{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T07:17:25Z","timestamp":1761808645398,"version":"3.40.5"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T00:00:00Z","timestamp":1705017600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T00:00:00Z","timestamp":1705017600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Mach. Intell. Res."],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s11633-022-1413-5","type":"journal-article","created":{"date-parts":[[2024,1,12]],"date-time":"2024-01-12T16:02:34Z","timestamp":1705075354000},"page":"585-596","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Strategy for Aircraft Pursuit-evasion Games via Self-play Iteration"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8035-5586","authenticated-orcid":false,"given":"Xin","family":"Wang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7002-9800","authenticated-orcid":false,"given":"Qing-Lai","family":"Wei","sequence":"additional","affiliation":[]},{"given":"Tao","family":"Li","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6046-4497","authenticated-orcid":false,"given":"Jie","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,12]]},"reference":[{"key":"1413_CR1","volume-title":"Differential Gaines: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization","author":"R Isaacs","year":"1999","unstructured":"R. Isaacs. Differential Gaines: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization, New York, USA: Dover Publications, 1999."},{"issue":"11","key":"1413_CR2","doi-asserted-by":"publisher","first-page":"1501","DOI":"10.1287\/mnsc.42.11.1501","volume":"42","author":"P K Chintagunta","year":"1996","unstructured":"P. K. Chintagunta, V. R. Rao. Pricing strategies in a dynamic duopoly: A differential game model. Management Science, vol. 42, no. 11, pp. 1501\u20131514, 1996. DOI: https:\/\/doi.org\/10.5555\/2777472.2777473.","journal-title":"Management Science"},{"key":"1413_CR3","doi-asserted-by":"publisher","DOI":"10.1142\/2875","volume-title":"Game Theory","author":"L A Petrosyan","year":"1996","unstructured":"L. A. Petrosyan, N. A. Zenkevich. Game Theory, Singapore: World Scientific Publishing Co Pte Ltd, 1996."},{"issue":"5","key":"1413_CR4","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1007\/s11633-021-1282-3","volume":"18","author":"Y Mousavi","year":"2021","unstructured":"Y. Mousavi, A. Zarei, A. Mousavi, M. Biari. Robust optimal higher-order-observer-based dynamic sliding mode control for VTOL unmanned aerial vehicles. International Journal of Automation and Computing, vol. 18, no. 5, pp. 802\u2013813, 2021. DOI: https:\/\/doi.org\/10.1007\/s11633-021-1282-3.","journal-title":"International Journal of Automation and Computing"},{"issue":"1","key":"1413_CR5","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.automatica.2010.10.033","volume":"47","author":"H G Zhang","year":"2011","unstructured":"H. G. Zhang, Q. L. Wei, D. R. Liu. An iterative adaptive dynamic programming method for solving a class of nonlinear zero-sum differential games. Automatica, vol. 47, no. 1, pp. 207\u2013214, 2011. DOI: https:\/\/doi.org\/10.1016\/j.automatica.2010.10.033.","journal-title":"Automatica"},{"issue":"2","key":"1413_CR6","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/BF02169496","volume":"2","author":"N Greenwood","year":"1992","unstructured":"N. Greenwood. A differential game in three dimensions: The aerial dogfight scenario. Dynamics and Control, vol. 2, no. 2, pp. 161\u2013200, 1992. DOI: https:\/\/doi.org\/10.1007\/BF02169496.","journal-title":"Dynamics and Control"},{"issue":"1","key":"1413_CR7","doi-asserted-by":"publisher","first-page":"105","DOI":"10.2514\/1.3960","volume":"29","author":"K Horie","year":"2006","unstructured":"K. Horie, B. A. Conway. Optimal fighter pursuit-evasion maneuvers found via two-sided optimization. Journal of Guidance, Control, and Dynamics, vol. 29, no. 1, pp. 105\u2013112, 2006. DOI: https:\/\/doi.org\/10.2514\/1.3960.","journal-title":"Journal of Guidance, Control, and Dynamics"},{"doi-asserted-by":"publisher","unstructured":"Z. Y. Li, H. Zhu, Z. Yang, Y. Z. Luo. A dimension-reduction solution of free-time differential games for spacecraft pursuit-evasion. Acta Astronautica, vol. 163, pp.201-210, 2019. DOI: https:\/\/doi.org\/10.1016\/j.actaastro.2019.01.011.","key":"1413_CR8","DOI":"10.1016\/j.actaastro.2019.01.011"},{"doi-asserted-by":"publisher","unstructured":"J. F. Zhou, L. Zhao, H. Li, J. H. Cheng, S. Wang. Compensation control strategy for orbital pursuit-evasion problem with imperfect information. Applied Sciences, vol.11, no.4, Article number 1400, 2021. DOI: https:\/\/doi.org\/10.3390\/app11041400.","key":"1413_CR9","DOI":"10.3390\/app11041400"},{"issue":"2","key":"1413_CR10","doi-asserted-by":"publisher","first-page":"481","DOI":"10.1007\/s00182-018-0638-6","volume":"48","author":"M Salimi","year":"2019","unstructured":"M. Salimi, M. Ferrara. Differential game of optimal pursuit of one evader by many pursuers. International Journal of Game Theory, vol. 48, no. 2, pp. 481\u2013490, 2019. DOI: https:\/\/doi.org\/10.1007\/s00182-018-0638-6.","journal-title":"International Journal of Game Theory"},{"issue":"5","key":"1413_CR11","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.1109\/TAC.2019.2926554","volume":"65","author":"V G Lopez","year":"2020","unstructured":"V. G. Lopez, F. L. Lewis, Y. Wan, E. N. Sanchez, L. L. Fan. Solutions for multiagent pursuit-evasion games on communication graphs: Finite-time capture and asymptotic behaviors. IEEE Transactions on Automatic Control, vol. 65, no. 5, pp. 1911\u20131923, 2020. DOI: https:\/\/doi.org\/10.1109\/TAC.2019.2926554.","journal-title":"IEEE Transactions on Automatic Control"},{"issue":"5","key":"1413_CR12","doi-asserted-by":"publisher","first-page":"2345","DOI":"10.1109\/TAC.2020.3003840","volume":"66","author":"E Garcia","year":"2021","unstructured":"E. Garcia, D. W. Casbeer, A. von Moll, M. Pachter. Multiple pursuer multiple evader differential games. IEEE Transactions on Automatic Control, vol. 66, no. 5, pp. 2345\u20132350, 2021. DOI: https:\/\/doi.org\/10.1109\/TAC.2020.3003840.","journal-title":"IEEE Transactions on Automatic Control"},{"key":"1413_CR13","series-title":"Ph.D. dissertation","volume-title":"Contributions to Pursuit-Evasion Game Theory","author":"D W Oyler","year":"2016","unstructured":"D. W. Oyler. Contributions to Pursuit-Evasion Game Theory, Ph.D. dissertation, University of Michigan, USA, 2016."},{"issue":"1","key":"1413_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10462-021-10118-9","volume":"55","author":"D Wang","year":"2022","unstructured":"D. Wang, M. M. Ha, M. M. Zhao. The intelligent critic framework for advanced optimal control. Artificial Intelh-gence Review, vol. 55, no. 1, pp. 1\u201322, 2022. DOI: https:\/\/doi.org\/10.1007\/s10462-021-10118-9.","journal-title":"Artificial Intelh-gence Review"},{"issue":"3","key":"1413_CR15","doi-asserted-by":"publisher","first-page":"604","DOI":"10.1137\/0331027","volume":"31","author":"P Soravia","year":"1993","unstructured":"P. Soravia. Pursuit-evasion problems and viscosity solutions of isaacs equations. SIAM Journal on Control and Optimization, vol. 31, no. 3, pp. 604\u2013623, 1993. DOI: https:\/\/doi.org\/10.1137\/0331027.","journal-title":"SIAM Journal on Control and Optimization"},{"issue":"4","key":"1413_CR16","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1109\/TNNLS.2016.2638863","volume":"29","author":"Q L Wei","year":"2018","unstructured":"Q. L. Wei, D. R. Liu, Q. Lin, R. Z. Song. Adaptive dynamic programming for discrete-time zero-sum games. IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 4, pp. 957\u2013969, 2018. DOI: https:\/\/doi.org\/10.1109\/TNNLS.2016.2638863.","journal-title":"IEEE Transactions on Neural Networks and Learning Systems"},{"key":"1413_CR17","volume-title":"Mathematical Theory of Optimal Processes","author":"L S Pontryagin","year":"1987","unstructured":"L. S. Pontryagin. Mathematical Theory of Optimal Processes, Boca Raton, USA: CRC Press, 1987."},{"issue":"4","key":"1413_CR18","doi-asserted-by":"publisher","first-page":"841","DOI":"10.2514\/1.G002911","volume":"41","author":"R W Carr","year":"2018","unstructured":"R. W. Carr, R. G. Cobb, M. Pachter, S. Pierce. Solution of a pursuit-evasion game using a near-optimal strategy. Journal of Guidance, Control, and Dynamics, vol. 41, no. 4, pp. 841\u2013850, 2018. DOI: https:\/\/doi.org\/10.2514\/1.G002911.","journal-title":"Journal of Guidance, Control, and Dynamics"},{"issue":"2","key":"1413_CR19","doi-asserted-by":"publisher","first-page":"474","DOI":"10.2514\/1.37962","volume":"32","author":"M Pontani","year":"2009","unstructured":"M. Pontani, B. A. Conway. Numerical solution of the three-dimensional orbital pursuit-evasion game. Journal of Guidance, Control, and Dynamics, vol. 32, no. 2, pp. 474\u2013487, 2009. DOI: https:\/\/doi.org\/10.2514\/1.37962.","journal-title":"Journal of Guidance, Control, and Dynamics"},{"issue":"2","key":"1413_CR20","doi-asserted-by":"publisher","first-page":"3706","DOI":"10.1002\/rnc.4962","volume":"30","author":"Y L Yang","year":"2020","unstructured":"Y. L. Yang, K. G. Vamvoudakis, H. Modares. Safe reinforcement learning for dynamical games. International Journal of Robust and Nonlinear Control, vol. 30, no. 2, pp. 3706\u20133726, 2020. DOI: https:\/\/doi.org\/10.1002\/rnc.4962.","journal-title":"International Journal of Robust and Nonlinear Control"},{"issue":"7","key":"1413_CR21","doi-asserted-by":"publisher","first-page":"1262","DOI":"10.1109\/JAS.2022.105692","volume":"9","author":"M M Ha","year":"2022","unstructured":"M. M. Ha, D. Wang, D. R. Liu. Discounted iterative adaptive critic designs with novel stability analysis for tracking control. IEEE\/CAA Journal of Automatica Sanica, vol. 9, no. 7, pp. 1262\u20131272, 2022. DOI: https:\/\/doi.org\/10.1109\/JAS.2022.105692.","journal-title":"IEEE\/CAA Journal of Automatica Sanica"},{"issue":"7","key":"1413_CR22","doi-asserted-by":"publisher","first-page":"3316","DOI":"10.1016\/j.jfranklin.2019.12.017","volume":"357","author":"Y Yang","year":"2020","unstructured":"Y. Yang, D. Ding, H. Xiong, Y. Yin, D. Wunsch. Online barrier-actor-critic learning for H\u221e, control with full-state constraints and input saturation. Journal of the Franklin Institute, vol. 357, no. 7, pp. 3316\u20133344, 2020. DOI: https:\/\/doi.org\/10.1016\/j.jfranklin.2019.12.017.","journal-title":"Journal of the Franklin Institute"},{"issue":"16","key":"1413_CR23","doi-asserted-by":"publisher","first-page":"7886","DOI":"10.1002\/rnc.5719","volume":"31","author":"Y Kartal","year":"2021","unstructured":"Y. Kartal, K. Subbarao, A. Dogan, F. Lewis. Optimal game theoretic solution of the pursuit-evasion intercept problem using on-policy reinforcement learning. International Journal of Robust and Nonhnear Control, vol. 31, no. 16, pp. 7886\u20137903, 2021. DOI: https:\/\/doi.org\/10.1002\/rnc.5719.","journal-title":"International Journal of Robust and Nonhnear Control"},{"issue":"2","key":"1413_CR24","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1109\/TCYB.2019.2914869","volume":"51","author":"J Selvakumar","year":"2021","unstructured":"J. Selvakumar, E. Bakolas. Feedback strategies for a reach-avoid game with a single evader and multiple pursuers. IEEE Transactions on Cybernetics, vol. 51, no. 2, pp. 696\u2013707, 2021. DOI: https:\/\/doi.org\/10.1109\/TCYB.2019.2914869.","journal-title":"IEEE Transactions on Cybernetics"},{"issue":"4","key":"1413_CR25","doi-asserted-by":"publisher","first-page":"361","DOI":"10.1007\/s40313-015-0180-8","volume":"26","author":"H Xu","year":"2015","unstructured":"H. Xu. Finite-horizon near optimal design of nonhnear two-player zero-sum game in presence of completely unknown dynamics. Journal of Control, Automation and Electrical Systems, vol. 26, no. 4, pp. 361\u2013370, 2015. DOI: https:\/\/doi.org\/10.1007\/s40313-015-0180-8.","journal-title":"Journal of Control, Automation and Electrical Systems"},{"issue":"10","key":"1413_CR26","doi-asserted-by":"publisher","first-page":"6488","DOI":"10.1109\/TSMC.2019.2962629","volume":"51","author":"C X Mu","year":"2021","unstructured":"C. X. Mu, K. Wang, C. Y. Sun. Policy-iteration-based learning for nonlinear player game systems with constrained inputs. IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 10, pp. 6488\u20136502, 2021. DOI: https:\/\/doi.org\/10.1109\/TSMC.2019.2962629.","journal-title":"IEEE Transactions on Systems, Man, and Cybernetics: Systems"},{"key":"1413_CR27","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.neucom.2015.12.021","volume":"185","author":"X H Cui","year":"2016","unstructured":"X. H. Cui, H. G. Zhang, Y. H. Luo, P. F. Zu. Online finite-horizon optimal learning algorithm for nonzero-sum games with partially unknown dynamics and constrained inputs. Neurocomputing, vol. 185, pp. 37\u201344, 2016. DOI: https:\/\/doi.org\/10.1016\/j.neucom.2015.12.021.","journal-title":"Neurocomputing"},{"key":"1413_CR28","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.23919\/ACC45564.2020.9147205","volume-title":"An introduction to pursuit-evasion differential games","author":"I E Weintraub","year":"2020","unstructured":"I. E. Weintraub, M. Pachter, E. Garcia. An introduction to pursuit-evasion differential games. In Proceedings of American Control Conference, IEEE, Denver, USA, pp. 1049\u20131066, 2020. DOI: https:\/\/doi.org\/10.23919\/ACC45564.2020.9147205."},{"issue":"3","key":"1413_CR29","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/BF00939876","volume":"78","author":"M H Breitner","year":"1993","unstructured":"M. H. Breitner, H. J. Pesch, W. Grimm. Complex differential games of pursuit-evasion type with state constraints, Part 1: Necessary conditions for optimal open-loop strategies. Journal of Optimization Theory and Applications, vol. 78, no. 3, pp. 419\u2013441, 1993. DOI: https:\/\/doi.org\/10.1007\/BF00939876.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"1413_CR30","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/s00032-011-0163-6","volume":"79","author":"A Bressan","year":"2011","unstructured":"A. Bressan. Noncooperative differential games. Milan Journal of Mathematics, vol. 79, pp. 357\u2013427, 2011.","journal-title":"Milan Journal of Mathematics"},{"issue":"3","key":"1413_CR31","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/BF02275347","volume":"89","author":"A S El-Bakry","year":"1996","unstructured":"A. S. El-Bakry, R. A. Tapia, T. Tsuchiya, Y. Zhang. On the formulation and theory of the newton interior-point method for nonhnear programming. Journal of Optimization Theory and Applications, vol. 89, no. 3, pp. 507\u2013541, 1996. DOI: https:\/\/doi.org\/10.1007\/BF02275347.","journal-title":"Journal of Optimization Theory and Applications"},{"key":"1413_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492900002518","volume":"4","author":"P T Boggs","year":"1995","unstructured":"P. T. Boggs, J. W. Tolle. Sequential quadratic programming. Acta Numerica, vol. 4, pp. 1\u201351, 1995. DOI: https:\/\/doi.org\/10.1017\/S0962492900002518.","journal-title":"Acta Numerica"},{"key":"1413_CR33","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719857","volume-title":"Trust-Region Methods","author":"A R Conn","year":"2000","unstructured":"A. R. Conn, N. I. M. Gould, P. L. Toint. Trust-Region Methods, Philadelphia, USA: SIAM, 2000."},{"doi-asserted-by":"publisher","unstructured":"F. Austin, G. Carbone, M. Falco, H. Hinz, M. Lewis. Automated maneuvering decisions for air-to-air combat. In Proceedings of Guidance, Navigation and Control Conference, Monterey, USA, pp. 659\u2013669, 1987. DOI: https:\/\/doi.org\/10.2514\/6.1987-2393.","key":"1413_CR34","DOI":"10.2514\/6.1987-2393"}],"container-title":["Machine Intelligence Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11633-022-1413-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11633-022-1413-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11633-022-1413-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T09:21:52Z","timestamp":1714987312000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11633-022-1413-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,12]]},"references-count":34,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["1413"],"URL":"https:\/\/doi.org\/10.1007\/s11633-022-1413-5","relation":{},"ISSN":["2731-538X","2731-5398"],"issn-type":[{"type":"print","value":"2731-538X"},{"type":"electronic","value":"2731-5398"}],"subject":[],"published":{"date-parts":[[2024,1,12]]},"assertion":[{"value":"7 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 December 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declared that they have no conflicts of interest to this work.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations of conflict of interest"}}]}}