Some nonlinear optimal control problems with closed‐form solutions
Michael Margaliot, Gideon Langholz · International Journal of Robust and Nonlinear Control · 2001
Abstract 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. Copyright © 2001 John Wiley & Sons, Ltd.