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.

The parameters governing the arm model of a second-order robot control problem are studied using the Runge–Kutta–Butcher (RK–Butcher) algorithm. The exact solution of the system of equations representing the arm model of a robot are compared with the corresponding discrete solutions (approximate solutions) at different time intervals using the RK–Butcher algorithm. The absolute error between the exact and discrete solutions is also determined. A detailed well-composed comparison is carried out using the results and graphs obtained.