Iteration Domain Research Articles

Iterative learning control in prosumer-based microgrids with hierarchical control

Power systems are subject to fundamental changes due to the increasing infeed of renewable energy sources. Taking the accompanying decentralization of power generation into account, the concept of prosumer-based microgrids gives the opportunity to rethink structuring and operation of power systems from scratch. In a prosumer-based microgrid, each power grid node can feed energy into the grid and draw energy from the grid. The concept allows for spatial aggregation such that also an interaction between microgrids can be represented as a prosumer-based microgrid. The contribution of this work is threefold: (i) we propose a decentralized hierarchical control approach in a network including different time scales, (ii) we use iterative learning control to compensate periodic demand patterns and save lower-layer control energy and (iii) we assure asymptotic stability and monotonic convergence in the iteration domain for the linearized dynamics and validate the performance by simulating the nonlinear dynamics.

Optimal Cyclic Spooling Control for Kite-Based Energy Systems

This paper presents a control strategy for optimizing the the spooling speeds of tethered energy harvesting systems that generate energy through cyclic spooling motions which consist of high-tension spool-out and low-tension spool-in. Specifically, we fuse continuous-time optimal control tools, including Pontryagin’s Maximum Principle, with an iteration domain co-state correction, to develop an optimal spooling controller for energy extraction. In this work, we focus our simulation results specifically on an ocean kite system where the goal is to optimize the spooling profile while remaining at a consistent operating depth and corresponding average tether length. This paper demonstrates a 14-45% improvement (depending on the operating tether length and environmental flow speed) in power generation compared to a baseline, heuristic, control strategy.

An Improved Approach to Iterative Learning Control for Uncertain Systems

For iterative learning control (ILC) algorithms to date, there is a fundamental tradeoff between plant model knowledge and convergence rate in the iteration domain. This article presents a new fast ILC (FILC) method that uses a novel error term in the ILC learning law based on techniques from sliding mode control (SMC). The input signal is guaranteed to remain bounded in the time and iteration domains and is insensitive to noise due to the unique structure of the FILC learning algorithm. Moreover, the FILC approach does not require end-user tuning of arbitrary gains, which is useful for uncertain systems with significant uncertainty. The stability and convergence properties for the FILC system are presented using the Lyapunov analysis techniques. Simulation and experimental system results on a manufacturing system compare FILC with the existing ILC techniques and demonstrate that FILC achieves improved iteration convergence while retaining stability when plant uncertainty is high.

Compensation‐based data‐driven ILC with input and output package dropouts

SummaryThis paper explores the problem of random data loss at both input and output sides and proposes a compensation‐based data‐driven iterative learning control (cDDILC) to refrain from deteriorating of the control performance due to the data loss. A linear data model is first established to describe the input‐output dynamics of a repetitive control system in the iteration domain. The linear data model, which only virtually exists in the computer without any physical backgrounds, is employed as a predictive model to estimate and compensate the lost output data. Meanwhile, the lost input data is replaced by the corresponding input of the same time instant in the latest previous iterations. Then, a cDDILC is proposed by introducing two Bernoulli random variables to describe the stochastic data loss at both input and output sides. The proposed cDDILC method is data driven and independent of a precise plant model. Although the design and analysis of the cDDILC start from a MIMO linear repetitive system, one can easily extend the results to a MIMO nonlinear nonaffine one. Theoretical analysis and simulations confirm the efficiency of the proposed cDDILC method.

Robust Monotonically Convergent Spatial Iterative Learning Control: Interval Systems Analysis via Discrete Fourier Transform

Additive manufacturing (AM) systems use a layer-by-layer paradigm to build three-dimensional structures. There are myriad of advantages to AM; however, challenges with real-time actuation and sensing relegate AM processes to be largely open-loop processes. In this paper, we build upon the spatial iterative learning control (SILC) strategy to close the loop in the iteration domain in AM systems, enabling autonomous process control in the absence of real-time sensing. We approximate the steady-state partial differential equations of AM systems by discrete two-dimensional convolution operators and assume uncertain spatially varying kernels to have a more realistic representation of these complex processes. From this system description, we formalize the robust monotonic convergence (RMC) criterion for SILC. Importantly, we use discrete Fourier transform-based tools to study spatial dynamics, a practical framework for data-rich spatial sensors used in AM. The theoretical results are complemented with experiments on the AM process electrohydrodynamic jet printing, demonstrating that the RMC criterion can predict the design boundary for convergent behavior for norm-optimal SILC.

Finite-Time Consensus for Linear Multi-Agent Systems Using Data-Driven Terminal ILC

In this brief, the finite time consensus problem for a class of unknown linear multi-agent systems is considered. Firstly, a linear mapping relationship between the agent’s terminal output and the control input along the iteration domain is established. Then, a novel distributed data-driven iterative learning consensus protocol is constructed only using the I/O data of each agent and its neighbors. Meanwhile, a convergence condition that does not depend on model information is derived for the multi-agent system. It is shown that the proposed protocol can guarantee that all agents achieve the finite-time consensus objective. Finally, an example of numerical simulation is given to verify the effectiveness of the proposed design.

Adaptive iterative learning control for a class of fractional-order nonlinear systems

Based on the discussions on the properties of fractional integral and Caputo fractional derivative, an adaptive iterative learning control approach is proposed for a class of fractional-order nonlinear system (FONS) with unknown time-varying parameter. With the design of learning controller and adaptive learning law for unknown parameter, the tracking error sequence converges to zero in the iteration domain while all the closed-loop signals remain bounded. Finally, a numerical example is given to verify the validity of the designed method.

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.

Adaptive iterative learning control for MIMO nonlinear systems performing iteration-varying tasks

The present work aims to develop a novel adaptive iterative learning control(AILC) method for nonlinear multiple input multiple output (MIMO) systems that execute various control missions with iteration-varying magnitude-time scales. In order to reduce the variations of the systems, this work proposes a series of time scaling transformations to normalize the iteration-varying trial lengths. An AILC scheme is then developed for the transformed control systems on a uniform trial length, which is shown to be capable of ensuring the asymptotic convergence of the tracking error. In other words, the proposed AILC algorithm is able to relax the constraint in conventional ILC where the control task must remain the same in the iteration domain. Additionally, the basic assumption in classic ILC that the control system must repeat on a fixed finite period is also removed. The convergence analysis of the AILC is derived rigorously according to the composite energy function (CEF) methodology. It is shown that the newly developed learning control strategy works well for control plants with either time-invariant or time-varying parametric uncertainties. To show the effectiveness of the AILC, three examples are illustrated in the end. Meanwhile, the proposed learning method is also implemented to a traditional X–Y table system.

Optimizing the Execution of Dynamic Robot Movements With Learning Control

High-speed robotics typically involves fast dynamic trajectories with large accelerations. Kinematic optimization using compact representations can lead to an efficient online computation of these dynamic movements, however successful execution requires accurate models or aggressive tracking with high-gain feedback. Learning to track such references in a safe and reliable way, whenever accurate models are not available, is an open problem. Stability issues surrounding the learning performance, in the iteration domain, can prevent the successful implementation of model-based learning approaches. To this end, in this paper we propose a new adaptive and cautious iterative learning control (ILC) algorithm where the stability of the control updates is analyzed probabilistically: the covariance estimates of the adapted local linear models are used to increase the probability of update monotonicity, exercising caution during learning. The resulting learning controller can be implemented efficiently using a recursive approach. We evaluate it extensively in simulations as well as in our robot table tennis setup for tracking dynamic hitting movements. Testing with two seven degree of freedom anthropomorphic robot arms, we show improved and more stable tracking performance over high-gain proportional and derivative (PD) control, model-free ILC (simple PD feedback type) and model-based ILC without cautious adaptation.

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.

PDα‐type iterative learning control for fractional‐order linear continuous‐time switched systems

AbstractFor a class of fractional‐order linear continuous‐time switched systems specified by an arbitrary switching rule, this paper proposes a PDα‐type fractional‐order iterative learning control algorithm. For systems disturbed by bounded measurement noise, the robustness of PDα‐type algorithm is first discussed in the iteration domain and the tracking performance is analyzed. Next, a sufficient condition for monotone convergence of the algorithm is studied when external noise is absent. The results of analysis and simulation illustrate the feasibility and effectiveness of the proposed control algorithm.

Adaptive iterative learning control for switched nonlinear continuous-time systems

ABSTRACTIn this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.

A comparison of compensation methods for random input data dropouts in networked iterative learning control system

In this paper, for a class of linear networked iterative learning control (ILC) systems, methods to compensate dropped input data in time or iteration domain are compared. Specifically, the transition matrices of input error at the controller side with the two methods are derived first, respectively. After that, the varieties of eigenvalues and elements in the lower triangular of the transition matrices are analyzed. Through analyzing the varieties, it can be easily found that the two methods guarantee the convergence of input error at the controller side, while only the compensation in iteration domain guarantees the convergence of input error at the actuator side. Due to the introduction of networks, the convergence of output error is determined by the input error at the actuator side. Hence, a conclusion could be made naturally that the output error converges to zero with compensation in iteration domain, while compensation in time domain cannot guarantee that. Finally, numerical experiments are given to corroborate the theoretical analysis.

Nonrepetitive trajectory tracking for nonlinear autonomous agents with asymmetric output constraints using parametric iterative learning control

SummaryIn this paper, we present a novel parametric iterative learning control (ILC) algorithm to deal with trajectory tracking problems for a class of nonlinear autonomous agents that are subject to actuator faults. Unlike most of the ILC literature, the desired trajectories in this work can be iteration dependent, and the initial position of the agent in each iteration can be random. Both parametric and nonparametric system unknowns and uncertainties, in particular the control input gain functions that are not fully known, are considered. A new type of universal barrier functions is proposed to guarantee the satisfaction of asymmetric constraint requirements, feasibility of the controller, and prescribed tracking performance. We show that under the proposed algorithm, the distance and angle tracking errors can uniformly converge to an arbitrarily small positive number and zero, respectively, over the iteration domain, beyond a small user‐prescribed initial time interval in each iteration. A numerical simulation is presented in the end to demonstrate the efficacy of the proposed algorithm.

Convergence Analysis of Iterative Learning Control Systems Over Networks With Successive Input Data Compensation in Iteration Domain

This paper analyzes the convergence of iterative learning control for a class of discrete-time systems over networks with successive input data compensation. Specifically, the successively dropped input data in current iterations are compensated by the one actuator received correctly with the same time instant label in the latest iteration. Through analyzing the variation of elements in the transition matrices of the input errors at the controller side, the convergence of output errors is addressed. The analysis shows the selection range of learning gain is determined by the maximum number of input data dropped successively. Moreover, the convergence of system with successive input data compensation is guaranteed by trading the convergence speed, and the more input data are successively compensated in iteration domain, the more convergence speed of the system is reduced. Finally, numerical experiments are given to corroborate the theoretical analysis.

Open-Closed-Loop Iterative Learning Control for Linear Systems With Iteratively Variable Trail Lengths

This paper addresses the open-closed-loop iterative learning control (ILC) issue for linear systems with iteratively variable trail lengths. Due to the varying trail lengths in iteration domain, some tracking information would be lost at the previous iterations. To compensate the absent information, an open-closed-loop ILC scheme composing of a feed-forward ILC part and a feedback control part is designed. The convergence of ILC tracking error in mathematical expectation sense is guaranteed by the feed-forward part. The tracking information of the current iteration is employed by feedback control part to compensate the missing tracking information at the previous iterations. To deal with the iteratively variable trail lengths, a modified tracking error at desired trail length is adopted in the designed ILC scheme. It is shown that the mathematical expectation of tracking error is convergent to zero. Two illustrative examples are carried out to show the effectiveness of the proposed ILC schemes.

High-Precision Tracking of Piezoelectric Actuator Using Iterative Learning Control and Direct Inverse Compensation of Hysteresis

Rate-dependent hysteretic nonlinearity, which is an inherent characteristic of piezoelectric actuators (PEAs), causes a significant challenge in precise motion control of piezoelectric nanopositioning stages. In this paper, by assuming that the model of PEA takes a Hammerstein structure, a novel control strategy that combines iterative learning control (ILC) and the direct inverse of hysteresis is proposed to compensate for both nonlinearities and uncertainties of system simultaneously. Different from those existing direct inverse compensation methods whose control performance highly relies on the accuracy of the hysteresis model, the proposed control strategy is more robust by adding an additional ILC loop. Since ILC is essentially a feedforward control scheme that fully utilizes the input and output information in previous iterations, the tracking precision can be improved promptly in the iteration domain. Comparative experiments are performed to test the efficacy of the proposed algorithm for polynomial, triangular, and step signals. Results show that it is superior to pure proportional–integral (PI) controller and even PI controller combined with inverse compensator in the sense that the root mean square, relative, as well as maximal absolute errors of output tracking have been decreased remarkably within five iterations.

A Survey on High-Order Internal Model Based Iterative Learning Control

Iterative learning control (ILC) has been developed for decades and is mainly used to solve the repetitive control tasks. However, in the actual operation of systems, there are many non-strictly repetitive or iteration-varying factors, such as the iteration-varying reference trajectory, non-repetitive system parameters, iteration-related initial states, iteration-dependent input and output disturbances, etc. In order to solve the non-strictly repetitive problems, the High-Order Internal Model (HOIM)-based ILC is proposed. HOIM can be formulated as a polynomial in the iteration domain, which is auto-regressive. HOIM-based ILC for nonlinear systems is more complex than HOIM-based ILC for linear systems, and when the system parameters change iteratively, the Lyapunov-based analysis method is used instead of traditional contraction mapping method. Not only can HOIM be integrated into the traditional ILC, it can be also combined with other control methods, such as adaptive control, terminal control, repetitive control and so on. In this paper, we review the advances in HOIM-based ILC, systematically sort out the development and main contents of HOIM, summarize its main applications and extensions, and finally put forward some further development directions.

High-Order Internal Model-Based Iterative Learning Control for 2-D Linear FMMI Systems With Iteration-Varying Trajectory Tracking

This paper is concerned with iterative learning control (ILC) algorithms for two-dimensional (2-D) linear discrete systems described by the first Fornasini–Marchesini model (FMMI) with iteration-varying reference trajectories/profiles. The variation of reference trajectories in iteration domain is represented by a high-order internal model (HOIM) formula. Robustness and convergence of two types of HOIM-based ILC laws with different boundary conditions are investigated, respectively. A strategy employed in this paper is to reconstruct the HOIM-based ILC process of the 2-D linear FMMI system into a set of 2-D linear inequalities or a 2-D linear Roesser model such that sufficient robustness/convergence conditions of the HOIM-based ILC laws are obtained. Under random boundary conditions, the designed ILC law (9) is capable to drive the ILC tracking error into a bounded range. Moreover, under the HOIM-based boundary conditions, a perfect tracking to the iteration-varying reference trajectories can be achieved by utilizing the proposed ILC law (32). Two simulation examples are given to validate the effectiveness of the two proposed ILC algorithms.