A computational method for solving optimal control and parameter estimation of linear systems using Haar wavelets

Abstract

In this article, a computational method based on Haar wavelet in time-domain for solving the problem of optimal control of the linear time invariant systems for any finite time interval is proposed. Haar wavelet integral operational matrix and the properties of Kronecker product are utilized to find the approximated optimal trajectory and optimal control law of the linear systems with respect to a quadratic cost function by solving only the linear algebraic equations. It is shown that parameter estimation of linear system can be done easily using the idea proposed. On the basis of Haar function properties, the results of the article, which include the time information, are illustrated in two examples.

Keywords:

• Haar wavelet
• Optimal control
• Parameter estimation
• Integral operational matrix

Acknowledgement

This research project was partially financially supported under Research Grant 8101004-1-1 provided by University of Tehran and partially by the German Academic Exchange Service (DAAD).