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Journal articles on the topic 'Discrete optimal control problems'

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Published: 10 December 2022
Last updated: 19 February 2023

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1

Ulybyshev, Yuri. "Discrete Pseudocontrol Sets for Optimal Control Problems." Journal of Guidance, Control, and Dynamics 33, no. 4 (July 2010): 1133–42. http://dx.doi.org/10.2514/1.47315.

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2

Marinković, Boban. "Sensitivity analysis for discrete optimal control problems." Mathematical Methods of Operations Research 63, no. 3 (November 10, 2005): 513–24. http://dx.doi.org/10.1007/s00186-005-0029-1.

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3

Marinković, Boban. "Optimality conditions for discrete optimal control problems." Optimization Methods and Software 22, no. 6 (December 2007): 959–69. http://dx.doi.org/10.1080/10556780701485314.

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4

Chryssoverghi, I., and A. Bacopoulos. "Discrete approximation of relaxed optimal control problems." Journal of Optimization Theory and Applications 65, no. 3 (June 1990): 395–407. http://dx.doi.org/10.1007/bf00939558.

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5

Teo, K. L., Y. Liu, and C. J. Goh. "Nonlinearly constrained discrete-time optimal-control problems." Applied Mathematics and Computation 38, no. 3 (August 1990): 227–48. http://dx.doi.org/10.1016/0096-3003(90)90024-w.

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6

Zhang, Ying, Changjun Yu, Yingtao Xu, and Kok Lay Teo. "Minimizing control variation in discrete-time optimal control problems." Journal of Computational and Applied Mathematics 292 (January 2016): 292–306. http://dx.doi.org/10.1016/j.cam.2015.07.010.

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7

Ding, Wandi, Raymond Hendon, Brandon Cathey, Evan Lancaster, and Robert Germick. "Discrete time optimal control applied to pest control problems." Involve, a Journal of Mathematics 7, no. 4 (May 31, 2014): 479–89. http://dx.doi.org/10.2140/involve.2014.7.479.

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8

Lefebvre, Mario, and Moussa Kounta. "Discrete homing problems." Archives of Control Sciences 23, no. 1 (March 1, 2013): 5–18. http://dx.doi.org/10.2478/v10170-011-0039-6.

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Abstract We consider the so-called homing problem for discrete-time Markov chains. The aim is to optimally control the Markov chain until it hits a given boundary. Depending on a parameter in the cost function, the optimizer either wants to maximize or minimize the time spent by the controlled process in the continuation region. Particular problems are considered and solved explicitly. Both the optimal control and the value function are obtained
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9

Philipp, Eduardo A., Laura S. Aragone, and Lisandro A. Parente. "Discrete time schemes for optimal control problems with monotone controls." Computational and Applied Mathematics 34, no. 3 (May 28, 2014): 847–63. http://dx.doi.org/10.1007/s40314-014-0149-4.

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10

Apanapudor, J. S., F. M. Aderibigbe, and F. Z. Okwonu. "An Optimal Penalty Constant For Discrete Optimal Control Regulator Problems." Journal of Physics: Conference Series 1529 (April 2020): 042073. http://dx.doi.org/10.1088/1742-6596/1529/4/042073.

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11

Rasina, Irina, and Oles Fesko. "Degenerate optimal control problems for nonuniform discrete systems." Program Systems: Theory and Applications 8, no. 2 (2017): 3–18. http://dx.doi.org/10.25209/2079-3316-2017-8-2-3-18.

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12

El-Kady, Mamdouh. "JACOBI DISCRETE APPROXIMATION FOR SOLVING OPTIMAL CONTROL PROBLEMS." Journal of the Korean Mathematical Society 49, no. 1 (January 1, 2012): 99–112. http://dx.doi.org/10.4134/jkms.2012.49.1.099.

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13

Fisher, M. E., and L. S. Jennings. "Discrete-time optimal control problems with general constraints." ACM Transactions on Mathematical Software 18, no. 4 (December 1992): 401–13. http://dx.doi.org/10.1145/138351.138356.

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14

Zaslavski, Alexander J. "Agreeable solutions of discrete time optimal control problems." Optimization Letters 8, no. 8 (January 7, 2014): 2173–84. http://dx.doi.org/10.1007/s11590-013-0719-1.

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15

Aragone, Laura S., Lisandro A. Parente, and Eduardo A. Philipp. "Fully discrete schemes for monotone optimal control problems." Computational and Applied Mathematics 37, no. 2 (September 19, 2016): 1047–65. http://dx.doi.org/10.1007/s40314-016-0384-y.

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16

Lee, H. W. J., K. L. Teo, V. Rehbock, and L. S. Jennings. "Control parametrization enhancing technique for optimal discrete-valued control problems." Automatica 35, no. 8 (August 1999): 1401–7. http://dx.doi.org/10.1016/s0005-1098(99)00050-3.

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17

Yang, X. Q., and K. L. Teo. "Necessary optimality conditions for bicriterion discrete optimal control problems." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 3 (January 1999): 392–402. http://dx.doi.org/10.1017/s0334270000010973.

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AbstractIn management science and system engineering, problems with two incommensurate objectives are often detected. Bicriterion optimization finds an optimal solution for the problems. In this paper it is shown that bicriterion discrete optimal control problems can be solved by using a parametric optimization technique with relaxed convexity assumptions. Some necessary optimality conditions for discrete optimal control problems subject to a linear state difference equation are derived. It is shown that in this case no adjoint equation is required.
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18

Sergeev, S. I. "Discrete optimization by optimal control methods I. Separable problems." Automation and Remote Control 67, no. 4 (April 2006): 552–61. http://dx.doi.org/10.1134/s0005117906040047.

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19

Kurina, Galina. "Linear-Quadratic Optimal Control Problems for Discrete Descriptor Systems." IFAC Proceedings Volumes 34, no. 13 (August 2001): 261–66. http://dx.doi.org/10.1016/s1474-6670(17)39000-6.

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20

Torres, Delfim F. M. "Integrals of Motion for Discrete-Time Optimal Control Problems." IFAC Proceedings Volumes 36, no. 8 (June 2003): 33–38. http://dx.doi.org/10.1016/s1474-6670(17)35756-7.

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21

Almeida, Ricardo, and Delfim F. M. Torres. "A discrete method to solve fractional optimal control problems." Nonlinear Dynamics 80, no. 4 (April 13, 2014): 1811–16. http://dx.doi.org/10.1007/s11071-014-1378-1.

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22

Woon, Siew Fang, Volker Rehbock, and Ryan Loxton. "Towards global solutions of optimal discrete-valued control problems." Optimal Control Applications and Methods 33, no. 5 (August 12, 2011): 576–94. http://dx.doi.org/10.1002/oca.1015.

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23

Bonnans, Joseph Frédéric, Justina Gianatti, and Francisco J. Silva. "On the time discretization of stochastic optimal control problems: The dynamic programming approach." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 63. http://dx.doi.org/10.1051/cocv/2018045.

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In this work, we consider the time discretization of stochastic optimal control problems. Under general assumptions on the data, we prove the convergence of the value functions associated with the discrete time problems to the value function of the original problem. Moreover, we prove that any sequence of optimal solutions of discrete problems is minimizing for the continuous one. As a consequence of the Dynamic Programming Principle for the discrete problems, the minimizing sequence can be taken in discrete time feedback form.
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24

Zhu, Jinghao, and Zhiqiang Zou. "An approximation to discrete optimal feedback controls." International Journal of Mathematics and Mathematical Sciences 2003, no. 47 (2003): 2989–3001. http://dx.doi.org/10.1155/s0161171203211042.

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We study discrete solutions of nonlinear optimal control problems. By value functions, we construct difference equations to approximate the optimal control on each interval of “small” time. We aim to find a discrete optimal feedback control. An algorithm is proposed for computing the solution of the optimal control problem.
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25

Toan, Nguyen Thi. "Differential stability of discrete optimal control problems with mixed contraints." Positivity 25, no. 4 (January 29, 2021): 1229–54. http://dx.doi.org/10.1007/s11117-021-00812-x.

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26

Chung, Hoam, Elijah Polak, and Shankar Sastry. "An Accelerator for Packages Solving Discrete-Time Optimal Control Problems." IFAC Proceedings Volumes 41, no. 2 (2008): 14295–300. http://dx.doi.org/10.3182/20080706-5-kr-1001.02422.

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27

Rasina, I. V. "Degenerate problems of optimal control for discrete-continuous (hybrid) systems." Automation and Remote Control 74, no. 2 (February 2013): 196–206. http://dx.doi.org/10.1134/s0005117913020033.

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28

Lozovanu, D. "Discrete optimal control problems and dynamic games with p players." Electronic Notes in Discrete Mathematics 8 (May 2001): 58–61. http://dx.doi.org/10.1016/s1571-0653(05)80079-4.

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29

Liao, Aiping. "Some efficient algorithms for unconstrained discrete-time optimal control problems." Applied Mathematics and Computation 87, no. 2-3 (December 1997): 175–98. http://dx.doi.org/10.1016/s0096-3003(96)00228-7.

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30

Marinković, Boban. "Optimality Conditions in Discrete Optimal Control Problems with State Constraints." Numerical Functional Analysis and Optimization 28, no. 7-8 (August 14, 2007): 945–55. http://dx.doi.org/10.1080/01630560701493271.

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31

Wright, Stephen J. "Solution of discrete-time optimal control problems on parallel computers." Parallel Computing 16, no. 2-3 (December 1990): 221–37. http://dx.doi.org/10.1016/0167-8191(90)90060-m.

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32

Elliott, Robert, Xun Li, and Yuan-Hua Ni. "Discrete time mean-field stochastic linear-quadratic optimal control problems." Automatica 49, no. 11 (November 2013): 3222–33. http://dx.doi.org/10.1016/j.automatica.2013.08.017.

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33

Ralph, Daniel. "A Parallel Method for Unconstrained Discrete-Time Optimal Control Problems." SIAM Journal on Optimization 6, no. 2 (May 1996): 488–512. http://dx.doi.org/10.1137/0806026.

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34

Gachpazan, Mortaza, Akbar Hashemi Borzabadi, and Ali Vahidian Kamyad. "A measure-theoretical approach for solving discrete optimal control problems." Applied Mathematics and Computation 173, no. 2 (February 2006): 736–52. http://dx.doi.org/10.1016/j.amc.2005.04.009.

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35

Tsai, Y. A., F. A. Casiello, and K. A. Loparo. "Discrete-time entropy formulation of optimal and adaptive control problems." IEEE Transactions on Automatic Control 37, no. 7 (July 1992): 1083–88. http://dx.doi.org/10.1109/9.148379.

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36

Wu, C. Z., K. L. Teo, and V. Rehbock. "A filled function method for optimal discrete-valued control problems." Journal of Global Optimization 44, no. 2 (July 16, 2008): 213–25. http://dx.doi.org/10.1007/s10898-008-9319-5.

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37

Mehdi Fateh, Mohammad, and Maryam Baluchzadeh. "Discrete optimal control for robot manipulators." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 33, no. 1/2 (December 20, 2013): 423–44. http://dx.doi.org/10.1108/compel-10-2012-0204.

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Purpose – Applying discrete linear optimal control to robot manipulators faces two challenging problems, namely nonlinearity and uncertainty. This paper aims to overcome nonlinearity and uncertainty to design the discrete optimal control for electrically driven robot manipulators. Design/methodology/approach – Two novel discrete optimal control approaches are presented. In the first approach, a control-oriented model is applied for the discrete linear quadratic control while modeling error is estimated and compensated by a robust time-delay controller. Instead of the torque control strategy, the voltage control strategy is used for obtaining an optimal control that is free from the manipulator dynamics. In the second approach, a discrete optimal controller is designed by using a particle swarm optimization algorithm. Findings – The first controller can overcome uncertainties, guarantee stability and provide a good tracking performance by using an online optimal algorithm whereas the second controller is an off-line optimal algorithm. The first control approach is verified by stability analysis. A comparison through simulations on a three-link electrically driven robot manipulator shows superiority of the first approach over the second approach. Another comparison shows that the first approach is superior to a bounded torque control approach in the presence of uncertainties. Originality/value – The originality of this paper is to present two novel optimal control approaches for tracking control of electrically driven robot manipulators with considering the actuator dynamics. The novelty is that the proposed control approaches are free from the robot's model by using the voltage control strategy. The first approach is a novel discrete linear quadratic control design supported by a time-delay uncertainty compensator. The second approach is an off-line optimal design by using the particle swarm optimization.
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38

Wang, Hui. "Some control problems with random intervention times." Advances in Applied Probability 33, no. 2 (June 2001): 404–22. http://dx.doi.org/10.1017/s0001867800010867.

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We consider the problem of optimally tracking a Brownian motion by a sequence of impulse controls, in such a way as to minimize the total expected cost that consists of a quadratic deviation cost and a proportional control cost. The main feature of our model is that the control can only be exerted at the arrival times of an exogenous uncontrolled Poisson process (signal). In other words, the set of possible intervention times are discrete, random and determined by the signal process (not by the decision maker). We discuss both the discounted problem and the ergodic problem, where explicit solutions can be found. We also derive the asymptotic behavior of the optimal control policies and the value functions as the intensity of the Poisson process goes to infinity, or roughly speaking, as the set of admissible controls goes from the discrete-time impulse control to the continuous-time bounded variation control.
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39

Xing, Xiaoqing, and Yanping Chen. "Superconvergence of Mixed Methods for Optimal Control Problems Governed by Parabolic Equations." Advances in Applied Mathematics and Mechanics 3, no. 4 (August 2011): 401–19. http://dx.doi.org/10.4208/aamm.10-m1006.

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AbstractIn this paper, we investigate the superconvergence results for optimal control problems governed by parabolic equations with semidiscrete mixed finite element approximation. We use the lowest order mixed finite element spaces to discrete the state and costate variables while use piecewise constant function to discrete the control variable. Superconvergence estimates for both the state variable and its gradient variable are obtained.
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40

PANTOJA, J. F. A. DE O., and D. Q. MAYNE. "Sequential quadratic programming algorithm for discrete optimal control problems with control inequality constraints." International Journal of Control 53, no. 4 (April 1991): 823–36. http://dx.doi.org/10.1080/00207179108953650.

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41

Wong, Kar Hung. "On the computational algorithms for time-lag optimal control problems." Bulletin of the Australian Mathematical Society 32, no. 2 (October 1985): 309–11. http://dx.doi.org/10.1017/s0004972700009989.

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In this thesis we study the following two types of hereditary optimal control problems: (i) problems governed by systems of ordinary differential equations with discrete time-delayed arguments appearing in both the state and the control variables; (ii) problems governed by parabolic partial differential equations with Neumann boundary conditions involving time-delays.
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42

Zhu, Qixin, and Guangming Xie. "Finite-Horizon Optimal Control of Discrete-Time Switched Linear Systems." Mathematical Problems in Engineering 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/483568.

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Finite-horizon optimal control problems for discrete-time switched linear control systems are investigated in this paper. Two kinds of quadratic cost functions are considered. The weight matrices are different. One is subsystem dependent; the other is time dependent. For a switched linear control system, not only the control input but also the switching signals are control factors and are needed to be designed in order to minimize cost function. As a result, optimal design for switched linear control systems is more complicated than that of non-switched ones. By using the principle of dynamic programming, the optimal control laws including both the optimal switching signal and the optimal control inputs are obtained for the two problems. Two examples are given to verify the theory results in this paper.
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43

Keerthi, S., and E. Gilbert. "An existence theorem for discrete-time infinite-horizon optimal control problems." IEEE Transactions on Automatic Control 30, no. 9 (September 1985): 907–9. http://dx.doi.org/10.1109/tac.1985.1104084.

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44

Hayek, Naïla. "Infinite horizon multiobjective optimal control problems in the discrete time case." Optimization 60, no. 4 (April 2011): 509–29. http://dx.doi.org/10.1080/02331930903480352.

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45

Rao, Christopher V. "Sparsity of Linear Discrete-Time Optimal Control Problems With $l_1$ Objectives." IEEE Transactions on Automatic Control 63, no. 2 (February 2018): 513–17. http://dx.doi.org/10.1109/tac.2017.2732286.

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46

Damm, Tobias, Lars Grüne, Marleen Stieler, and Karl Worthmann. "An Exponential Turnpike Theorem for Dissipative Discrete Time Optimal Control Problems." SIAM Journal on Control and Optimization 52, no. 3 (January 2014): 1935–57. http://dx.doi.org/10.1137/120888934.

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47

Marinković, Boban. "2-Regularity and 2-Normality Conditions in Discrete Optimal Control Problems." Numerical Functional Analysis and Optimization 29, no. 11-12 (December 4, 2008): 1286–98. http://dx.doi.org/10.1080/01630560802580836.

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48

Postlethwaite, I., M. C. Tsai, and D. W. Gu. "State-space approach to discrete-time super-optimal H∞ control problems." International Journal of Control 49, no. 1 (January 1, 1989): 247–68. http://dx.doi.org/10.1080/00207178908961243.

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49

Chen, Yanping, and Fenglin Huang. "Spectral Method Approximation of Flow Optimal Control Problems withH1-Norm State Constraint." Numerical Mathematics: Theory, Methods and Applications 10, no. 3 (June 20, 2017): 614–38. http://dx.doi.org/10.4208/nmtma.2017.m1419.

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AbstractIn this paper, we consider an optimal control problem governed by Stokes equations withH1-norm state constraint. The control problem is approximated by spectral method, which provides very accurate approximation with a relatively small number of unknowns. Choosing appropriate basis functions leads to discrete system with sparse matrices. We first present the optimality conditions of the exact and the discrete optimal control systems, then derive both a priori and a posteriori error estimates. Finally, an illustrative numerical experiment indicates that the proposed method is competitive, and the estimator can indicate the errors very well.
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50

LUBE, GERT, and BENJAMIN TEWS. "OPTIMAL CONTROL OF SINGULARLY PERTURBED ADVECTION-DIFFUSION-REACTION PROBLEMS." Mathematical Models and Methods in Applied Sciences 20, no. 03 (March 2010): 375–95. http://dx.doi.org/10.1142/s0218202510004271.

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In this paper, we consider the numerical analysis of quadratic optimal control problems governed by a linear advection-diffusion-reaction equation without control constraints. In the case of dominating advection, the Galerkin discretization is stabilized via the one- or two-level variant of the local projection approach which leads to a symmetric optimality system at the discrete level. The optimal control problem simultaneously covers distributed and Robin boundary control. In the singularly perturbed case, the boundary control at inflow and/or characteristic parts of the boundary can be seen as regularization of a Dirichlet boundary control. Some numerical tests illustrate the analytical results.
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