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Two-Dimensional Techniques for Linear Discrete-Time Systems

  • Dong ShenEmail author
  • Xuefang Li
Chapter

Abstract

This chapter presents the two-dimensional (2D) techniques for addressing the tracking problem of linear discrete-time stochastic systems with varying trial lengths. The Kalman filtering technique is applied to derive the recursive learning gain matrix which guarantees the mean square convergence of the input error to zero. As a consequence, the tracking error will converge asymptotically in mean square sense. The learning gain matrix is derived by optimizing the trace of input error covariance matrix. The precise form of the learning gain matrix depends on statistical properties of random trial lengths and it motivates us to further consider an implementable algorithm.

References

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    Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, New YorkCrossRefGoogle Scholar
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    Zhou W, Yu M, Huang D (2015) A high-order internal model based iterative learning control scheme for discrete linear time-varying systems. Int J Autom Comput 12(3):330–336CrossRefGoogle Scholar
  3. 3.
    Liu C, Shen D, Wang J (2018) A two-dimensional approach to iterative learning control with randomly varying trial lengths. J Syst Sci ComplexGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing University of Chemical TechnologyBeijingChina
  2. 2.Department of Electrical and Electronic EngineeringImperial College LondonLondonUK

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