Eigenseries solutions to optimal control problem and controllability problems on hyperbolic PDES

Hee Dae Kwon, Jeehyun Lee, Sung Dae Yang

Research output: Contribution to journalArticle


A terminal-state tracking optimal control problem for linear hyperbolic equations with distributed control is studied in this paper. An analytic solution formula for the optimal control problem is derived in the form of eigenseries. We show that the optimal solution satisfies the approximate controllability property. An explicit solution formula for the exact controllability problem is also expressed by the eigenseries formula when the target state and the controlled state have matching boundary conditions. We demonstrate by numerical simulations that the optimal solutions expressed by the series formula approach the target functions.

Original languageEnglish
Pages (from-to)305-325
Number of pages21
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number2
Publication statusPublished - 2010 Mar 1


All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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