Neural AILC for Error Tracking Against Arbitrary Initial Shifts

A survey of methods for handling initial state shifts in iterative learning control

This paper introduces three types of controllers: a PID-type iterative learning controller, an adaptive iterative learning controller, and an optimal iterative learning controller, and reviews the history and research status of initial shifts rectifying algorithms. Initial state shifts have attracted research attention because they affect both the tracking performance and system stability. This study focuses on the current common initial shifts rectifying methods and analyzes the underlying mechanism in detail. To verify the effectiveness of the presented initial shifts rectifying algorithms, we simulated those using ideal first- and second-order systems. Finally, directions for the future development of iterative learning control (ILC) and some challenging topics related to initial shifts rectifying for ILC are presented. This article aims to introduce recent developments and advances in initial shifts rectifying algorithms and discuss the directions for their further exploration.

Adaptive Learning Control Algorithms for Infinite-Duration Tracking

Learning control is applicable to systems that operate periodically or over finite time intervals. Currently, there is a lack of research results about learning control approaches to infinite-duration tracking, without requiring periodicity or repeatability. This article addresses the problem of adaptive learning control (ALC) for systems performing infinite-duration tasks. Instead of using integral adaptation, incremental adaptive mechanisms are exploited, by which the numerical integration for implementation can be avoided. The comparison with the conventional integral adaptive mechanisms indicates that the suggested methodology can be an alternative to the adaptive system designs. Using an error-tracking approach, the approximation-based backstepping design is carried out for systems in the strict-feedback form, where a novel integral Lyapunov function is shown to be efficient in the treatment of state-dependent control gain. Theoretical results for the performance analysis are presented in detail. In particular, the robust convergence of the tracking error is established, while the boundedness of the variables of the closed-loop system is characterized, with the aid of a key technical lemma. It is shown that the proposed control method can provide satisfactory tracking performance and simplify the controller designs. Numerical results are presented to demonstrate effectiveness of the learning control schemes.

Improving Tracking Accuracy for Repetitive Learning Systems by High-Order Extended State Observers

For systems executing repetitive tasks, how to realize the perfect tracking objective is generally desirable, for which an effective method called "iterative learning control (ILC)" emerges thanks to the incorporation of the repetitive execution of systems into an ILC design framework. However, nonrepetitive (iteration-varying) uncertainties are often inevitable in practice and greatly degrade the tracking accuracy of ILC, which has not been treated well, regardless of considerable robust ILC results. This motivates this article to develop a new design method to improve the tracking accuracy of ILC by adopting a high-order extended state observer (ESO) to address ill effects of nonrepetitive uncertainties and uncertain system models. With the designed ESO-based ILC, the robust tracking of any desired trajectory can be achieved such that the tracking error can be decreased to vary in a small bound depending continuously on the bounds of high-order variations of nonrepetitive uncertainties with respect to the iteration. It makes the tracking accuracy of ILC possible to be regulated through the design of ESO, of which the validity is demonstrated by including a simulation example.

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.

Learning Tracking Over Unknown Fading Channels Based on Iterative Estimation

With fast developments in communication technologies, a large number of practical systems adopt the networked control structure. For this structure, the fading problem is an emerging issue among other network problems. It has not been extensively investigated how to guarantee superior control performance in the presence of unknown fading channels. This article presents a learning strategy for gradually improving the tracking performance. To this end, an iterative estimation mechanism is first introduced to provide necessary statistical information such that the biased signals after transmission can be corrected before being utilized. Then, learning control algorithms incorporating with a decreasing step-size sequence are designed for both output and input fading cases. The convergence in both mean-square and almost-sure senses of the proposed schemes is strictly proved under mild conditions. Illustrative simulations verify the effectiveness of the entire learning framework.

Neural-Network-Based Adaptive Singularity-Free Fixed-Time Attitude Tracking Control for Spacecrafts

In this article, a neural-network-based adaptive fixed-time control scheme is proposed for the attitude tracking of uncertain rigid spacecrafts. A novel singularity-free fixed-time switching function is presented with the directly nonsingular property, and by introducing an auxiliary function to complete the switching function in the controller design process, the potential singularity problem caused by the inverse of the error-related matrix could be avoided. Then, an adaptive neural controller is developed to guarantee that the attitude tracking error and angular velocity error can both converge into the neighborhood of the equilibrium within a fixed time. With the proposed control scheme, no piecewise continuous functions are required any more in the controller design to avoid the singularity, and the fixed-time stability of the entire closed-loop system in the reaching phase and sliding phase is analyzed with a rigorous theoretical proof. Comparative simulations are given to show the effectiveness and superiority of the proposed scheme.

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.

An Active Repetitive Learning Control Method for Lateral Suspension Systems of High-Speed Trains

This article presents a novel perspective to improve the ride quality of high-speed trains (HSTs), namely, by virtue of the periodicity of lateral dynamics to suppress the lateral vibration of HST. To resolve the contradiction between the complex HST model and the effective controller design, a simplified three-degrees-of-freedom (3-DOF) quarter-vehicle model is first employed for controller design, while a 17-DOF full-vehicle model is built for efficiency verification, where periodic and random track irregularities are considered, respectively. An active repetitive learning control (RLC) method is proposed to achieve the periodic tracking control, where the learning convergence is proved rigorously in a Lyapunov way. The configuration of RLC-based lateral suspensions is economical in the sense that only four actuators and six sensors are needed. It is verified by simulation that, compared with the dynamic matrix controller, the proposed RLC controller has greatly reduced the lateral vibration of a vehicle body, especially the lateral acceleration in the frequency range of (0, 3] Hz to which human body is strongly sensitive.

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.

Echo State Network-Based Backstepping Adaptive Iterative Learning Control for Strict-Feedback Systems: An Error-Tracking Approach

In this article, an echo state network (ESN)-based backstepping adaptive iterative learning control scheme is proposed for nonlinear strict-feedback systems performing the same operation repeatedly over a finite-time interval. Different from most of the output tracking approaches, an error-tracking approach is presented using the backstepping technique, such that the tracking error can follow a prespecified error trajectory without any requirement on the initial value of system states. Then, a novel Lyapunov function is constructed to deal with the unknown state-dependent gain function of the controller design. The uncertain nonlinearities are approximated by employing ESNs with simple feedback structures, and the weight update laws are developed by combining the parameter adaptation in the time domain and iteration domain. Moreover, the proposed control scheme is further extended to handle the strict-feedback systems with input saturations. Through the Lyapunov-like synthesis, the closed-loop stability and error convergence of the proposed error-tracking control scheme are analyzed in the presence of the approximation errors. Numerical simulations are provided to verify the effectiveness of the proposed scheme.

Performance Enhancement of Learning Tracking Systems Over Fading Channels With Multiplicative and Additive Randomness

This paper applies learning control to repetitive systems over fading channels at both output and input sides to improve tracking performance without applying restrictive fading conditions. Both multiplicative and additive randomness of the fading channel are addressed, and the effects of fading communication on the data are carefully analyzed. A decreasing gain sequence and a moving-average operator are introduced to modify the generic learning control algorithm to reduce the fading effect and improve control system performance. Results reveal that the tracking error converges to zero in the mean-square sense as the iteration number increases. Illustrative simulations are presented to verify the theoretical results.

Convergence Conditions for Solving Robust Iterative Learning Control Problems Under Nonrepetitive Model Uncertainties

Learning from saved measurement and control data to refine the performance of output tracking is the core feature of iterative learning control (ILC). Even though this implementation process of ILC does not need any model knowledge, ILC typically requires the strict repetitiveness of the control systems, especially on the plant models of them. The questions of interest in this paper are: 1) whether and how can robust ILC problems be solved with respect to the nonrepetitive (or iteration-dependent) model uncertainties and 2) can convergence conditions be developed with the effective contraction mapping (CM)-based approach to ILC? The answers to these questions are affirmative, and the CM-based approach is applicable to robust ILC that accommodates certain nonrepetitive uncertainties, especially in the plant models. In particular, an H_∞ -norm condition is proposed to ensure the robust ILC convergence, which can be solved to determine learning gain matrices. Simulation tests are performed to illustrate the validity of our presented H_∞ -based analysis results.