknown initial states, an iteration-varying boundary layer is developed to construct an auxiliary terminal output error. This auxiliary terminal output error is then used to derive suitable adaptive laws for the weights of fuzzy neural network and the width of boundary layer. Based on a Lyapunov-like analysis, we show that the boundedness of control parameters, control input, and process output are guaranteed for each iteration. Furthermore, the norm of terminal output error will asymptotically converge to a tunable residual set whose size depends on the width of boundary layer as iteration number goes to infinity.