• Title/Summary/Keyword: Convergence Condition

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A Study on the Convergence Condition of ILC for Linear Discrete Time Nonminimum Phase Systems (이산 선형 비최소위상 시스템을 위한 반복 학습 제어의 수렴조건에 대한 연구)

  • Bae, Sung-Han;Ahn, Hyun-Sik;Jeong, Gu-Min
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.57 no.1
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    • pp.117-120
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    • 2008
  • This paper investigates the convergence condition of ADILC(iterative learning control with advanced output data) for nonminimum phase systems. ADILC has simple learning structure including both minimum phase and nonminimum phase systems. However, for nonminimum phase systems, the overall time horizon must be considered in input update law. This makes the dimension of convergence condition matrix large. In this paper, a new sufficient condition is proposed to satisfy the convergence condition. Also, it has been shown that this sufficient condition can be satisfied although it is not full impulse response.

THE CONVERGENCE BALL OF INEXACT NEWTON-LIKE METHOD IN BANACH SPACE UNDER WEAK LIPSHITZ CONDITION

  • Argyros, Ioannis K.;George, Santhosh
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.1
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    • pp.1-12
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    • 2015
  • We present a local convergence analysis for inexact Newton-like method in a Banach space under weaker Lipschitz condition. The convergence ball is enlarged and the estimates on the error distances are more precise under the same computational cost as in earlier studies such as [6, 7, 11, 18]. Some special cases are considered and applications for solving nonlinear systems using the Newton-arithmetic mean method are improved with the new convergence technique.

On the Convergence of ILC for Linear Discrete Time Nonminimum Phase Systems (이산 선형 시스템에 대한 반복 학습 제어의 수렴성에 대한 연구)

  • Jeong, Gu-Min;Ahn, Hyun-Sik
    • Proceedings of the KIEE Conference
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    • 2006.04a
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    • pp.225-227
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    • 2006
  • This note investigates the convergence condition of ADILC (iterative learning control with advanced output data) for nonminimum phase systems. ADILC has simple learning structure including both minimum phase and nonminimum phase systems. However, for nonminimum phase systems, the overall time horizon must be considered in input update law. This makes the dimension of convergence condition matrix large. In this paper, a new sufficient condition is proposed to satisfy the convergence condition. Also, it has been shown that this sufficient condition can be satisfied although it is not full impulse response.

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A Second-Order Iterative Learning Algorithm with Feedback Applicable to Nonlinear Systems (비선형 시스템에 적용가능한 피드백 사용형 2차 반복 학습제어 알고리즘)

  • 허경무;우광준
    • Journal of Institute of Control, Robotics and Systems
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    • v.4 no.5
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    • pp.608-615
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    • 1998
  • In this paper a second-order iterative learning control algorithm with feedback is proposed for the trajectory-tracking control of nonlinear dynamic systems with unidentified parameters. In contrast to other known methods, the proposed teaming control scheme utilize more than one past error history contained in the trajectories generated at prior iterations, and a feedback term is added in the learning control scheme for the enhancement of convergence speed and robustness to disturbances or system parameter variations. The convergence proof of the proposed algorithm is given in detail, and the sufficient condition for the convergence of the algorithm is provided. We also discuss the convergence performance of the algorithm when the initial condition at the beginning of each iteration differs from the previous value of the initial condition. The effectiveness of the proposed algorithm is shown by computer simulation result. It is shown that, by adding a feedback term in teaming control algorithm, convergence speed, robustness to disturbances and robustness to unmatched initial conditions can be improved.

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ENLARGING THE BALL OF CONVERGENCE OF SECANT-LIKE METHODS FOR NON-DIFFERENTIABLE OPERATORS

  • Argyros, Ioannis K.;Ren, Hongmin
    • Journal of the Korean Mathematical Society
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    • v.55 no.1
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    • pp.17-28
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    • 2018
  • In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.

A Study on the Second-order Iterative Learning Control Algorithm with Feedback (궤환을 갖는 2차 반복 학습제어 알고리즘에 관한 연구)

  • Huh, Kyung-Moo
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.5
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    • pp.629-635
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    • 1999
  • A second-order iterative learning control algorithm with feedback is proposed in this paper, in which a feedback term is added in the learning control scheme for the enhancement of convergence speed and robustness to disturbances or system parameter variations. The convergence proof of the proposed algorithm is givenl, and the sufficient condition for the convergence of the algorithm is provided. And it also includes the discussions about the convergence performance of the algorithm when the initial condition at the beginning of each iteration differs from the previous value of the initial. Simulation results show the validity and efficiency of the proposed algorithm.

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TWO-LAYER MUTI-PARAMETERIZED SCHWARZ ALTERNATING METHOD

  • Kim, Sang-Bae
    • Journal of applied mathematics & informatics
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    • v.9 no.1
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    • pp.101-124
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    • 2002
  • The convergence rate of a numerical procedure barred on Schwarz Alternating Method (SAM) for solving elliptic boundary value problems (BVP's) depends on the selection of the interface conditions applied on the interior boundaries of the overlapping subdomains. It hee been observed that the Robin condition(mixed interface condition), controlled by a parameter, can optimize SAM's convergence rate. Since the convergence rate is very sensitive to the parameter, Tang[17] suggested another interface condition called over-determined interface condition. Based on the over-determined interface condition, we formulate the two-layer multi-parameterized SAM. For the SAM and the one-dimensional elliptic model BVP's, we determine analytically the optimal values of the parameters. For the two-dimensional elliptic BVP's , we also formulate the two-layer multi-parameterized SAM and suggest a choice of multi-parameter to produce good convergence rate .

Convergence Conditions of Iterative Learning Control in the Frequency Domain (주파수 영역에서 반복 학습 제어의 수렴 조건)

  • Doh, Tae-Yong;Moon, Jung-Ho
    • Journal of the Korean Institute of Intelligent Systems
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    • v.13 no.2
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    • pp.175-179
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    • 2003
  • Convergence condition determines performance of iterative learning control (ILC), for example, convergence speed, remaining error, etc. Hence, the performance can be elevated and a feasible set of learning controllers grows if a less conservative condition is obtained. In the frequency domain, the $H_{\infty}$ norm of the transfer function between consecutive errors has been currently used to test convergence of a learning system. However, even if the convergence condition based on the $H_{\infty}$ norm has a clear property about monotonic convergence, it has a few drawbacks, especially in MIMO plants. In this paper, the relation between the condition and the monotonicity of convergence is clarified and a modified convergence condition is found out using a frequency domain Lyapunov equation, which supersedes the conventional one in the frequency domain.

LOCAL CONVERGENCE RESULTS FOR NEWTON'S METHOD

  • Argyros, Ioannis K.;Hilout, Said
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.2
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    • pp.267-275
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    • 2012
  • We present new results for the local convergence of Newton's method to a unique solution of an equation in a Banach space setting. Under a flexible gamma-type condition [12], [13], we extend the applicability of Newton's method by enlarging the radius and decreasing the ratio of convergence. The results can compare favorably to other ones using Newton-Kantorovich and Lipschitz conditions [3]-[7], [9]-[13]. Numerical examples are also provided.

APPROXIMATING COMMON FIXED POINTS FOR TOTAL ASYMPTOTICALLY NONEXPANSIVE MAPPINGS

  • Kim, Gang-Eun
    • Journal of applied mathematics & informatics
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    • v.30 no.1_2
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    • pp.71-82
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    • 2012
  • In this paper, we first show the weak convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings, which generalizes the result due to Khan and Fukhar-ud-din [1]. Next, we show the strong convergence of the modified Ishikawa iteration process with errors of two total asymptotically nonexpansive mappings satisfying Condition ($\mathbf{A}^{\prime}$), which generalizes the result due to Fukhar-ud-din and Khan [2].