Abstract
Radial basis function approximations of the control variables are used to convert a general nonlinear dynamical optimization into a nonlinear programming problem. Two novel implementations are presented, both of which utilize a nonlinear programming algorithm based upon a minimum correction strategy, to tune the coefficients of the basis functions. Heuristic rules are studied for adoptively locating centers and the sharpness of the radial basis functions. In addition to the two new spaced radial basis function direct optimization algorithms, a Chebychev orthogonal polynomial direct optimization algorithm is considered to validate the results obtained from radial basis function direct optimization algorithms. These issues are addressed using numerical studies for two single control variable optimal control problems and one multi-control variables optimal control problem.
Gong, Hyeon Cheol (1995). Study of direct optimization using radial basis functions. Texas A&M University. Texas A&M University. Libraries. Available electronically from
https : / /hdl .handle .net /1969 .1 /DISSERTATIONS -1574735.