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The model of multi-agent systems is reconstructed and the lumped faults, including external disturbances and actuator faults, are constructed. A new adaptive super-twisting sliding mode observer (ASTSMO) is constructed to estimate the undetectable lumped faults. The time-varying gain is introduced to solve the initial error problem and peak value problem. Then, based on the estimated results, an integral terminal sliding mode controller (ITSMC) is designed by integrating the fixed-time stability theory, which can effectively eliminate the nonlinear term and lumped faults. Finally, simulations are provided to illustrate the effectiveness and benefits of the proposed theoretical results.<\/jats:p>","DOI":"10.1177\/01423312221150292","type":"journal-article","created":{"date-parts":[[2023,1,30]],"date-time":"2023-01-30T07:04:18Z","timestamp":1675062258000},"page":"2081-2090","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":6,"title":["Sliding mode fault-tolerant consensus control for heterogeneous multi-agent systems based on finite-time observer and controller"],"prefix":"10.1177","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2283-8835","authenticated-orcid":false,"given":"Pu","family":"Yang","sequence":"first","affiliation":[{"name":"College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, P.R. 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