• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.445-464
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• 2019

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51-60] and Benavides et al. [Math. Nachr. 248(2003), 62-71].

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.3
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• pp.363-368
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• 2004

In this paper, the robustness property of 2nd-order iterative learning control(ILC) method for a class of linear and nonlinear discrete-time dynamic systems is studied. 2nd-order ILC method has the PD-type learning algorithm based on both time-domain performance and iteration-domain performance. It is proved that the 2nd-order ILC method has robustness in the presence of state disturbances, measurement noise and initial state error. In the absence of state disturbances, measurement noise and initialization error, the convergence of the 2nd-order ILC algorithm is guaranteed. A numerical example is given to show the robustness and convergence property according to the learning parameters.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.69-81
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• 2024

In this paper, we provide certain fixed point results for a generalized 𝛼-nonexpansive mapping, as well as a new iterative algorithm called SRJ-iteration for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and ∆-convergence theorem for generalized 𝛼-nonexpansive mapping in CAT(0) space. Finally, we present a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature. Our results obtained in this paper improve, extend and unify results of Abbas et al. [10], Thakur et al. [22] and Piri et al. [19].

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.194-203
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• 2008

Iterative learning control (ILC) is a simple and effective method for the control of systems that perform the same task repetitively. ILC algorithm uses the repetitiveness of the task to track the desired trajectory. In this paper, we propose a PID (proportional plus integral and derivative) type ILC update law for control discrete-time single input single-output (SISO) linear time-invariant (LTI) systems, performing repetitive tasks. In this approach, the input of controlled system in current cycle is modified by applying the PID strategy on the error achieved between the system output and the desired trajectory in a last previous iteration. The convergence of the presented scheme is analyzed and its convergence condition is obtained in terms of the PID coefficients. An optimal design method is proposed to determine the PID coefficients. It is also shown that under some given conditions, this optimal iterative learning controller can guarantee the monotonic convergence. An illustrative example is given to demonstrate the effectiveness of the proposed technique.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.409-425
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• 2015

In this paper, a new iterative scheme based on the extra-gradient-like method for finding a common element of the set of fixed points of a finite family of nonexpansive mappings and the set of solutions of modified variational inequalities in Banach spaces. A strong convergence theorem for this iterative scheme in Banach spaces is established. Our results extend recent results announced by many others.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.881-894
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• 2022

In this paper, we consider a class of random generalized nonlinear mixed variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings in real Hilbert spaces. We suggest and analyze an iterative algorithm for finding the approximate solution of this class of inclusions. Further, we discuss the convergence analysis of the iterative algorithm under some appropriate conditions. Our results can be viewed as a refinement and improvement of some known results in the literature.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.4
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• pp.284-295
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• 2003

The servo tracks of disk drives are constructed at the time of manufacture with the equipment of servo track writer. Because of the imperfection of servo track writer, disk vibrations and head fluctuations during servo track writing process, the constructed servo tracks might deviate from perfect circles and take eccentric shapes. The servo track writing error should be corrected because it might cause interference with adjacent tracks and irrecoverable operation error of disk drives. The servo track writing error is repeated every disk rotation and so is periodic time function. In this paper, we propose a new correction algorithm of servo track writing error based on iterative teaming approach. Our correction algorithm can learn iteratively the servo track writing error as accurately as is desired. Furthermore, our algorithm is robust to system model errors, is computationally simple, and has fast convergence rate. In order to demonstrate the generality and practical use of our work, we present the convergence analysis of our correction algorithm and some simulation results.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.225-237
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• 2012

In this paper, we introduce a new iterative scheme to investigate the problem of nding a common element of nonexpansive mappings and the set of solutions of generalized variational inequalities for a $k$-strict pseudo-contraction by relaxed extra-gradient methods. Strong convergence theorems are established in $q$-uniformly smooth Banach spaces.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.169.3-169
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• 2001

This paper introduces a new approach to analysis of error convergence for a class of iterative learning control systems. First, a nonlinear plant is represented using a Takagi-Sugeno(T-S) fuzzy model. Then each iterative learning controller is designed for each linear plant in the T-S fuzzy model. From the view point of two-dimensional(2-D) system theory, we transform the proposed learning systems to a 2-D error equation, which is also established in the form of T-S fuzzy model. We analysis the error convergence in the sense of induced 2 L -norm, where the effects of disturbances and initial conditions on 2-D error are considered. The iterative learning controller design problem to guarantee the error convergence can be reduced to linear matrix inequality problems. In comparison with others, our learning algorithm ...

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.171-179
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• 2008

This paper addresses the synthesis of an iterative learning controller for a class of linear systems with norm-bounded parameter uncertainties. We take into account an iterative learning algorithm with current cycle feedback in order to achieve both robust convergence and robust stability. The synthesis problem of the developed iterative learning control (ILC) system is reformulated as the ${\gamma}$-suboptimal $H_{\infty}$ control problem via the linear fractional transformation (LFT). A sufficient convergence condition of the ILC system is presented in terms of linear matrix inequalities (LMIs). Furthermore, the ILC system with fast convergence rate is constructed using a convex optimization technique with LMI constraints. The simulation results demonstrate the effectiveness of the proposed method.