{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:40:51Z","timestamp":1760060451760,"version":"build-2065373602"},"reference-count":32,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Accurate trajectory control during atmospheric entry is critical for the success of Mars landing missions, where strong non-linearities and uncertain dynamics pose significant challenges to conventional control strategies. This study develops a computational framework that integrates fuzzy parameter-varying models with Lyapunov-based analysis to achieve robust trajectory stabilization of Mars entry vehicles. The non-linear longitudinal dynamics are reformulated via sector-bounded approximation into a Takagi\u2013Sugeno fuzzy parameter-varying model, enabling systematic gain-scheduled controller synthesis. To reduce the conservatism typically associated with quadratic Lyapunov functions, a fuzzy Lyapunov function approach is adopted, in conjunction with the Full-Block S-procedure, to derive less restrictive stability conditions expressed as linear matrix inequalities. Based on this formulation, several controllers are designed to accommodate the variations in atmospheric density and flight conditions. The proposed methodology is validated through numerical simulations, including Monte Carlo dispersion and parametric sensitivity analyses. The results demonstrate improved stability, faster convergence, and enhanced robustness compared to existing fuzzy control schemes. Overall, this work contributes a systematic and less conservative control design methodology for aerospace applications operating under severe non-linearities and uncertainties.<\/jats:p>","DOI":"10.3390\/computation13090205","type":"journal-article","created":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T13:27:44Z","timestamp":1756733264000},"page":"205","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Fuzzy Lyapunov-Based Gain-Scheduled Control for Mars Entry Vehicles: A Computational Framework for Robust Non-Linear Trajectory Stabilization"],"prefix":"10.3390","volume":"13","author":[{"given":"Hongyang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Min","sequence":"additional","affiliation":[{"name":"School of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9533-2096","authenticated-orcid":false,"given":"Shengkun","family":"Xie","sequence":"additional","affiliation":[{"name":"Global Management Studies, Ted Rogers School of Management, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"649","DOI":"10.1007\/s11431-016-9035-5","article-title":"Mission overview and key technologies of the first Mars probe of China","volume":"60","author":"Ye","year":"2017","journal-title":"Sci.-China-Technol. 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