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Control Optim."],"published-print":{"date-parts":[[2026,6,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>At present, in the optimal control problem of nonzero-sum games, the designed event-triggered controller needs to continuously detect and calculate the triggered error, which will increase the communication burden of the network. In addition, the persistent excitation (PE) conditions in the design are difficult to verify,\u00a0and the issue of input saturation is not considered. The optimal control designed in this paper takes these problems into consideration. This paper proposes a self-triggered control method to address the issue of continuous detection and calculation of triggered errors. First, the control input saturation is solved by using a nonquadratic cost function. Then the learning rules of the critic neural network are constructed by using the experience replay technique and a stabilization operator, which not only can get the approximate optimal control, but also can obtain the PE condition that is easier to verify, and remove the assumption of the initial admissible control. Theoretical proof is provided to establish that the proposed self-triggered adaptive control law stabilizes the closed-loop system. Finally, the efficacy of this method is validated through numerical simulation.<\/jats:p>","DOI":"10.1137\/24m1673693","type":"journal-article","created":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T08:00:31Z","timestamp":1781164831000},"page":"1930-1949","source":"Crossref","is-referenced-by-count":0,"title":["Self-Triggered Optimal Saturation Control for Nonzero-Sum Differential Game Systems without Initial Admissible Control"],"prefix":"10.1137","volume":"64","author":[{"given":"Yibo","family":"Shi","sequence":"first","affiliation":[{"name":"Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6772-5191","authenticated-orcid":true,"given":"Chaoli","family":"Wang","sequence":"additional","affiliation":[{"name":"Corresponding author. Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Engang","family":"Tian","sequence":"additional","affiliation":[{"name":"Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2017.2674633"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1109\/TII.2022.3168034"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2013.2295351"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/23M1579960"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2011.03.005"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2012.2203336"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1109\/TSMC.2019.2962629"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2017.2771560"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/20M1321152"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2019.05.071"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2019.2953613"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2019.07.029"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2019.09.088"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3071545"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2021.3057438"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2013.09.043"},{"key":"ref17","doi-asserted-by":"crossref","unstructured":"T. Dierks and S. Jagannathan, Optimal control of affine nonlinear continuous-time systems, in Proceedings of the 2010 American Control Conference, Baltimore, MD, IEEE, 2010, pp. 1568\u20131573.","DOI":"10.1109\/ACC.2010.5531586"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.05.011"},{"key":"ref19","doi-asserted-by":"crossref","unstructured":"S. E. Lyshevski, Optimal control of nonlinear continuous-time systems: Design of bounded controllers via generalized nonquadratic functionals, in Proceedings of the 1998 American Control Conference, Philadelphia, Pennsylvania, IEEE, 1998, pp. 205\u2013209.","DOI":"10.1109\/ACC.1998.694659"},{"key":"ref20","volume-title":"Dynamic Noncooperative Game Theory","author":"Ba\u015far T.","year":"1999","edition":"2"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2020.2976787"},{"key":"ref22","volume-title":"Principles of Mathematical Analysis","author":"Udin W. 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