HONN-Based Adaptive ILC for Pure-Feedback Nonaffine Discrete-Time Systems With Unknown Control Directions

A Novel Accelerated Multistage Learning Control Mechanism via Virtual Performance Reduction

This study uses a multistage learning mechanism concept to investigate the accelerated learning control for stochastic systems. In this mechanism, the learning iterations are divided into successive stages, with each stage comprising several iterations. The learning gain is constant in each stage to accelerate the learning process and decreases it from one stage to another to eliminate the noise effect asymptotically. The critical issue is determining the switching iteration when a new stage starts. This study resolves this issue by calculating a virtual performance index of the mean-squared input error and its estimated upper bound. Specifically, the ideal, practical, and improved multistage learning control schemes are proposed to determine the switching iteration and generate the learning gain sequence. The ideal scheme achieves the best performance at the cost of a large computation burden, and the practical scheme saves computation cost, but the performance is not excellent. The improved scheme significantly approximates the best performance by introducing additional stretching parameters to the performance index. Illustrative simulations are provided to verify the theoretical results.

A Probabilistically Quantized Learning Control Framework for Networked Linear Systems

In this article, we consider quantized learning control for linear networked systems with additive channel noise. Our objective is to achieve high tracking performance while reducing the communication burden on the communication network. To address this problem, we propose an integrated framework consisting of two modules: a probabilistic quantizer and a learning scheme. The employed probabilistic quantizer is developed by employing a Bernoulli distribution driven by the quantization errors. Three learning control schemes are studied, namely, a constant gain, a decreasing gain sequence satisfying certain conditions, and an optimal gain sequence that is recursively generated based on a performance index. We show that the control with a constant gain can only ensure the input error sequence to converge to a bounded sphere in a mean-square sense, where the radius of this sphere is proportional to the constant gain. On the contrary, we show that the control that employs any of the two proposed gain sequences drives the input error to zero in the mean-square sense. In addition, we show that the convergence rate associated with the constant gain is exponential, whereas the rate associated with the proposed gain sequences is not faster than a specific exponential trend. Illustrative simulations are provided to demonstrate the convergence rate properties and steady-state tracking performance associated with each gain, and their robustness against modeling uncertainties.

Design and Analysis of Data-Driven Learning Control: An Optimization-Based Approach

Learning to perform perfect tracking tasks based on measurement data is desirable in the controller design of systems operating repetitively. This motivates this article to seek an optimization-based design and analysis approach for data-driven learning control systems by focusing on iterative learning control (ILC) of repetitive systems with unknown nonlinear time-varying dynamics. It is shown that perfect output tracking can be realized with updating inputs, where no explicit model knowledge but only measured input-output data are leveraged. In particular, adaptive updating strategies are proposed to obtain parameter estimations of nonlinearities. A double-dynamics analysis approach is applied to establish ILC convergence, together with boundedness of input, output, and estimated parameters, which benefits from employing properties of nonnegative matrices. Simulations are implemented to verify the validity of our optimization-based adaptive ILC.

Accelerated Learning Control for Point-to-Point Tracking Systems

In this study, we investigate the accelerated learning control schemes for point-to-point tracking systems (PTSs) with measurement noise. The asymptotic convergence of the generated input sequence has been a long-standing open issue for point-to-point tracking problems because there are infinite possible input candidates that can drive the system dynamics to track the desired reference at specified time instants. An accelerated gradient algorithm and its generalized version with a novel direction regulation matrix are proposed, with the learning gain is adaptively triggered by the practical tracking errors. The learning gain remains constant at the early stage and begins to decrease after a certain number of iterations. The input sequence generated by the proposed scheme converges to a specified limit for any fixed initial input, with the limit being closest to the initial input, in a certain sense. Numerical simulations are provided to verify the theoretical results.

Neural-Network-Based Iterative Learning Control for Multiple Tasks

Iterative learning control (ILC) can synthesize the feedforward control signal for the trajectory tracking control of a repetitive task, even when the system has strong nonlinear dynamics. This makes ILC be one of the most popular methods for trajectory tracking control. Restriction on a repetitive task, however, limits its application to multiple trajectories. This article proposes a neural-network-based ILC (NN-ILC) to deal with nonrepetitive tasks very effectively. A position-based ILC is designed to compensate the tracking error, based on which the multiple outputs of the ILC (ILC outputs) for multiple tasks are expressed as a function of the reference position, velocity, and acceleration. The proposed NN-ILC divides the ILC outputs of multiple tasks into two parts: the linear and nonlinear portions. The first part is expressed by a linear function, which is the linear portion of the function of the ILC outputs. The second part is expressed by a nonlinear function, which is estimated by complementary neural networks including a general neural network and a switching neural network. Finally, the two parts are combined and the ILC outputs of multiple tasks are expressed as a neural-network-based function. Two advantages of the proposed NN-ILC are emphasized. First, the ILC outputs of multiple tasks are compressed into a function by the proposed method, and thus, the memories can be saved. Second, in terms of generalizability, the neural-network-based function of the ILC outputs can easily predict position compensation for multiple tasks without extra iterative learning processes. Experimental results on a robot arm show that the proposed NN-ILC method can easily realize the ILC of multiple tasks. It can save memory comparing with the method of storing the data of multiple tasks and can predict the ILC output of any task, which can accelerate the iterative learning process.

Convergence Analysis of Robust Iterative Learning Control Against Nonrepetitive Uncertainties: System Equivalence Transformation

This article is concerned with the robust convergence analysis of iterative learning control (ILC) against nonrepetitive uncertainties, where the contradiction between convergence conditions for the output tracking error and the input signal (or error) is addressed. A system equivalence transformation (SET) is proposed for robust ILC such that given any desired reference trajectories, the output tracking problems for general nonsquare multi-input, multi-output (MIMO) systems can be equivalently transformed into those for the specific class of square MIMO systems with the same input and output numbers. As a benefit of SET, a unified condition is only needed to guarantee both the uniform boundedness of all system signals and the robust convergence of the output tracking error, which avoids causing the condition contradiction problem in implementing the double-dynamics analysis approach to ILC. Simulation examples are included to demonstrate the validity of our established robust ILC results.

Learning Tracking Control Over Unknown Fading Channels Without System Information

A novel data-driven learning control scheme is proposed for unknown systems with unknown fading sensor channels. The fading randomness is modeled by multiplicative and additive random variables subject to certain unknown distributions. In this scheme, we propose an error transmission mode and an iterative gradient estimation method. Unlike the conventional transmission mode where the output is directly transmitted back to the controller, in the error transmission mode, we send the desired reference to the plant such that tracking errors can be calculated locally and then transmitted back through the fading channel. Using the faded tracking error data only, the gradient for updating input is iteratively estimated by a random difference technique along the iteration axis. This gradient acts as the updating term of the control signal; therefore, information on the system and the fading channel is no longer required. The proposed scheme is proved effective in tracking the desired reference under random fading communication environments. Theoretical results are verified by simulations.

Design and Implementation of an Accelerated Error Convergence Criterion for Norm Optimal Iterative Learning Controller

Designing an optimal iterative learning control is a huge challenge for linear and nonlinear dynamic systems. For such complex systems, standard Norm optimal iterative learning control (NOILC) is an important consideration. This paper presents a novel NOILC error convergence technique for a discrete-time method. The primary effort of the controller is to converge the error efficiently and quickly in an optimally successful way. A new iterative learning algorithm based on feedback based on reliability against input disruption was proposed in this paper. The illustration of the simulations authenticates the process suggested. The numerical example simulated on MATLAB@2019 and the mollified results affirm the validation of the designed algorithm.

Convergence Analysis of Saturated Iterative Learning Control Systems With Locally Lipschitz Nonlinearities

In this article, the robust trajectory tracking problem of iterative learning control (ILC) for uncertain nonlinear systems is considered, and the effects from locally Lipschitz nonlinearities, input saturations, and nonzero system relative degrees are treated. A saturated ILC algorithm is given, with the convergence analysis exploited using a composite energy function-based approach. It is shown that the tracking error can be guaranteed to converge both pointwisely and uniformly. Furthermore, the input updating signal can be ensured to eventually satisfy the input saturation requirements with increasing iterations. Two examples are given to demonstrate the validity of saturated ILC for systems with the relative degree of one, input saturation, and locally Lipschitz nonlinearity.