期刊
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
卷 85, 期 7, 页码 499-515出版社
WILEY-V C H VERLAG GMBH
DOI: 10.1002/zamm.200310190
关键词
optimal control; stability of periodic solutions; robotics; non-smooth optimization; eigenvalue optimization; differential equations with discontinuities
We present a numerical method that optimizes the open-loop stability of solutions of periodic optimal control problems. We consider general periodic processes that may have several phases, each characterized by its own set of differential equations, and discontinuities of the state variables and the right hand side between phases. Stability is measured in terms of the spectral radius of the monodromy matrix which results in a nonsmooth optimization criterion. We have applied this method to design walking robots that can perform stable periodic gaits without any sensors or feedback; three such examples are presented in this paper.
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