Convergence Ratio Profile for Optimal Control Problems Governed by Ordinary Differential Equations with Matrix Coefficients

Abstract

The geometric convergence ratio, the main focus of a discretized scheme for constrained quadratic control problem was examined. In order to allow for the numerical applications of the developed scheme, discretizing the time interval and using Euler’s scheme for its differential constraint obtained a finite dimensional approximation. Applying the penalty function method, an unconstrained problem was obtained on function minimization with bilinear form expression. This finally led to the construction of an operator. The Scheme was applied to a sampled problem and it exhibited geometric convergence ratio, α, in the open interval (0, 1) as depicted in column 6 of Table 1.