{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:49:33Z","timestamp":1760230173359,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2022,7,10]],"date-time":"2022-07-10T00:00:00Z","timestamp":1657411200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"Korea government (MSIT)","doi-asserted-by":"publisher","award":["2021R1A2C2010585","2022-0-00469"],"award-info":[{"award-number":["2021R1A2C2010585","2022-0-00469"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010418","name":"Korea government (MSIT)","doi-asserted-by":"publisher","award":["2021R1A2C2010585","2022-0-00469"],"award-info":[{"award-number":["2021R1A2C2010585","2022-0-00469"]}],"id":[{"id":"10.13039\/501100010418","id-type":"DOI","asserted-by":"publisher"}]},{"name":"BK21 FOUR Program","award":["2021R1A2C2010585","2022-0-00469"],"award-info":[{"award-number":["2021R1A2C2010585","2022-0-00469"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>One of the crucial problems in control theory is the tracking of exogenous signals by controlled systems. In general, such exogenous signals are generated by exosystems. These tracking problems are formulated as optimal regulation problems for designing optimal tracking control laws. For such a class of optimal regulation problems, we derive a reduced set of novel Francis\u2013Byrnes\u2013Isidori partial differential equations that achieve output regulation asymptotically and are computationally efficient. Moreover, the optimal regulation for systems on Euclidean space is generalized to systems on manifolds. In the proposed technique, the system dynamics on manifolds is stably embedded into Euclidean space, and an optimal feedback control law is designed by employing well studied, output regulation techniques in Euclidean space. The proposed technique is demonstrated with two representative examples: The quadcopter tracking control and the rigid body tracking control. It is concluded from the numerical studies that the proposed technique achieves output regulation asymptotically in contrast to classical approaches.<\/jats:p>","DOI":"10.3390\/s22145170","type":"journal-article","created":{"date-parts":[[2022,7,11]],"date-time":"2022-07-11T00:06:21Z","timestamp":1657497981000},"page":"5170","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Model Predictive Regulation on Manifolds in Euclidean Space"],"prefix":"10.3390","volume":"22","author":[{"given":"Karmvir Singh","family":"Phogat","sequence":"first","affiliation":[{"name":"Ernst & Young (EY) AI Lab, EY Office Garnet BTP, Bangalore 560048, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6496-4189","authenticated-orcid":false,"given":"Dong Eui","family":"Chang","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3682","DOI":"10.3182\/20140824-6-ZA-1003.00196","article-title":"Model predictive regulation","volume":"47","author":"Aguilar","year":"2014","journal-title":"IFAC Proc. Vol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1137\/0315033","article-title":"The linear multivariable regulator problem","volume":"15","author":"Francis","year":"1977","journal-title":"SIAM J. Control Optim."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1109\/9.45168","article-title":"Output regulation of nonlinear systems","volume":"35","author":"Isidori","year":"1990","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Krener, A.J. (1992). The construction of optimal linear and nonlinear regulators. Systems, Models and Feedback: Theory and Applications, Springer Science & Business Media.","DOI":"10.1007\/978-1-4757-2204-8_21"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1016\/0021-8928(61)90005-3","article-title":"On the optimal stabilization of nonlinear systems","volume":"25","year":"1961","journal-title":"J. Appl. Math. Mech."},{"key":"ref_6","unstructured":"Krener, A.J. (2022, June 04). Nonlinear Systems Toolbox. Available online: https:\/\/www.math.ucdavis.edu\/\u223ckrener."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1693","DOI":"10.1007\/s00332-016-9316-7","article-title":"Feedback integrators","volume":"26","author":"Chang","year":"2016","journal-title":"J. Nonlinear Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4981","DOI":"10.1002\/rnc.4294","article-title":"On controller design for systems on manifolds in Euclidean space","volume":"28","author":"Chang","year":"2018","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1165","DOI":"10.1007\/s00332-018-9514-6","article-title":"Feedback integrators for nonholonomic mechanical systems","volume":"29","author":"Chang","year":"2019","journal-title":"J. Nonlinear Sci."},{"key":"ref_10","first-page":"251","article-title":"Continuous-time approximated parametric output-feedback nonlinear model predictive control","volume":"54","author":"Kallies","year":"2021","journal-title":"IFAC Proc. Vol."},{"key":"ref_11","first-page":"31","article-title":"Adaptive horizon model predictive control","volume":"51","author":"Krener","year":"2018","journal-title":"IFAC Proc. Vol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1007\/s11424-021-1165-2","article-title":"Sampled-data semi-global robust output regulation for a class of nonlinear systems","volume":"34","author":"Liu","year":"2021","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Krener, A.J. (2019, January 11\u201313). Series solution of stochastic HJB equations. Proceedings of the IEEE 58th Conference on Decision and Control (CDC), Nice, France.","DOI":"10.1109\/CDC40024.2019.9029243"},{"key":"ref_14","unstructured":"Krener, A.J. (1998, January 16\u201318). The existence of optimal regulators. Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.ifacol.2018.10.174","article-title":"Adaptive horizon model predictive regulation","volume":"51","author":"Krener","year":"2018","journal-title":"IFAC-PapersOnLine"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Park, S., Her, J., Kim, J., and Lee, D. (2016, January 9\u201314). Design, modeling and control of omni-directional aerial robot. Proceedings of the IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Daejeon, Korea.","DOI":"10.1109\/IROS.2016.7759254"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/14\/5170\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:47:35Z","timestamp":1760140055000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/14\/5170"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,10]]},"references-count":16,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["s22145170"],"URL":"https:\/\/doi.org\/10.3390\/s22145170","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,7,10]]}}}