Second-order switching time optimization for nonlinear time-varying dynamic systems

Elliot R. Johnson*, Todd D. Murphey

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


This technical note gives a method for calculating the first and second derivatives of a cost function with respect to switching times for systems with piecewise second-differentiable dynamics. Differential equations governing the linear and bilinear operators required for calculating the derivatives are presented. Example optimizations of linear and nonlinear systems are presented as evidence for the value of second-order optimization methods. One example converges in 33 iterations using second-order methods whereas the first-order algorithm requires over 30000 iterations.

Original languageEnglish (US)
Article number5765434
Pages (from-to)1953-1957
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number8
StatePublished - Aug 2011


  • Optimization
  • Switched systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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