{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T07:03:39Z","timestamp":1758265419337,"version":"3.41.2"},"reference-count":26,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T00:00:00Z","timestamp":1543708800000},"content-version":"vor","delay-in-days":335,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51867006"],"award-info":[{"award-number":["51867006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>A proper Hamilton\u2010Jacobi\u2010Isaacs (HJI) inequality must be solved in a nonlinear H<jats:sub>\u221e<\/jats:sub> control problem. The sum of squares (SOS) method can now be used to solve an analytically unsolvable nonlinear problem. A HJI inequality suitable for SOS approach is derived in the paper. The SOS algorithm for solving the HJI inequality is also provided. Conservativeness of the SOS method is then discussed in the paper. The conservativeness of the SOS approach is caused by the method itself, because it is really a synthesis method over the entire state space. To reduce the conservativeness, a local H<jats:sub>\u221e<\/jats:sub> design on a restricted state\u2010space region is proposed. But the SOS approach for the local H<jats:sub>\u221e<\/jats:sub> design also suffers from the conservativeness problem, because the S\u2010procedure for solving the set\u2010containment constraint provides only a sufficient condition. The above\u2010mentioned sources of conservativeness are peculiar for the SOS approaches. So a proper approach must be carefully selected in the design process to get a reasonable result. A design example is also given in the paper.<\/jats:p>","DOI":"10.1155\/2018\/8325609","type":"journal-article","created":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T23:35:30Z","timestamp":1543793730000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Sum of Squares Approach for Nonlinear H<sub>\u221e<\/sub> Control"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0795-3782","authenticated-orcid":false,"given":"Ai-ping","family":"Pang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9910-4907","authenticated-orcid":false,"given":"Zhen","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming-han","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guang-xiong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin-mu","family":"Wu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ze-tao","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,12,2]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_10_1_2","DOI":"10.1109\/TFUZZ.2016.2633323"},{"doi-asserted-by":"publisher","key":"e_1_2_10_2_2","DOI":"10.1109\/TCSI.2016.2632718"},{"doi-asserted-by":"publisher","key":"e_1_2_10_3_2","DOI":"10.1155\/2018\/8953035"},{"key":"e_1_2_10_4_2","first-page":"10","article-title":"H\u221e state Feedback design for supercavitating vehicles","volume":"34","author":"Pang A.-P.","year":"2017","journal-title":"Journal of Control Theory and Applications"},{"doi-asserted-by":"publisher","key":"e_1_2_10_5_2","DOI":"10.1109\/9.376058"},{"volume-title":"Applied H\u221e Control [M]","year":"2010","author":"Wang G. 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