{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:35:06Z","timestamp":1760060106610,"version":"build-2065373602"},"reference-count":20,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,8,12]],"date-time":"2025-08-12T00:00:00Z","timestamp":1754956800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"University of Jeddah","award":["UJ-24-DR-20377-1"],"award-info":[{"award-number":["UJ-24-DR-20377-1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates the stabilization problem of a class of nonlinear systems characterized by non-minimum phase behavior within each subsystem, with a focus on an application to a gantry crane system that employs friction to control its swing angle. In practical crane operations, the demand for accelerated system response is critical to improving productivity; however, this often induces significant variations in the swing angle, potentially destabilizing the system. To overcome this challenge, we propose a hybrid control approach that combines the concept of multi-diffeomorphism with symmetry considerations to enhance the smoothness of transient responses. Unlike classical input\u2013output feedback linearization, which typically relies on a single diffeomorphism and may compromise the zero dynamics stability, the proposed method distributes the transformation across multiple diffeomorphisms, ensuring balanced and coordinated transient behavior. The design involves the simultaneous development of subsystem-dependent feedback controllers, which collaboratively guarantee the global stability of the overall closed-loop nonlinear gantry crane system. The Lyapunov stability framework is employed to rigorously demonstrate that the tracking errors converge asymptotically to meet the desired performance specifications. In addition, the simulation results demonstrate that the developed hybrid control approach notably enhances the system\u2019s responsiveness while preserving both symmetry and the stability of the zero dynamics. Specifically, the swing angle decreases by over 90% in less than 2 s, highlighting the method\u2019s efficiency in minimizing oscillations during fast operations. This study highlights the practical benefits of integrating symmetry-aware multi-diffeomorphism techniques into nonlinear control design. Such techniques are found to be particularly effective for underactuated mechanical systems like gantry cranes.<\/jats:p>","DOI":"10.3390\/sym17081302","type":"journal-article","created":{"date-parts":[[2025,8,12]],"date-time":"2025-08-12T15:51:02Z","timestamp":1755013862000},"page":"1302","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Hybrid Control Strategy for a Gantry Crane with the Concept of Multi-Diffeomorphism"],"prefix":"10.3390","volume":"17","author":[{"given":"Samia","family":"Snoussi","sequence":"first","affiliation":[{"name":"Department of Computer Science and Artificial Intelligence, University of Jeddah, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2960-8151","authenticated-orcid":false,"given":"Khalil","family":"Jouili","sequence":"additional","affiliation":[{"name":"Laboratory of Advanced Systems, Polytechnic School of Tunisia (EPT), B.P. 743, Marsa 2078, Tunisia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4504-6929","authenticated-orcid":false,"given":"Sahbi","family":"Boubaker","sequence":"additional","affiliation":[{"name":"Department of Computer & Network Engineering, College of Computer Science and Engineering, University of Jeddah, Jeddah 21959, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"8333","DOI":"10.1016\/j.jfranklin.2017.10.026","article-title":"3D Cooperative Control of Tower Cranes Using Robust Adaptive Techniques","volume":"354","author":"Le","year":"2017","journal-title":"J. Frankl. Inst."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1007\/s12555-012-9305-z","article-title":"Partial Feedback Linearization Control of a Three-Dimensional Overhead Crane","volume":"11","author":"Tuan","year":"2013","journal-title":"Int. J. Control Autom. Syst."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1109\/TCST.2003.821964","article-title":"Nominal Performance Recovery by PID+Q Controller and Its Application to Anti-Swing Control of Crane Lifter with Visual Feedback","volume":"12","author":"Matsuo","year":"2004","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1177\/1077546309103421","article-title":"A Fuzzy-Tuned PID Anti-Swing Control of Automatic Gantry Crane","volume":"16","author":"Solihin","year":"2010","journal-title":"J. Vib. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1109\/TMECH.2010.2093907","article-title":"Sliding-Mode Antisway Control of an Offshore Container Crane","volume":"17","author":"Ngo","year":"2012","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1049\/iet-cta.2010.0764","article-title":"An Adaptive Sliding Mode Control of Container Cranes","volume":"6","author":"Ngo","year":"2012","journal-title":"IET Control Theory Appl."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2283","DOI":"10.1016\/j.jfranklin.2013.02.011","article-title":"Super Twisting Control of a Parametrically Excited Overhead Crane","volume":"351","author":"Collado","year":"2014","journal-title":"J. Frankl. Inst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1177\/0142331213492369","article-title":"Partial Feedback Linearization and Sliding Mode Techniques for 2D Crane Control","volume":"36","author":"Tuan","year":"2014","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_9","first-page":"171","article-title":"Active Sway Control of a Gantry Crane by an Electrical Ducted Fan","volume":"20","author":"Maghsoudi","year":"2015","journal-title":"Int. J. Acoust. Vib."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1177\/0142331215607615","article-title":"Control of a Gantry Crane Using Input-Shaping Schemes with Distributed Delay","volume":"39","author":"Maghsoudi","year":"2017","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1443","DOI":"10.1177\/0142331216640871","article-title":"Output-Based Command Shaping Technique for an Effective Payload Sway Control of a 3D Crane with Hoisting","volume":"39","author":"Abdullahi","year":"2016","journal-title":"Trans. Inst. Meas. Control"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1109\/TAC.1985.1103912","article-title":"Ripple-Free Deadbeat Control of SISO Discrete Systems","volume":"30","author":"Sirisena","year":"1985","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1080\/0020717060061002","article-title":"Ripple-Free Tracking with Robustness","volume":"79","author":"Paz","year":"2006","journal-title":"Int. J. Control"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Isidori, A. (1995). Nonlinear Control Systems: An Introduction, Springer.","DOI":"10.1007\/978-1-84628-615-5"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3847","DOI":"10.1109\/TFUZZ.2018.2851208","article-title":"Fuzzy-Approximation-Based Adaptive Output-Feedback Control for Uncertain Non-Smooth Nonlinear Systems","volume":"26","author":"Zhao","year":"2018","journal-title":"IEEE Trans. Fuzzy Syst."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5378","DOI":"10.1109\/TII.2018.2805707","article-title":"Peak-to-Peak Filtering for Networked Nonlinear DC Motor Systems with Quantization","volume":"14","author":"Chang","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_17","unstructured":"Wang, M., Dimirovski, G.M., and Zhao, J. (2008, January 11\u201313). H\u221e Control for a Class of Non-Minimum Phase Cascade Switched Nonlinear Systems. Proceedings of the American Control Conference, Seattle, WA, USA."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.cnsns.2014.11.018","article-title":"Stabilization of Non-Minimum Phase Switched Nonlinear Systems with the Concept of Multi-Diffeomorphism","volume":"23","author":"Jouili","year":"2015","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1016\/j.sysconle.2012.07.001","article-title":"Stabilization of Non-Minimum Phase Switched Nonlinear Systems with Application to Multi-Agent Systems","volume":"61","author":"Yang","year":"2012","journal-title":"Syst. Control Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/j.automatica.2014.11.019","article-title":"Adaptive Tracking Control for a Class of Uncertain Switched Nonlinear Systems","volume":"52","author":"Zhao","year":"2015","journal-title":"Automatica"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1302\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:25:33Z","timestamp":1760034333000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/8\/1302"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,12]]},"references-count":20,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["sym17081302"],"URL":"https:\/\/doi.org\/10.3390\/sym17081302","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2025,8,12]]}}}