Iterative Learning Control Under Networked Structure
Iterative learning control (ILC) is an intelligent control method for repetitive systems that can achieve precise tracking performance within a finite time interval. Here, repetitive systems mean those can complete the desired tasks in a given time interval and repeat it for iterations. For these systems, ILC can continuously adjust its control signal based on the data of input, output, and the tracking error from the previous iterations; therefore, the tracking performance can be gradually improved as the number of iterations increases.
With the fast development of communication technology, more and more industrial systems have adopted the networked control structure to increase the robustness, flexibility, and safety of the whole system. However, networked control structure will unavoidably induce new issues such as data dropout, communication delay, signal fading, and limited bandwidth. These issues constitute our major concern in the current research.
First, we conducted a series of research on ILC in the presence of random data dropouts and established a systematic research framework. Particularly, we extended the research from five dimensions including the type of systems, the model of data dropouts, data dropping position, algorithm design, and convergence analysis, which produces systematic results. From the perspective of system type, we extend the related research to stochastic linear and nonlinear systems; from the perspective of data dropout modeling, we propose finite-length stochastic sequence model and Markov chain model in addition to the conventional Bernoulli model; from the perspective of dropping position, we investigate the general case that both input and output signals suffer random loss during transmission and prove that the asynchronism between input updates of the plant and controller can be described by a Markov chain; from the perspective of algorithm design, we present the first successive update scheme and its strict convergence analysis; and from the perspective of convergence analysis, we establish both mean square and almost sure convergence for the proposed intermittent and successive update schemes, which are the strongest convergence in the sense of stochastic analysis. In addition, we also consider the complicated case where data dropout, transmission disorder, and communication delay are coupled in the network, in the meantime the storage affords the space for data of one iteration merely. We propose a novel renewal mechanism for the buffer and a recognition mechanism for the controller to solve the previously mentioned difficulties.
Next, in consideration of the operation safety and physical limitations, system running process may be terminated randomly before the desired end and restarted, which brings us the ILC problem under randomly varying iteration length circumstances. We investigate this problem from the aspects of modeling random lengths, designing algorithms, and analyzing performance to conduct fundamental contributions. From the perspective of modeling random lengths, we propose several stochastic models for both discrete-time and continuous-time systems and depict the necessary conditions of systems to achieve precise tracking. From the perspective of algorithm design, we propose multiple data compensation mechanisms for different scenarios and provide direct and indirect updating schemes. From the perspective of convergence analysis, we propose novel analyzing techniques and establish solid convergence for various types of systems.
Further, to effectively reduce the channel burden of information exchange, data quantization is a common method. Aiming to quantized ILC, we proposed a so-called error quantization scheme, which can guarantee asymptotically precise tracking performance for a logarithmic quantizer. Moreover, we present a combined design scheme of quantization and encoding-decoding mechanism, where by suitable encoding-decoding mechanism, even a uniform quantizer can ensure zero-error tracking performance. Besides, a formula of possible tight bounds is also provided for the uniform quantizer. In addition, we also address the quantized ILC problem in the presence of random data dropouts.
Finally, we study ILC for systems with fading channel recently, where the fading channel implies the signals during information exchange will be affected in the form of multiplying a random variable. We demonstrate the essential influence generated by the fading channel at both input and output sides, propose learning control algorithm as well as strict analysis. Particularly, the input signal after fading transmission may destroy the system operation stability, for which we propose an effective improvement based on the moving average technique.
In summary, we have conducted a series of research on the ILC problem under the networked structure, where we focus on the uncertainty and randomness induced by the networked structure, explore the essential learning ability, and seek for algorithm design and analysis frameworks to achieve acceptable tracking performance. In the future, focusing on the specific demands and existing issues in the networked control systems, we will conduct our efforts on the learning ability evaluation, learning algorithm development, and tracking performance analysis.
The book
About the author
Dr. Shen received his Ph.D. degree from Academy of Mathematics and System Science, Chinese Academy of Sciences. Then, he was a Post-Doctor Fellow with Institute of Automation, Chinese Academy of Sciences. Following that, he joined the College of Information Science and Technology, Beijing University of Chemical Technology, Beijing, where he served as an Associate Professor and Full Professor successively. Currently, he is a Full Professor with the School of Mathematics, Renmin University of China, Beijing, and a PI with Engineering Research Center of Finance Computation and Digital Engineering, Ministry of Education. His research interests include iterative learning control, optimization and control of stochastic systems, and artificial intelligence.
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