Computational efficiency of a functional expansion algorithm for linear quadratic optimal control

A comparison of several algorithms for the solution of linear quadratic optimal control problems is presented. The unique feature of the present work is that it considers a method based on an expansion of the control and state in terms of Chebyshev polynomials. The comparison is based on the number of floating point operations required to compute the time history of the optimal control for a linear quadratic control problem. Comparisons between the Chebyshev expansion method and three methods chosen from A.V. Ramesh et al. (1989) are summarized. At first glance, it appears that the Chebyshev method is asymptotically inferior to the other methods since its expression is of degree two higher.<
>