Two numerical methods for nonlinearconstrained quadratic optimal controlproblems using linear B-splinefunctions

This paper presents two numerical methods for solving the nonlinear con- strained 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 constrianed optimal control to a non linear 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 , Integrationmatrix , Collocation method