Linear quadratic optimal control via fourier-based state parameterization

V. Yen, M. Nagurka

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


A method for determining the optimal control of unconstrained and linearly constrained linear dynamic systems with quadratic performance indices is presented. The method is based on a modified Fourier series approximation ofeachstate variable that converts the linear quadratic (LQ) problem into a mathematical programming problem. In particular, it is shown that an unconstrained LQ problem can be cast as an unconstrained quadratic programming problem where the necessary condition of optimality is derived as a system of linear algebraic equations. Furthermore, it is shown that a linearly constrained LQ problem can be converted into a general quadratic programming problem. Simulation studies for constrained LQ systems, including a bang-bang control problem, demonstrate that the approach is accurate. The results also indicate that in solving high order unconstrained LQ problems the approach is computationally more efficient and robust than standard methods.

Original languageEnglish
Pages (from-to)206-215
Number of pages10
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Issue number2
StatePublished - 1 Jan 1991
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications


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