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  • 标题:Time Optimal Feedback Control using Chebyshev Polynomials and Gröbner Basis ∗
  • 本地全文:下载
  • 作者:Deepak U. Patil ; Debraj Chakraborty
  • 期刊名称:IFAC PapersOnLine
  • 印刷版ISSN:2405-8963
  • 出版年度:2015
  • 卷号:48
  • 期号:14
  • 页码:50-55
  • DOI:10.1016/j.ifacol.2015.09.432
  • 语种:English
  • 出版社:Elsevier
  • 摘要:AbstractThe problem of synthesizing time optimal “feedback” control for a single input linear time invariant system with constrained control input is considered. It is well known that the optimal open loop control is bang-bang and the switching takes place according to some switching surfaces in the state space. A parametric representation of the switching surfaces using Pontryagins’ minimum principle (PMP) is first computed. This parametric representation is in general not semi-algebraic. For such situations, Chebyshev polynomials are used to approximate the switching surfaces. Then, a Gröbner basis based elimination algorithm is used to find an implicit representation for approximated switching surfaces. The computed representation is used to construct a state feedback based nested switching logic which will achieve a near time optimal state transfer of system states to the origin.
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