Optimal control of time-varying singular systems using the RK–Butcher algorithm

Abstract

The problem of optimal control of time-varying linear singular systems with quadratic performance index has been studied using the Runge–Kutta–Butcher algorithm. The results obtained using the Runge–Kutta (RK) method based on the arithmetic mean (RKAM) and the RK–Butcher algorithms are compared with the exact solutions of the time-varying optimal control of linear singular systems. It is observed that the result obtained using the RK–Butcher algorithm is closer to the true solution of the problem. Stability regions for the RKAM algorithm, the single-term Walsh series method and the RK–Butcher algorithms are presented. Error graphs for the simulated results and exact solutions are presented in graphical form to highlight the efficiency of the RK–Butcher algorithm. This algorithm can easily be implemented using a digital computer. An additional advantage of this method is that the solution can be obtained for any length of time for this type of optimal control of time-varying linear singular systems.

Keywords:

• Optimal control
• Time-varying singular systems
• Runge–Kutta arithmetic mean algorithm
• RK–Butcher algorithm

Acknowledgements

K. M. would like to thank Professor J.Y. Park for his kind help and fruitful discussion during his stay in Pusan National University, Pusan, South Korea. He would also like to thank the Korean Science and Engineering Foundation (KOSEF), Republic of Korea, for financial assistance provided under the Brain Pool Program.