Some nonlinear optimal control problems with closed-form solutions

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Optimal controllers guarantee many desirable properties including stability and robustness of the closed-loop system. Unfortunately, the design of optimal controllers is generally very difficult because it requires solving an associated Hamilton-Jacobi-Bellman equation. In this paper we develop a new approach that allows the formulation of some nonlinear optimal control problems whose solution can be stated explicitly as a state-feedback controller. The approach is based on using Young's inequality to derive explicit conditions by which the solution of the associated Hamilton-Jacobi-Bellman equation is simplified. This allows us to formulate large families of nonlinear optimal control problems with closed-form solutions. We demonstrate this by developing optimal controllers for a Lotka-Volterra system.

Original languageEnglish
Pages (from-to)1365-1374
Number of pages10
JournalInternational Journal of Robust and Nonlinear Control
Issue number14
StatePublished - 15 Dec 2001


  • Hamilton-Jacobi-Bellman equation
  • Nonlinear optimal control
  • Robustness
  • Young's inequality


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