Comparison of Two Methods for Linear Time Invariance Quadratic Optimal Control Problems

Adane Akate

Adane Akate College of natural and computational sciences, Department of mathematics, Mekdela Amba University, Dessie

Keywords: Optimal control, Legendre scaling function, Chebyshev scaling function, operational matrix integration

Abstract

In this paper we have studied the linear time invariance quadratic optimal control problems with unknown coefficients. The linear time invariance problems were parameterized based on control-state parameterization technique such that the objective function and the constraints are in terms of state variables and control variables. These two methods were converting the linear time invariance quadratic optimal control problems into quadratic programming problems and the converted problems were solved using MATLAB. When we increase the order of polynomial (M), then the computational results of the proposed methods gave better results but when we compare these two methods, Legendre scaling function was better than Chebyshev scaling function with regard to optimal value. Hence, the Legendre scaling function method is more suitable for solving the linear time invariance quadratic optimal control problems.

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