Lagrange lemma and the optimal control of diffusions II: Nonlinear Lagrange functionals

Peter Kosmol, Michele Pavon

Research output: Contribution to journalArticlepeer-review


In (Kosmol, 1991; Kosmol and Pavon, 1993) a new elementary approach to optimal control problems relying on the Lagrange lemma was described which appears to be technically, and conceptually, much simpler than existing methods, and, furthermore, provides a unified variational approach. In (Kosmol and Pavon, 1992) this method was further clarified and developed for linear Lagrange functionals. We devote this second paper to nonlinear Lagrange functionals. The power of this approach is here clearly demonstrated. In particular, it is shown that the nonlinear Lagrange functional induced by the value function of the problem is just one of the many functionals which may effectively be employed to solve control problems, see Examples 1 and 2 in Section 3. Moreover, in our approach, we can deal in the same framework with problems with state constraints, or nonsmooth problems. Hence, the Lagrange functionals approach provides new tools to solve control problems which may be readily applied even when existing approaches fail.

Original languageEnglish (US)
Pages (from-to)215-221
Number of pages7
JournalSystems and Control Letters
Issue number3
StatePublished - Feb 13 1995


  • Calculus of variations
  • Lagrange lemma
  • Optimal control
  • Variational methods

ASJC Scopus subject areas

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering


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