Two numerical methods for nonlinear constrained quadratic optimal control problems using linear B-spline functions

Abstract

This paper presents two numerical methods for solving the nonlinear constrained optimal control problems including quadratic performance index. The methods are based upon linear B-spline functions. The properties of B-spline functions are presented. Two operational matrices of integration are introduced for related procedures. These matrices are then utilized to reduce the solution of the nonlinear constrained optimal control to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the presented techniques.

Keywords

• optimal control problem
• linear b-spline function
• integration matrix
• collocation method