0364859 20240111140800.820111007235959.9 6 s. DVD Rom cav_un_epca*0364893978-1-4577-1061-21026-1031DenverIEEE2011 stability linear system tracking cav_un_auth*0252057 Anderle Milan Teorie řízení Department of Control Theory TŘ TR UTIA-B Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101074 Čelikovský Sergej Teorie řízení Department of Control Theory TŘ TR UTIA-B Department of Control Theory Ústav teorie informace a automatizace AV ČR, v. v. i. textový dokument 298 kB GAP103/10/0628 GA ČR CZ cav_un_auth*0274748 LA09026 GA MŠk cav_un_auth*0253177 CEZ:AV0Z10750506 This paper aims to the further improve of the previously developed design for the Acrobot walking based on the partial exact feedback linearization of order 3. Namely, such an exact system transformation leads to an almost linear system where error dynamics along trajectory to be tracked is a 4 dimensional linear time varying system having 3 time varying entries only. Unlike previous approaches treating time varying entries as uncertainties with various extent of conservatism, the present paper takes into the account an information about these time varying functions including their derivatives up to order 4. Using that, the time varying state and the feedback transformation enable to design a fundamental matrix of the error dynamics in an explicit form and pre-designed stability properties. In particular, product of that fundamental matrix at the end of the single support walking phase by the impact map Jacobian enables directly prove stability of the hybrid cyclic walking like trajectory by computing certain 4x4 matrix and determining numerically whether its eigenvalues lie within the unit circle. This combination of analytical and numerical computations provides the justification of the exponential stability of the walking-like trajectory tracking. Moreover, it is supported by numerical simulations showing practically unlimited number of steps of the Acrobot ”walking”. cav_un_auth*0274745 CACSD 2011 Denver Colorado 28.09.2011-30.09.2011 US 2012 BC http://hdl.handle.net/11104/0200231 2011 textový dokument 298 kB cav_un_epca*0364893 Proceedings of the 2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD) 978-1-4577-1061-2 1026 1031 Denver IEEE 2011