بررسی تصادفی کنترل یادگیری تکراری

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.

In our daily lives, the ability to repeatedly work on a given task would lead to constant improvements. For example, in basketball set shooting, as the number of attempts increases, the shooter is able to increase the hit ratio since he/she may adjust the angle and speed to reduce the shooting deviation shot by shot. The basic reason for this is that we are able to learn from experiences and subsequently improve our behaviors. This basic cognition has motivated research on iterative learning control (ILC). That is, ILC is a control method that improves its control performance by learning from previous control performance. Specifically, ILC is usually designed for systems that are able to complete some task over a fixed time interval and perform them repeatedly. In such systems, the input and output information of past cycles, as well as the tracking objective, are used to formulate the input signal for the next iteration, so that the tracking performance can be improved as the number of cycles increases to infinity. Thus, ILC has the following features: (1) the system can finish a task in a limited time, (2) the system can be reset to the same initial value, and (3) the tracking objective is iteration-invariant. The main idea of ILC is shown in Fig. 1.In Fig. 1, yd denotes the reference trajectory. Based on the input of the kth iteration, uk, as well as the tracking error ek = yd − yk, the input uk+1 for the next iteration, i.e., the (k + 1)th iteration, is constructed. Meanwhile, the input uk+1 is also stored into the memory for the (k + 2)th iteration. Thus, a closed loop feedback is formed along the iteration index. By comparing ILC with our daily lives, we find that the previous information on inputs and outputs of the plant corresponds to the experiences faced in our daily lives. Persons usually decide on a strategy for a given task based on previous experiences, while the strategy here is equivalent to the input signal of ILC. Note that the previous experiences would help us to improve our behavior; thus, it is reasonable to believe that information on the previous operation may help to improve the control performance to some extent. The major advantage of ILC is that the design of control law only requires the tracking references and input/output signals. In other words, not much information about the plant is required and it may even be completely unknown. However, the algorithm is simple and effective. It is important to note that ILC adjusts the control along the iteration index rather than the time index, which is the main difference with other control methods such as proportional-integral-derivative (PID) control. PID control is a widely used feedback control. However, for iteration type systems, PID generates the same tracking error during each iteration since no previous information is used, while ILC reduces the tracking error iteration by iteration. Additionally, ILC differs from adaptive control, which also learns from previous operation information. Adaptive control aims to adjust the parameter of a given controller, while ILC aims to construct the input signal directly. The concept of ILC may be traced back to a paper published in 1978 by Uchiyama [1]. However, this paper failed to attract widespread attention as it was written in Japanese. Three papers that were published in 1984 [2], [3] and [4] resulted in further the research on ILC. Subsequently, large amounts of literature have been published on various related issues, such as research monographs [5], [6], [7], [8] and [9], survey papers [10], [11] and [12], and special issues of academic journals [13], [14], [15] and [16]. ILC has recently become an important branch of intelligent control, and its use is widespread in many practical applications such as robotics [17], [18], [19] and [20], hard disk drives [21] and [22], and industrial processes [23] and [24].

In this paper, research into SILC is surveyed and analyzed. Specifically, SILC for linear stochastic systems and nonlinear systems are first discussed according to the key approaches. As stated earlier, the Kalman filtering based approach and stochastic approximation based approaches are the two major approaches for SILC. Then, SILC for systems with other stochastic signals including packet losses, asynchronism, and time delays are discussed, which, as one could see, is still at the first stage. Moreover, some promising directions are briefly reviewed, namely SILC for point-to-point control, SILC for iteration-varying references tracking, and decentralized/distributed coordinated SILC, respectively. We believe that there is scope for further development in this area. It is worth noting that studies into the application of SILC are very few. Most papers give numerical simulation results such as [34], which considers two different models of an inductor for angular speed tracking control. However, practical applications are yet to be identified. As is well known, random disturbances/noises are inevitable in practical systems, and more effort is therefore welcomed in this regard. However, it should be mentioned that although we have try our best to seek as many related SILC papers as possible, we may have missed some important papers. Besides, more attention has been given to SILC by academics and engineers, thus many related papers may be currently in press awaiting publication. Nevertheless, we believe that this paper may help readers to understand the history, current status, and trend of SILC, and it is hoped more publications on this attractive subject will be realized in the future.