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Автор: Grafiati

Опубліковано: 4 травня 2024

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1

Barron, E. N., and R. Jensen. "Relaxed Minimax Control." SIAM Journal on Control and Optimization 33, no. 4 (July 1995): 1028–39. http://dx.doi.org/10.1137/s0363012993250530.

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2

Bahlali, Khaled, Meriem Mezerdi, and Brahim Mezerdi. "On the relaxed mean-field stochastic control problem." Stochastics and Dynamics 18, no. 03 (May 18, 2018): 1850024. http://dx.doi.org/10.1142/s0219493718500247.

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Анотація:

This paper is concerned with optimal control problems for systems governed by mean-field stochastic differential equation, in which the control enters both the drift and the diffusion coefficient. We prove that the relaxed state process, associated with measure valued controls, is governed by an orthogonal martingale measure rather than a Brownian motion. In particular, we show by a counter example that replacing the drift and diffusion coefficient by their relaxed counterparts does not define a true relaxed control problem. We establish the existence of an optimal relaxed control, which can be approximated by a sequence of strict controls. Moreover, under some convexity conditions, we show that the optimal control is realized by a strict control.

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3

Bahlali, Seïd, Brahim Mezerdi, and Boualem Djehiche. "Approximation and optimality necessary conditions in relaxed stochastic control problems." Journal of Applied Mathematics and Stochastic Analysis 2006 (June 1, 2006): 1–23. http://dx.doi.org/10.1155/jamsa/2006/72762.

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We consider a control problem where the state variable is a solution of a stochastic differential equation (SDE) in which the control enters both the drift and the diffusion coefficient. We study the relaxed problem for which admissible controls are measure-valued processes and the state variable is governed by an SDE driven by an orthogonal martingale measure. Under some mild conditions on the coefficients and pathwise uniqueness, we prove that every diffusion process associated to a relaxed control is a strong limit of a sequence of diffusion processes associated to strict controls. As a consequence, we show that the strict and the relaxed control problems have the same value function and that an optimal relaxed control exists. Moreover we derive a maximum principle of the Pontriagin type, extending the well-known Peng stochastic maximum principle to the class of measure-valued controls.

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4

Azhmyakov, V., and W. Schmidt. "Approximations of Relaxed Optimal Control Problems." Journal of Optimization Theory and Applications 130, no. 1 (November 4, 2006): 61–78. http://dx.doi.org/10.1007/s10957-006-9085-9.

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5

Pappas, Georgios. "A note on relaxed control functions." Journal of Mathematical Analysis and Applications 114, no. 2 (March 1986): 429–32. http://dx.doi.org/10.1016/0022-247x(86)90096-x.

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6

Nagabhushan, B. L. "Control configuration of a relaxed stability airship." Journal of Aircraft 28, no. 9 (September 1991): 558–63. http://dx.doi.org/10.2514/3.46064.

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7

Fitzgerald, E. A., Y. H. Xie, D. Monroe, G. P. Watson, J. M. Kuo, and P. J. Silverman. "Defect Control in Relaxed, Graded GeSi/Si." Materials Science Forum 143-147 (October 1993): 471–82. http://dx.doi.org/10.4028/www.scientific.net/msf.143-147.471.

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8

VIRK, G. S. "Algorithms for relaxed control problems with delay." International Journal of Control 46, no. 4 (October 1987): 1267–94. http://dx.doi.org/10.1080/00207178708933968.

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9

Lou, Hongwei, and Weihan Wang. "Turnpike properties of optimal relaxed control problems." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 74. http://dx.doi.org/10.1051/cocv/2018064.

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In this paper, three kinds of turnpike properties for optimal relaxed control problems are considered. Under some convexity and controllability assumptions, we obtain the uniform boundedness of the optimal pairs and the adjoint functions. On the basis, we prove the integral turnpike property, the mean square turnpike property and the exponential turnpike property, respectively.

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10

Lincoln, Bo, and Anders Rantzer. "Relaxed Optimal Control of Piecewise Linear Systems." IFAC Proceedings Volumes 36, no. 6 (June 2003): 385–90. http://dx.doi.org/10.1016/s1474-6670(17)36462-5.

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11

Aydonat, Utku, and Tarek S. Abdelrahman. "Relaxed Concurrency Control in Software Transactional Memory." IEEE Transactions on Parallel and Distributed Systems 23, no. 7 (July 2012): 1312–25. http://dx.doi.org/10.1109/tpds.2011.287.

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12

TUCKER, MIRIAM E. "Glycemic Control Targets Relaxed in New Guidelines." Hospitalist News 2, no. 6 (June 2009): 1–3. http://dx.doi.org/10.1016/s1875-9122(09)70126-9.

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13

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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14

Bishop, Adrian N., Mohammad Deghat, Brian D. O. Anderson, and Yiguang Hong. "Distributed formation control with relaxed motion requirements." International Journal of Robust and Nonlinear Control 25, no. 17 (October 15, 2014): 3210–30. http://dx.doi.org/10.1002/rnc.3250.

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15

Mazliak, Laurent. "Comparison between optimal costs for relaxed and non-relaxed control problems with jumps." Systems & Control Letters 17, no. 4 (October 1991): 315–19. http://dx.doi.org/10.1016/0167-6911(91)90147-7.

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16

Ben Gherbal, H., A. Redjil, and O. Kebiri. "THE RELAXED MAXIMUM PRINCIPLE FOR G-STOCHASTIC CONTROL SYSTEMS WITH CONTROLLED JUMPS." Advances in Mathematics: Scientific Journal 11, no. 12 (December 24, 2022): 1313–43. http://dx.doi.org/10.37418/amsj.11.12.11.

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Анотація:

This paper is concerned with optimal control of systems driven by G-stochastic differential equations (G-SDEs), with controlled jump term. We study the relaxed problem, in which admissible controls are measure-valued processes and the state variable is governed by an G-SDE\ driven by a counting measure valued process called relaxed Poisson measure such that the compensator is a product measure. Under some conditions on the coefficients, using the G-chattering lemma, we show that the strict and the relaxed control problems have the same value function. Additionally, we derive a maximum principle for this control problem.

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17

Bai, M. R., and N. Hadjisavvas. "Relaxed Quasimonotone Operators and Relaxed Quasiconvex Functions." Journal of Optimization Theory and Applications 138, no. 3 (April 12, 2008): 329–39. http://dx.doi.org/10.1007/s10957-008-9382-6.

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18

Bishop, Adrian N. "A Very Relaxed Control Law for Bearing-Only Triangular Formation Control." IFAC Proceedings Volumes 44, no. 1 (January 2011): 5991–98. http://dx.doi.org/10.3182/20110828-6-it-1002.00105.

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19

Jayawardhana, Bayu. "Towards a Generic Constructive Nonlinear Control Design Tool Using Relaxed Control." IEEE Transactions on Automatic Control 60, no. 12 (December 2015): 3293–98. http://dx.doi.org/10.1109/tac.2015.2414828.

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20

Lou, Hongwei. "Analysis of the Optimal Relaxed Control to an Optimal Control Problem." Applied Mathematics and Optimization 59, no. 1 (May 1, 2008): 75–97. http://dx.doi.org/10.1007/s00245-008-9045-x.

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21

Yamamoto, Hidehiro, and Takeshi Furuhashi. "A New Fuzzy Inference Method for Symbolic Stability Analysis of Multigranular Intelligent Control System." Journal of Robotics and Mechatronics 12, no. 6 (December 20, 2000): 664–74. http://dx.doi.org/10.20965/jrm.2000.p0664.

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Анотація:

Fuzzy inference has a multigranular architecture consisting of symbols and continuous values, and has worked well to incorporate experts' know-how into fuzzy controls. Stability analysis of fuzzy control systems is one of the main topics of fuzzy control. A recently proposed stability analysis method on the symbolic level opened the door to the design of stable fuzzy controller using symbols. However the validity of the stability analysis in the symbolic system is not guaranteed in the continuous system. To guarantee this validity, a nonseparate condition has been introduced. If the fuzzy control system is asymptotically stable in the symbolic system and the system satisfies the nonseparate condition, the continuous system is also asymptotically stable. However this condition is too conservative. The new condition called a relaxed nonseparate condition has been proposed and the class of control systems with guaranteed discretization has been expanded. However the relaxed condition has been applicable only to controf systems having symmetric membership functions. This paper presents a new fuzzy inference method that makes the relaxed condition applicable to fuzzy control systems with asymmetric membership functions. Simulations are done to demonstrate the effectiveness of the new fuzzy inference method. The proof of the expansion of the relaxed nonseparate condition is also given.

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22

Goebel, Rafal, Christophe Prieur, and Andrew R. Teel. "RELAXED CHARACTERIZATIONS OF SMOOTH PATCHY CONTROL LYAPUNOV FUNCTIONS." IFAC Proceedings Volumes 40, no. 12 (2007): 486–91. http://dx.doi.org/10.3182/20070822-3-za-2920.00080.

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23

Cabib, Elio. "A relaxed control problem for two-phase conductors." ANNALI DELL UNIVERSITA DI FERRARA 33, no. 1 (January 1987): 207–18. http://dx.doi.org/10.1007/bf02825030.

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24

Chryssoverghi, I., and A. Bacopoulos. "Approximation of relaxed nonlinear parabolic optimal control problems." Journal of Optimization Theory and Applications 77, no. 1 (April 1993): 31–50. http://dx.doi.org/10.1007/bf00940778.

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25

Kim, Jae-Han, Sharon P. Shoemaker, and David A. Mills. "Relaxed control of sugar utilization in Lactobacillus brevis." Microbiology 155, no. 4 (April 1, 2009): 1351–59. http://dx.doi.org/10.1099/mic.0.024653-0.

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Анотація:

Prioritization of sugar consumption is a common theme in bacterial growth and a problem for complete utilization of five and six carbon sugars derived from lignocellulose. Growth studies show that Lactobacillus brevis simultaneously consumes numerous carbon sources and appears to lack normal hierarchical control of carbohydrate utilization. Analysis of several independent L. brevis isolates indicated that co-utilization of xylose and glucose is a common trait for this species. Moreover, carbohydrates that can be used as a single carbon source are simultaneously utilized with glucose. Analysis of the proteome of L. brevis cells grown on glucose, xylose or a glucose/xylose mixture revealed the constitutive expression of the enzymes of the heterofermentative pathway. In addition, fermentative mass balances between mixed sugar inputs and end-products indicated that both glucose and xylose are simultaneously metabolized through the heterofermentative pathway. Proteomic and mRNA analyses revealed that genes in the xyl operon were expressed in the cells grown on xylose or on glucose/xylose mixtures but not in those grown on glucose alone. However, the expression level of XylA and XylB proteins in cells grown on a glucose/xylose mixture was reduced 2.7-fold from that observed in cells grown solely on xylose. These results suggest that regulation of xylose utilization in L. brevis is not stringently controlled as seen in other lactic acid bacteria, where carbon catabolite repression operates to prioritize carbohydrate utilization more rigorously.

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26

Yezza, A. "Relaxed Optimal Control Problems Governed by Integral Equations." Journal of Mathematical Analysis and Applications 175, no. 1 (May 1993): 126–42. http://dx.doi.org/10.1006/jmaa.1993.1158.

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27

Warga, Jack. "Relaxed Derivatives and Extremality Conditions in Optimal Control." Set-Valued and Variational Analysis 20, no. 3 (October 6, 2011): 467–75. http://dx.doi.org/10.1007/s11228-011-0196-6.

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28

Carlson, D. A. "Nonconvex and relaxed infinite-horizon optimal control problems." Journal of Optimization Theory and Applications 78, no. 3 (September 1993): 465–91. http://dx.doi.org/10.1007/bf00939878.

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29

Roubćček, T. "Convergent computational method for relaxed optimal control problems." Journal of Optimization Theory and Applications 69, no. 3 (June 1991): 589–603. http://dx.doi.org/10.1007/bf00940690.

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30

Pan, Yongping, Alexey Bobtsov, Mohamed Darouach, and Young‐Hoon Joo. "Learning from adaptive control under relaxed excitation conditions." International Journal of Adaptive Control and Signal Processing 33, no. 12 (November 19, 2019): 1723–25. http://dx.doi.org/10.1002/acs.3075.

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31

Rosenblueth, J. "Constant relaxed controls with noncommensurate delays." IMA Journal of Mathematical Control and Information 13, no. 2 (June 1, 1996): 195–209. http://dx.doi.org/10.1093/imamci/13.2.195.

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32

Manna, Utpal, and Debopriya Mukherjee. "Optimal relaxed control of stochastic hereditary evolution equations with Lévy noise." ESAIM: Control, Optimisation and Calculus of Variations 25 (2019): 61. http://dx.doi.org/10.1051/cocv/2018066.

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Анотація:

Existence theory of optimal relaxed control problem for a class of stochastic hereditary evolution equations driven by Lévy noise has been studied. We formulate the problem in the martingale sense of Stroock and Varadhan to establish existence of optimal controls. The construction of the solution is based on the classical Faedo–Galerkin approximation, the compactness method and the Jakubowski version of the Skorokhod theorem for nonmetric spaces, and certain compactness properties of the class of Young measures on Suslin metrizable control sets. As application of the abstract theory, Oldroyd and Jeffreys fluids have been studied and existence of optimal relaxed control is established. Existence and uniqueness of a strong solution and uniqueness in law for the two-dimensional Oldroyd and Jeffreys fluids are also shown.

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33

Geoffroy, Michel H., Yvesner Marcelin, and Diana Nedelcheva. "Convergence of relaxed minimizers in set optimization." Optimization Letters 11, no. 8 (September 12, 2016): 1677–90. http://dx.doi.org/10.1007/s11590-016-1079-4.

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34

Martinelli, Andrea, Matilde Gargiani, and John Lygeros. "Data-driven optimal control with a relaxed linear program." Automatica 136 (February 2022): 110052. http://dx.doi.org/10.1016/j.automatica.2021.110052.

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35

Adel, H. Den, M. A. Koenders, and K. J. Bakker. "The analysis of relaxed criteria for erosion-control filters." Canadian Geotechnical Journal 31, no. 6 (December 1, 1994): 829–40. http://dx.doi.org/10.1139/t94-100.

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Анотація:

To optimize the design of erosion-control filters a transport model is presented for moving base material in horizontally loaded filters that are not geometrically stable. Supporting experimental work is used to obtain the parameters in a descriptive quantitative mathematical model. A set of three fixed parameters describes most experiments. Exceptions are where the filter to base grain-size ratio is so small that geometrical obstruction takes place and where this ratio is so large that the turbulences in the flow cause the sand surface under the filter to ripple. The latter case is described with a slightly amended parameter to allow for the amount of fluctuation in the problem. Key words : filtration, transport, experiments, theory, granular material, barriers.

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36

RUMP, CHRISTOPHER M., and SHALER STIDHAM JR. "Relaxed asynchronous flow-control algorithms for multiclass service networks." IIE Transactions 32, no. 9 (September 2000): 873–80. http://dx.doi.org/10.1080/07408170008967446.

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37

Chryssoverghi, I., J. Coletsos, and B. Kokkinis. "Classical and relaxed optimization methods for optimal control problems." International Mathematical Forum 2 (2007): 1477–98. http://dx.doi.org/10.12988/imf.2007.07135.

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38

Mezerdi, Brahim, and Seid Bahlali. "Necessary conditions for optimality in relaxed stochastic control problems." Stochastics and Stochastic Reports 73, no. 3-4 (January 2002): 201–18. http://dx.doi.org/10.1080/1045112021000025925.

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39

Wilke, Daniel N., Schalk Kok, and Albert A. Groenwold. "Relaxed error control in shape optimization that utilizes remeshing." International Journal for Numerical Methods in Engineering 94, no. 3 (February 1, 2013): 273–89. http://dx.doi.org/10.1002/nme.4445.

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40

Lou, Hongwei. "Existence and Nonexistence Results of an Optimal Control Problem by Using Relaxed Control." SIAM Journal on Control and Optimization 46, no. 6 (January 2007): 1923–41. http://dx.doi.org/10.1137/050628386.

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41

Annunziato, M., and A. Borzì. "A sequential quadratic Hamiltonian scheme to compute optimal relaxed controls." ESAIM: Control, Optimisation and Calculus of Variations 27 (2021): 49. http://dx.doi.org/10.1051/cocv/2021041.

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Анотація:

A new sequential quadratic Hamiltonian method for computing optimal relaxed controls for a class of optimal control problems governed by ordinary differential equations is presented. This iterative approach is based on the characterisation of optimal controls by means of the Pontryagin maximum principle in the framework of Young measures, and it belongs to the family of successive approximations schemes. The ability of the proposed optimisation framework to solve problems with regular and relaxed controls, including cases with oscillations and concentration effects, is demonstrated by results of numerical experiments. In all cases, the sequential quadratic Hamiltonian scheme appears robust and efficient, in agreement with convergence results of the theoretical investigation presented in this paper.

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42

Rosenblueth, J. F. "Certain classes of properly relaxed delayed controls." IMA Journal of Mathematical Control and Information 18, no. 1 (March 1, 2001): 31–52. http://dx.doi.org/10.1093/imamci/18.1.31.

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43

WILSON, S. J. "Convergence of a conditional gradient method for relaxed controls in time-lag control problems." International Journal of Systems Science 18, no. 5 (January 1987): 819–29. http://dx.doi.org/10.1080/00207728708964011.

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44

Reisinger, Christoph, and Yufei Zhang. "Regularity and Stability of Feedback Relaxed Controls." SIAM Journal on Control and Optimization 59, no. 5 (January 2021): 3118–51. http://dx.doi.org/10.1137/20m1312435.

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45

Artstein, Zvi. "Rapid Oscillations, Chattering Systems, and Relaxed Controls." SIAM Journal on Control and Optimization 27, no. 5 (September 1989): 940–48. http://dx.doi.org/10.1137/0327050.

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46

Labed, Saloua. "MAXIMUM PRINCIPLE FOR SINGULAR CONTROL PROBLEMS OF SYSTEMS DRIVEN BY MARTINGALE MEASURES." Advances in Mathematics: Scientific Journal 12, no. 1 (January 23, 2023): 193–216. http://dx.doi.org/10.37418/amsj.12.1.13.

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Анотація:

We provide necessary optimality conditions for singular controlled stochastic differential equations driven by an orthogonal continuous martingale measure. The control is allowed to enter both the drift and diffusion coefficient and has two components, the first being relaxed and the second singular, the domain of the first control does not need to be convex, and for the relaxing method, we show by a counter-example that replacing the drift and diffusion coefficients by their relaxed counterparts does not define a true relaxed control problem. The maximum principle for these systems is established by means of spike variation techniques on the relaxed part of the control and a convex perturbation on the singular one. Our result is a generalization of Peng's maximum principle to singular control problems.

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47

Peaucelle, D., B. Andrievsky, V. Mahout, and A. Fradkov. "Robust Simple Adaptive Control with Relaxed Passivity and PID control of a Helicopter Benchmark." IFAC Proceedings Volumes 44, no. 1 (January 2011): 2315–20. http://dx.doi.org/10.3182/20110828-6-it-1002.01128.

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48

Yu, Hongxia, Xiangpeng Xie, Jiawei Zhang, Donghong Ning, and Yuan-Wei Jing. "Relaxed fuzzy observer-based output feedback control synthesis of discrete-time nonlinear control systems." Complexity 21, S1 (March 28, 2016): 593–601. http://dx.doi.org/10.1002/cplx.21775.

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49

Seo, Joohwan, Joonho Lee, Eunkyu Baek, Roberto Horowitz, and Jongeun Choi. "Safety-Critical Control With Nonaffine Control Inputs Via a Relaxed Control Barrier Function for an Autonomous Vehicle." IEEE Robotics and Automation Letters 7, no. 2 (April 2022): 1944–51. http://dx.doi.org/10.1109/lra.2022.3142408.

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50

Liu, Z., J. S. Ume, and S. M. Kang. "General Strongly Nonlinear Quasivariational Inequalities with Relaxed Lipschitz and Relaxed Monotone Mappings." Journal of Optimization Theory and Applications 114, no. 3 (September 2002): 639–56. http://dx.doi.org/10.1023/a:1016079130417.

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