Optimal control of singular systems using the rk–butcher algorithm

Abstract

In this article, the Runge–Kutta (RK)–Butcher algorithm is used to study the optimal control of linear singular systems with quadratic performance cost. The obtained discrete solutions using the RK–Butcher algorithms are compared with the exact solutions of the optimal control problem and are found to be very accurate. Stability analysis for the RK–Butcher algorithm is presented. Error graphs for discrete and exact solutions are presented in a graphical form to show the efficiency of this method. This RK–Butcher algorithm can be easily implemented in a digital computer and the solution can be obtained for any length of time.

^†On leave from National Institute of Technology, Thiruchirappalli, India

Keywords:

• Optimal control
• Singular systems
• Single term Walsh series
• RK–Butcher algorithm

Acknowledgement

The author Dr. K. Murugesan would like to thank Professor Jong Yeoul Park, Department of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea, for the financial assistance provided under the Brain Pool Program by the Korean Science and Engineering Foundation (KOSEF), Republic of Korea.

Notes

^†On leave from National Institute of Technology, Thiruchirappalli, India