Newton-method based iterative learning control method for nonlinear systems

A novel iterative learning control (ILC) algorithm was developed and applied to an active flow control problem. The technique uses pulsed air jets to delay flow separation on a two-element high-lift wing. The ILC algorithm uses position-based pressure measurements to update the actuation. The method was experimentally tested on a wing model in a 0.9 m × 0.6 m low-speed wind tunnel at the University of Southampton. Compressed air and fast switching solenoid valves were used as actuators to excite the flow, and the pressure distribution around the chord of the wing was measured as a feedback control signal for the ILC controller. Experimental results showed that the actuation was able to delay the separation and increase the lift by approximately 10%–15%. By using the ILC algorithm, the controller was able to find the optimum control input and maintain the improvement despite sudden changes of the separation position.

An estimation-based iterative learning control (ILC) algorithm is applied to a realistic industrial manipulator model. By measuring the acceleration of the end-effector, the arm angular position accuracy is improved when the measurements are fused with motor angle observations. The estimation problem is formulated in a Bayesian estimation framework where three solutions are proposed: one using the extended Kalman filter (EKF), one using the unscented Kalman filter (UKF), and one using the particle filter (PF). The estimates are used in an ILC method to improve the accuracy for following a given reference trajectory. Since the ILC algorithm is repetitive no computational restrictions on the methods apply explicitly. In an extensive Monte Carlo simulation study it is shown that the PF method outperforms the other methods and that the ILC control law is substantially improved using the PF estimate.

Iterative learning control (ILC) involves a trade-off between perfect, fast attenuation of iteration-invariant disturbances and amplification of iteration-varying ones. The aim of this paper is to develop a nonlinear ILC framework that achieves fast convergence, robustness, and low converged error values in ILC. To this end, the method includes a deadzone nonlinearity in the learning update, which uses the difference in amplitude characteristics of repeating and varying disturbances to modify the learning gain for each error sample. A criterion for monotonic convergence of the nonlinear ILC algorithm is provided, which is used in combination with system measurements to select suitable design parameters. The proposed algorithm is validated using simulations, in which fast convergence to low error values is demonstrated.

This note considers the problem of iterative learning control (ILC) for a class of linear continuous-time multiple-input multiple-output (MIMO) systems with vector relative degree, where the trail length of control input is different from that of system state and output for a specific iteration. An iteration-average operator is included in the proposed ILC law to address the varying trail lengths. The proposed ILC algorithm allows that the control input length is iteration-varying during the ILC process, and can achieve desired trajectory tracking at control time interval. A numerical example is carried out to illustrate the effectiveness of the proposed ILC scheme.

ABSTRACTThis paper addresses the problem of iterative learning control (ILC) for a class of nonlinear continuous‐time systems with higher relative degree. The proposed ILC solution is a family of updating laws using differentiations of tracking error with the order less than the system relative degree. A unified convergence condition for this family of ILC updating laws is provided and proved to be independent of the highest order of differentiation. The application to path tracking of a robotic manipulator is presented to illustrate the effectiveness of the proposed method.

Iterative learning control is an intelligent control algorithm which imitates human learning process. Based on this concept, this paper discussed iterative learning control problem for a class parabolic linear distributed parameter systems with uncertainty coefficients. Iterative learning control algorithm with forgetting factor is proposed and the conditions for convergence of algorithm are established. Combining the matrix theory with the basic theory of distributed parameter systems gives rigorous convergence proof of the algorithm. Finally, by using the forward difference scheme of partial differential equation to solve the problems, the simulation results are presented to illustrate the feasibility of the algorithm.

Nonlinear iterative learning control with applications to lithographic machinery

In this paper, the iterative learning control (ILC) problem is investigated for a class of time-invariant parabolic singular distributed parameter systems. Initially, the singular distributed parameter systems is decomposed into infinite number of singular systems based on the separation principle. Meanwhile, the slow-fast subsystems are introduced via singular value decomposition method. Then, a novel mixed PD-type ILC algorithm with finite dimension is designed for the low dimensional slow part and the corresponding convergence conditions are manifested. With the proposed controller, the output error of high dimensional fast complement can satisfy the given value instead of neglecting the effect of high dimensional modes. Furthermore, under the aforesaid ILC law and the appropriate number of the low dimensional slow part, the resulting tracking error of parabolic singular distributed parameter systems can converge to any small tracking accuracy. Finally, simulation results on the distributed building automatic temperature system verify the convergence and effectiveness of the mixed PD-type ILC algorithm.

The problem of iterative learning control (ILC) is considered for a class of time-varying systems with random packet dropouts. It is assumed that an ILC scheme is implemented via a remote control system and that packet dropout occurs during the packet transmission between the ILC controller and the actuator of remote plant. The packet dropout is viewed as a binary switching sequence which is subject to the Bernoulli distribution. In order to eliminate the effect of packet dropouts on the convergence property of output error, the hold-input scheme is adopted to compensate the packet dropout at the actuator. It is shown that the hold-input scheme with average ILC can achieve asymptotical convergence along the iteration axis for discrete time-varying linear system. Numerical examples are provided to show the effectiveness of the proposed method.

ABSTRACTIn this paper, the iterative learning control problem for a class of nonlinear singular impulsive systems is discussed. Then, a D-type (derivative-type) iterative learning control algorithm is presented such that the output tracks the desired output trajectory as accurate as possible. Furthermore, the sufficient condition for the convergence of the proposed algorithm is established in detail. Finally, a numerical example is included to corroborate the theoretical analyses.

Iterative learning control for nonlinear stochastic systems with variable pass length

This article investigates the iterative learning control problem for a class of nonlinear heterogeneous multi-agent systems. The main contribution of this article is to apply iterative learning control algorithm to the multi-agent systems with multiple leaders, and solve the containment control problem of multi-agent systems in the sense of iterative learning control stability. Based on the framework of communication topologies, distributed iterative learning controllers are designed. And when the iterative learning control laws are applied to the systems, the containment errors between the followers’ states and the convex hull spanned by the leaders’ states over a finite-time interval are bounded, and furthermore, the containment errors can converge to zero as the iteration index approaches to infinity in the absence of initial errors. A simulation example is finally constructed to verify the effectiveness of the theoretical method.

In this paper we identify the similarities between iterative learning control (ILC) and root computing schemes for nonaffine static mapping functions. Applying the systematic approaches of numerical analysis, we developed several ILC algorithms and identify the convergence rate for each of them. Simulation results are given to certify these theorems.

Method to improve convergence performance of iterative learning control systems with bounded noise

Lots of iterative learning control (ILC) algorithms have been developed to improve tracking performance of systems that track same trajectory repetitively. In this paper, we use an open-closed-loop PD-type ILC scheme for the control of a class of nonlinear systems. Sufficient condition for guaranteeing the convergence of the learning scheme is given under a few reasonable assumptions, and then proved with linear operator theory. It is shown that the proportional coefficients of the ILC scheme is not a factor for guaranteeing the convergence, the condition is weaker than known results for similar ILC schemes.