Numerical Solution of the Optimal Periodic Control Problem Using Differential Flatness

Subbarao Varigonda, Tryphon T. Georgiou, Prodromos Daoutidis

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


Optimal periodic control (OPC) is of interest in many engineering applications. In practice, the numerical solution of the OPC problem has been found to be quite challenging. In this note, we present a method which uses differential flatness for the solution of OPC problems. The OPC problem is reformulated using the flatness of the underlying dynamical system to eliminate the differential equations and the periodicity constraints, resulting in simpler and generally more efficient computation. The effect of point-wise constraints and the analytical computation of the Jacobian matrix are also discussed. The approach is demonstrated using two examples.

Original languageEnglish (US)
Pages (from-to)271-275
Number of pages5
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2004

Bibliographical note

Funding Information:
Manuscript received September 24, 2002; revised April 29, 2003. Recommended by Associate Editor J. Huang. This work was supported in part by the Air Force Office of Scientific Research under Grant AF/F49620-00-0078, by the National Science Foundation under Grant ECS-9909219, and by a fellowship from the University of Minnesota Graduate School.


  • Differential flatness
  • Dynamic optimization
  • Optimal periodic control (OPC)


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