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Pursuit-evasion games with state constraints: dynamic programming and discrete-time approximations
1. | Dipartimento di Matematica P. e A., Universita di Padova, via Belzoni 7, 35131 Padova |
2. | Department of Mathematics, Saitama University, 255 Shimo-Okubo, Urawa, Saitama 338-8570, Japan |
3. | Dipartimento di Matematica Pura e Applicata, Università di Padova, Belzoni 7, 1-35131, Padova, Italy |
[1] |
Abbas Ja'afaru Badakaya, Aminu Sulaiman Halliru, Jamilu Adamu. Game value for a pursuit-evasion differential game problem in a Hilbert space. Journal of Dynamics and Games, 2022, 9 (1) : 1-12. doi: 10.3934/jdg.2021019 |
[2] |
Songtao Sun, Qiuhua Zhang, Ryan Loxton, Bin Li. Numerical solution of a pursuit-evasion differential game involving two spacecraft in low earth orbit. Journal of Industrial and Management Optimization, 2015, 11 (4) : 1127-1147. doi: 10.3934/jimo.2015.11.1127 |
[3] |
Zhen Wu, Feng Zhang. Maximum principle for discrete-time stochastic optimal control problem and stochastic game. Mathematical Control and Related Fields, 2022, 12 (2) : 475-493. doi: 10.3934/mcrf.2021031 |
[4] |
Qi-shuai Wang, Pei Li, Ting Lei, Xiao-feng Liu, Guo-ping Cai. A Dimension-reduction method for the finite-horizon spacecraft pursuit-evasion game. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022028 |
[5] |
Bingyan Liu, Xiongbing Ye, Xianzhou Dong, Lei Ni. Branching improved Deep Q Networks for solving pursuit-evasion strategy solution of spacecraft. Journal of Industrial and Management Optimization, 2022, 18 (2) : 1223-1245. doi: 10.3934/jimo.2021016 |
[6] |
Genglin Li, Youshan Tao, Michael Winkler. Large time behavior in a predator-prey system with indirect pursuit-evasion interaction. Discrete and Continuous Dynamical Systems - B, 2020, 25 (11) : 4383-4396. doi: 10.3934/dcdsb.2020102 |
[7] |
Dayong Qi, Yuanyuan Ke. Large time behavior in a predator-prey system with pursuit-evasion interaction. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021240 |
[8] |
Chao Liu, Bin Liu. Boundedness and asymptotic behavior in a predator-prey model with indirect pursuit-evasion interaction. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021255 |
[9] |
Sie Long Kek, Kok Lay Teo, Mohd Ismail Abd Aziz. Filtering solution of nonlinear stochastic optimal control problem in discrete-time with model-reality differences. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 207-222. doi: 10.3934/naco.2012.2.207 |
[10] |
Bara Kim, Jeongsim Kim. Explicit solution for the stationary distribution of a discrete-time finite buffer queue. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1121-1133. doi: 10.3934/jimo.2016.12.1121 |
[11] |
Fabio Camilli, Francisco Silva. A semi-discrete approximation for a first order mean field game problem. Networks and Heterogeneous Media, 2012, 7 (2) : 263-277. doi: 10.3934/nhm.2012.7.263 |
[12] |
Diogo A. Gomes. Viscosity solution methods and the discrete Aubry-Mather problem. Discrete and Continuous Dynamical Systems, 2005, 13 (1) : 103-116. doi: 10.3934/dcds.2005.13.103 |
[13] |
John A. Morgan. Interception in differential pursuit/evasion games. Journal of Dynamics and Games, 2016, 3 (4) : 335-354. doi: 10.3934/jdg.2016018 |
[14] |
Elena K. Kostousova. On polyhedral control synthesis for dynamical discrete-time systems under uncertainties and state constraints. Discrete and Continuous Dynamical Systems, 2018, 38 (12) : 6149-6162. doi: 10.3934/dcds.2018153 |
[15] |
Yuefen Chen, Yuanguo Zhu. Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems. Journal of Industrial and Management Optimization, 2018, 14 (3) : 913-930. doi: 10.3934/jimo.2017082 |
[16] |
Lixuan Zhang, Xuefei Yang. On pole assignment of high-order discrete-time linear systems with multiple state and input delays. Discrete and Continuous Dynamical Systems - S, 2022 doi: 10.3934/dcdss.2022022 |
[17] |
Jérome Lohéac, Jean-François Scheid. Time optimal control for a nonholonomic system with state constraint. Mathematical Control and Related Fields, 2013, 3 (2) : 185-208. doi: 10.3934/mcrf.2013.3.185 |
[18] |
Hongyan Yan, Yun Sun, Yuanguo Zhu. A linear-quadratic control problem of uncertain discrete-time switched systems. Journal of Industrial and Management Optimization, 2017, 13 (1) : 267-282. doi: 10.3934/jimo.2016016 |
[19] |
Yuyun Zhao, Yi Zhang, Tao Xu, Ling Bai, Qian Zhang. pth moment exponential stability of hybrid stochastic functional differential equations by feedback control based on discrete-time state observations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 209-226. doi: 10.3934/dcdsb.2017011 |
[20] |
Andrei V. Dmitruk, Nikolai P. Osmolovskii. Proof of the maximum principle for a problem with state constraints by the v-change of time variable. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2189-2204. doi: 10.3934/dcdsb.2019090 |
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