Model-free Iterative Learning Control Research Articles

Hybrid-based model-free iterative learning control with optimal performance

In this paper, a hybrid-based model-free iterative learning control algorithm is proposed to improve the robustness and convergence speed of model-free iterative learning control in noisy environments. The proposed algorithm divides the iterative process into a rapidly decreasing error phase and an error convergence phase, and uses different control algorithms in different phases, thus combining different advantages of the original algorithms. In addition to this, this work proves the convergence and robustness of the proposed algorithm and summarises the design idea of this controller. Finally, the convergence performance of the algorithm in noisy environments and in variable reference trajectory environment is simulated to demonstrate the effectiveness of the algorithm proposed in this work.

Trajectory Tracking within a Hierarchical Primitive-Based Learning Approach

A hierarchical learning control framework (HLF) has been validated on two affordable control laboratories: an active temperature control system (ATCS) and an electrical rheostatic braking system (EBS). The proposed HLF is data-driven and model-free, while being applicable on general control tracking tasks which are omnipresent. At the lowermost level, L1, virtual state-feedback control is learned from input–output data, using a recently proposed virtual state-feedback reference tuning (VSFRT) principle. L1 ensures a linear reference model tracking (or matching) and thus, indirect closed-loop control system (CLCS) linearization. On top of L1, an experiment-driven model-free iterative learning control (EDMFILC) is then applied for learning reference input–controlled outputs pairs, coined as primitives. The primitives’ signals at the L2 level encode the CLCS dynamics, which are not explicitly used in the learning phase. Data reusability is applied to derive monotonic and safely guaranteed learning convergence. The learning primitives in the L2 level are finally used in the uppermost and final L3 level, where a decomposition/recomposition operation enables prediction of the optimal reference input assuring optimal tracking of a previously unseen trajectory, without relearning by repetitions, as it was in level L2. Hence, the HLF enables control systems to generalize their tracking behavior to new scenarios by extrapolating their current knowledge base. The proposed HLF framework endows the CLCSs with learning, memorization and generalization features which are specific to intelligent organisms. This may be considered as an advancement towards intelligent, generalizable and adaptive control systems.

Model-free repetitive control design and implementation for dynamical galvanometer-based raster scanning

Data-driven repetitive control (RC) is proposed in this work to track online, dynamical raster trajectories in galvanometer-based scanning. To remove the requirement of a plant model in conventional model-based RC, we use model-free iterative learning control (ILC) to synthesize the data-driven repetitive controllers. Specifically, the frequency-domain plant-inversion and loop-shaping methods are both converted into time-domain trajectory tracking problems. The ILC is then applied to solve the trajectory tracking problems and subsequently derive the repetitive controllers from data. The stability conditions of both methods are analyzed and used to guide the data-driven control design. Experimental results on a commercially available galvanometer scanner demonstrate that the proposed methods improve the tracking error of a predefined raster scan by more than 30 times, as the conventional ILC does. Moreover, after applying data-driven RC, users can online assign various center positions and magnitudes of the raster trajectory. Once assigning a new reference in this continuous mode, the tracking error rapidly converges to the steady-state within ten periods.

Event-triggered data-driven control of discrete-time nonlinear systems with unknown disturbance

This paper is dedicated to event-triggered data-driven control of nonlinear systems with unknown disturbance via model free iterative learning approach. An extended state observer is employed to reconstruct the disturbance in system output. An event-triggered model free iterative learning control strategy is constructed by system input, system output and the reconstructed disturbance. Sufficient conditions are proposed to make the resultant tracking error system be uniform ultimate bounded. Simulation examples are provided to validate the effectiveness of the proposed scheme.

Model-Free Iterative Learning Control With Nonrepetitive Trajectories for Second-Order MIMO Nonlinear Systems—Application to a Delta Robot

A model-free iterative learning control strategy (ILC) in nonrepetitive trajectories, applied to robotic manipulators is presented in this article. The development of this ILC controller is derived in general case for second-order nonlinear multi-input multi-output (MIMO) systems subjected to external disturbances. Unlike most of the ILC implementations in the literature, which considers both the resetting condition and periodic trajectories; the proposed ILC controller is model-free and works under the practical alignment condition and noncyclic desired trajectories. Furthermore, these trajectories may vary in magnitude and in the starting and terminal points. The Lyapunov stability approach is combined with a time scale transformation to synthesize the control law. The asymptotic convergence of both the position and velocity tracking errors are demonstrated along the iteration axis. Finally, experimental results in pick and place operations of a parallel Delta robot are presented and discussed. These results are very effective and clearly point out the high potential of the developed model-free ILC technique for industrial robotic applications.

On Improving Transient Behavior and Steady-State Performance of Model-free Iterative Learning Control

A novel model-free iterative learning control algorithm is proposed in this paper to improve both the robustness against output disturbances and the tracking performance in steady-state. For model-free ILC, several methods have been investigated, such as the time-reversal error filtering, the Model-Free Inversion-based Iterative Control (MFIIC), and the Non-Linear Inversion-based Iterative Control (NLIIC). However, the time-reversal error filtering has a conservative learning rate. Other two methods, although with much faster error convergence, have either a high noise sensitivity or a non-optimized steady-state. To improve the performance and robustness of model-free ILC, we apply the time-reversal based ILC and recursively accelerate its error convergence using the online identified learning filter. The effectiveness of the proposed algorithm has been validated by a numerical simulation. The proposed approach not only improves the transient response of the MFIIC, but achieves lower tracking error in steady-state compared to that of the NLIIC.

A Model-Free Loop-Shaping Method based on Iterative Learning Control

Many techniques have been developed for the loop-shaping method in control design. While most loop-shaping methods apply a model of the open-loop controlled plant, the resulting performance depends on the accuracy of the dynamical model. This paper aims to develop a model-free loop-shaping technique. The core idea is to convert the model matching problem to a trajectory tracking problem. To achieve the desired loop gain, we need to determine the control input such that the system output tracks the impulse response of the loop gain function. In this paper, a model-free iterative learning control (ILC) algorithm is applied to solve this tracking problem. Once the ILC converges, the feedback controller that meets the desired loop gain can then be constructed. This method does not require the model of the controlled plant, hence it provides better performance of loop-shaping control design. The proposed method is validated through numerical simulation on a 3-rd order plant.

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.

A novel control strategy for balancing traffic flow in urban traffic network based on iterative learning control

Realistic modeling traffic flow dynamics in urban traffic network remains a big challenge at present due to the complex nonlinear characteristics of traffic flow. In this paper, a novel and model-free iterative learning control (ILC) strategy for balancing traffic flow in urban traffic network is proposed. To tackle the randomly varying trial lengths in the iteration domain of traffic system, an iterative-average operator is introduced in the proposed ILC law for tracking tasks with non-uniform trial lengths, which thus mitigates the requirement on classic ILC that all trial lengths must be identical. The learning convergence condition of the ILC strategy in iteration-average and expectation is derived through rigorous analysis. The performance and the effectiveness of the ILC strategy are analyzed by simulations on a test road network. The results show that the proposed ILC strategy can homogeneously balance the accumulation in the network and improve the network mobility.

Three-level hierarchical model-free learning approach to trajectory tracking control

This paper suggests a novel three-level model-free hierarchical learning approach that solves the reference trajectory tracking problem for control systems (CSs). The new approach consists of the low level, the intermediate level and the high level, it relies on past memorized optimal input output execution patterns and adaptively merges them using a similarity measure. The low level feedback control is carried out in a novel model-free framework using a neural network (NN) controwller tuned by Virtual Reference Feedback Tuning (VRFT) in order to linearize the closed-loop CS and to match a linear reference model. The NN controller is tuned in two phases, an offline one and an online one. Nonlinear Model Predictive Control (NMPC) is first employed in the novel offline tuning phase. The online tuning phase makes next use only of the process sign in the dynamic back-propagation mechanism that updates the NN parameters. After the NN controller is trained and the feedback CS is fixed, the optimal execution patterns (input/output patterns) are defined in terms of optimal control problems, which balance control accuracy and control effort. The input/output patterns are formulated over a feedback CS and are solved in a model-free Iterative Learning Control (ILC) framework for linear time-invariant systems at the intermediate level. Once the optimal executions are learned at the intermediate level over the feedback CS, they are stored in a database (DB). Then each time a new trajectory is to be tracked as required by the high level planner, similar patterns of executions are looked-up in the DB and are merged by the weighted average sum of most similar patterns resulted from a sort algorithm using a distance metric. The proposed approach is tested on the position control of a Single Input-Single Output nonlinear aerodynamic control system and shows trajectory tracking performance improvement with respect to the case when no learnt experience is used.

Optimal behaviour prediction using a primitive-based data-driven model-free iterative learning control approach

This paper suggests an optimal behaviour prediction mechanism for Multi Input-Multi Output control systems in a hierarchical control system structure, using previously learned solutions to simple tasks called primitives. The optimality of the behaviour is formulated as a reference trajectory tracking problem. The primitives are stored in a library of pairs of reference input/controlled output signals. The reference input primitives are optimized at the higher hierarchical level in a model-free iterative learning control (MFILC) framework without using knowledge of the controlled process. Learning of the reference input primitives is performed in a reduced subspace using radial basis functions for approximations. The convergence of the MFILC learning scheme is achieved via a Virtual Reference Feedback Tuning design of the feedback controllers in the lower level feedback control loops. The new complex trajectories to be tracked are decomposed into the output primitives regarded as basis functions. Next, the optimal reference input fed to the control system in order to track the desired new trajectory is then recomposed from the reference input primitives. The efficiency of this approach is demonstrated on a case study concerning the control of a two-axis positioning mechanism, and the experimental validation is offered.

Visual trajectory tracking of industrial manipulator with iterative learning control

Purpose – The purpose of this paper is to propose a more efficient strategy, which is easier to implement, i.e. the engineer can directly operate the target object without the robot to do a demonstration, and the manipulator is regulated to track the trajectory using vision feedback repetitively. Generally, the applications of industrial robotic manipulators are based on teaching playback strategy, i.e. the engineer should directly operate the manipulator to perform a demonstration and then the manipulator uses the recorded driving signals to perform repetitive tasks. Design/methodology/approach – In the teaching process, the engineer grasps the object with a camera on it to do a demonstration, during which a series of images are recorded. The desired trajectory is defined by the homography between the images captured at current and final poses. Tracking error is directly defined by the homography matrix, without 3D reconstruction. Model-free feedback-assisted iterative learning control strategy is used for repetitive tracking, where feed-forward control signal is generated by iterative learning control strategy and feedback control signal is generated by direct feedback control. Findings – The proposed framework is able to perform precise trajectory tracking by iterative learning, and is model-free so that the singularity problem is avoided which often occurs in conventional Jacobean-based visual servo systems. Besides, the framework is robust to image noise, which is shown in simulations and experiments. Originality/value – The proposed framework is model-free, so that it is more flexible for industrial use and easier to implement. Satisfactory tracking performance can be achieved in the presence of image noise. System convergence is analyzed and experiments are provided for evaluation.

A Simultaneous Iterative Learning Control and Dynamic Modeling Approach for A Class of Nonlinear Systems

This paper presents a novel simultaneous iterative learning control and dynamic modeling (SILCDM) approach. For a class of unknown and repeatable nonlinear discrete-time systems, a model-free iterative learning control (ILC) method is applied first. Meanwhile, by using the data generated during the repetitive operations, a novel iterative learning parameter estimation algorithm is proposed to calibrate the unknown time-varying parameter in the nonlinear system with known structure simultaneously. After the model parameter is well identified, the accurate dynamic model of the controlled plant is obtained. With this identified model, the model-free ILC method is then switched to a model-based optimal ILC method in order to get much better control performance. The theoretical analysis shows that the proposed pproach guarantees the convergence of both the system state and the parameter identification. The effectiveness of the SILCDM is further demonstrated through simulations.

Probabilistic tracking control for non-Gaussian stochastic process using novel iterative learning algorithms

A new generalised iterative learning algorithm is presented for complex dynamic non-Gaussian stochastic processes. After designed neural networks are used to approximate the output probability density function (PDF) of the stochastic system in the repetitive processes or the batch processes, the complex probabilistic tracking control to the output PDF is simplified into a parameter tuning problem between two adjacent repetitive processes. Under this framework, this article studies a novel model free iterative learning control problem and proposes a convex optimisation algorithm based on a set of designed linear matrix inequalities and L 1 optimisation index. It is noted that such an algorithm can improve the tracking performance and robustness for the closed-loop PDF control. A simulated example is given, which effectively demonstrates the use of the proposed control algorithm.

Model-free iterative learning control for LTI systems with actuator constraints

AbstractThis paper presents a model-free iterative learning control algorithm for linear time-invariant systems. At every trial, a finite impulse response filter to update the system input is calculated by solving a convex optimization problem that minimizes the next trial's tracking error taking into account actuator constraints. Simulation results show the ability of the proposed model-free method to deal with actuator constraints and to fully compensate for trial-invariant disturbances such as actuator cogging.