A new approach for a class of nonlinear optimal control problems using linear combination property of intervals. (English) Zbl 1238.49047

Tohidi, Emran; Skandari, Mohammad Hadi Noori

J. Comput. Model. 1, No. 2, 145-156 (2011).

Summary: Here, we consider a class of Optimal Control Problems (OCP) containing nonlinear dynamical systems with quadratic functionals of state variables. The major part of our technique is based upon Linear Combination Property of Intervals (LCPI) such that using this property the nonlinear dynamical system is converted to a linear one. The major difference of our approach from a large number of direct approaches for solving OCPs is that we finally solve a convex (linear or quadratic) programming problem with a global optimal solution. We also extend our technique to a class of optimal control problems governed by Differential Inclusions (DI). The proposed idea is illustrated by numerical examples. Moreover, a comparison is made with a discretization method.

MSC:

49M25	Discrete approximations in optimal control
49N10	Linear-quadratic optimal control problems
90C05	Linear programming
90C20	Quadratic programming

Keywords:

optimal control problem; nonlinear dynamical systems; linear combination property of intervals; convex (linear or quadratic) programming problem; discretization method