Stochastic Iterative Learning Control Research Articles

Fractional Stochastic Integro-Differential Equations with Nonintantaneous Impulses: Existence, Approximate Controllability and Stochastic Iterative Learning Control

In this paper, existence/uniqueness of solutions and approximate controllability concept for Caputo type stochastic fractional integro-differential equations (SFIDE) in a Hilbert space with a noninstantaneous impulsive effect are studied. In addition, we study different types of stochastic iterative learning control for SFIDEs with noninstantaneous impulses in Hilbert spaces. Finally, examples are given to support the obtained results.

Repetitive process based stochastic iterative learning control design for linear dynamics

A new set of iterative learning control laws for systems described by stochastic discrete linear dynamics is developed using the passivity based stability theory for discrete nonlinear repetitive processes. This setting allows the application of a nonlinear control law to discrete linear systems. The advantages of such a control law in tuning the performance of the design is demonstrated by a case study that also compares the performance of one member of this class of new laws against an existing design.

Stochastic iterative learning control with faded signals

Stochastic iterative learning control &#x0028 ILC &#x0029 is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists. Illustrative examples are provided to verify the effectiveness of the proposed schemes.

Probability Based Stochastic Iterative Learning Control for Batch Processes With Actuator Faults

This paper proposes a new stochastic composite iterative learning control for batch processes with actuator faults that happen with a certain kind of probability. The main contribution lies in the fact that stochastic control theory is used to analyze the stability issues and consider controller designs of batch processes with actuator faults that happen under various kinds of probability, which paves the way for reliable control theory. Firstly, the batch process is represented as a system with stochastic uncertainty for iterative learning control design; and with the state and output error, it is further treated into a two dimensions (2D) Rosser system with stochastic errors. Using such transformation, the iterative learning control design is transformed into the updating control law design. Secondly, 2D Lyapunov stochastic theory is used to design the controller with actuator faults under various kinds of probability, together with the stability results of the control system in terms of LMI conditions. Finally, the proposed method is tested on the injection molding process to demonstrate the effectiveness.

A Technical Overview of Recent Progresses on Stochastic Iterative Learning Control

This paper contributes to a technical overview of recent progresses on stochastic iterative learning control (ILC), where stochastic ILC implies the learning control for systems with various random signals and factors such as stochastic noises, random data dropouts and inherent random asynchronism. The fundamental principles of ILC are first briefed with emphasis on the system formulations and typical analysis methods. Then the recent progresses on stochastic ILC are reviewed in three parts: additive randomness case, multiplicative randomness case, and coupled randomness case, respectively. Three major approaches, i.e., expectation-based method, Kalman filtering-based method, and stochastic approximation-based method, are clarified. Promising research directions are also presented for further investigation.

Mean‐square error constrained approach to robust stochastic iterative learning control

A Kalman filtering-based robust iterative learning control algorithm is proposed in this study for linear stochastic systems with uncertain dynamics and unknown noise statistics. Firstly, a learning gain matrix is designed for the nominal case by minimising the trace of the mean-square matrix of the input tracking error. Theoretical results show that the proposed algorithm guarantees not only the asymptotic but also monotonic convergence of the input tracking error in the mean-square error sense, especially when random noises are Gaussian distributed the proposed algorithm is further proved to be asymptotically efficient. In addition, a new mean-square error constrained approach is presented in designing the robust learning gain matrix, taking into account model uncertainties. A sufficient condition is provided such that the mean-square matrix of the input tracking error is constrained within a predesigned upper bound which can monotonically converge to zero. Finally, numerical examples considering both structured and unstructured model uncertainties are included to illustrate the effectiveness of the proposed algorithms.

An optimal stochastic multivariable PID controller: a direct output tracking approach

ABSTRACTThis paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise. We consider multi-input multi-output linear time-invariant systems and a proportional-integral-derivative (PID) controller. The system under consideration needs not be stable. A recursive algorithm providing optimal time-varying PID gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs. The development of the proposed algorithm aims for per-time-sample minimisation of the mean-square output error in the presence of erroneous initial conditions, measurement noise, and process noise. Necessary and sufficient conditions are provided for the convergence of the output error covariance. In addition, convergence results are presented for discretised continuous-time plants. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. Performance comparison with an optimal stochastic iterative learning control scheme, an optimal PID controller, an adaptive PID controller, and a recent optimal stochastic PID controller are also included.

Stochastic iterative learning control for discrete linear time-invariant system with batch-varying reference trajectories

In this paper, we present adaptive iterative learning control (ILC) schemes for discrete linear time-invariant (LTI) stochastic system with batch-varying reference trajectories (BVRT). If reference trajectories change every batch, ILC shows a different convergence property from that of the identical reference trajectory. First, we derive the convergence property and propose deterministic adaptive ILC combined with iterative learning identification for LTI system with BVRT. If the state noise and measurement noise exist, convergence rate and tracking performance are degraded because the controller considers the difference arising from the noise as tracking error. To deal with such a problem, we propose two approaches. The first is based on a batch-domain Kalman filter, which uses the difference between the current output trajectory and the next reference trajectory as a state vector, while the second is based on a time-domain Kalman filter. In the second approach, the system is identified at the end of each batch in an iterative fashion using the observer/Kalman filter identification (OKID). Then, the stochastic problem is handled using Kalman filter with a steady-state Kalman gain obtained from the identification. Therefore, the second approach can track the reference trajectories of discrete LTI stochastic system using only the input–output information. Simulation examples are provided to show the effectiveness of the proposed schemes.

Survey on stochastic iterative learning control

Iterative learning control (ILC) is suitable for systems that are able to repeatedly complete several tasks over a fixed time interval. Since it was first proposed, ILC has been further developed through extensive efforts. However, there are few related results on systems with stochastic signals, where by stochastic signal we mean one that is described by a random variable. Stochastic iterative learning control (SILC) is defined as ILC for systems that contain stochastic signals including system noises, measurement noises, random packet losses, etc. This manuscript surveys the current state of the art in SILC from the perspective of key techniques, which are divided into three parts: SILC for linear stochastic systems, SILC for nonlinear stochastic systems, and systems with other stochastic signals. In addition, three promising directions are also provided, namely stochastic ILC for point-to-point control, stochastic ILC for iteration-varying reference tracking, and decentralized/distributed coordinated stochastic ILC, respectively.

Evaluation of Initial Input Effects on Discrete‐Time Stochastic Iterative Learning Control

AbstractThis paper is devoted to the performance evaluation of initial input effects on discrete‐time iterative learning control (ILC) when the plants are subject to random iteration‐varying disturbances. The optimal selection of initial input is provided from the viewpoints of both expectation and variance by investigating the derivative of the error function with respect to the initial input. It is shown that the nonrandom initial input minimizing the initial expected tracking error can enable the tracking error to possess the minimal expectation and variance at all iterations. Simulation tests are included to verify the theoretical study.

Discrete-time Intermittent Iterative Learning Controller with Independent Data Dropouts

In networked control systems (NCS), it is considered essential to design a robust controller such that the networked-system is stable against data dropouts during the network transfer. It has been shown that there is a critical data dropout rate over which the networked-system could be unstable; hence the desired task cannot be achieved. This paper shows that a desired task or trajectories can be still achieved even though there are feedback signal dropouts if the desired task is repetitive, as in the iterative learning control case. Specifically this paper shows how to design stochastic iterative learning control systems such that the networked-system with a repetitive task is robust stable against measurement and process noises and independent, intermittent output channel dropouts.

A Discrete-Time Stochastic Iterative Learning Control Algorithm for a Class of Nonlinear Systems

A Discrete-Time Stochastic Iterative Learning Control Algorithm for a Class of Nonlinear Systems

A stochastic iterative learning control algorithm with application to an induction motor

A recursive optimal algorithm, based on minimizing the input error covariance matrix, is derived to generate the learning gain matrix of a P-type ILC for linear discrete-time varying systems with arbitrary relative degree. It is shown that, in the case where the number of inputs is not greater than the number of outputs, the input error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of uncorrelated random state disturbance, reinitialization errors and measurement noise. The state error covariance matrix converges to zero at a rate inversely proportional to the number of iterations in the presence of measurement noise. In the case where the number of inputs is greater than the number of outputs, then the system output error converges to zero at a rate inversely proportional to the number of iterations in presence of measurement noise. Another suboptimal recursive algorithm is also proposed based on unknown system dynamics and unknown disturbance statistics. The convergence characteristics are shown to be similar to the ones of the optimal recursive algorithm. The proposed ILC algorithms are applied to two different models of an induction motor for angular speed tracking control. One model describes its dynamics in stator fixed (a, b) reference frame without current loops and the other model is also in stator fixed reference(a, b) reference frame but with high-gain current loops. The simulation results show good tracking performance in the presence of noise with erroneous model parameters and noise statistics. An open-loop control is also proposed to improve the tracking rate of the proposed ILC algorithms.