Singular optimal control for stochastic linear quadratic singular system using ant colony programming

Abstract

In this article, singular optimal control for stochastic linear singular system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation is computed by solving differential algebraic equation using a novel and nontraditional ACP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by the ACP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta method. An illustrative numerical example is presented for the proposed method.

Keywords:

• ant colony programming
• differential algebraic equation
• matrix Riccati differential equation
• Runge Kutta method
• singular optimal control
• stochastic linear singular system

AMS (MOS) Subject Classifications :

• 49 K 45
• 68 N 19
• 93 E 20

Acknowledgements

The authors are very much thankful to the referees for the valuable comments and suggestions for improving this manuscript. The work of the authors was supported by the Department of Science and Technology, Government of India, New Delhi under SERC Project No. SR/S4/MS: 485/07 dt. 21.04.2008.

Additional information

Notes on contributors

N. Kumaresan

Current address: Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia.