Optimization of the forcing term for the solution of two point boundary value problems
Sunday 15th January 2012
We present a new numerical method for the computation of the forcing term of minimal norm such that a two point boundary value problem admits a solution. The method relies on the following steps. The forcing term is written as a (truncated) Chebyshev series, whose coefficients are free parameters. A technique derived from automatic differentiation is used to solve the initial value problem, so that the final value is obtained as a series of polynomials whose coefficients depend explicitly on (the coefficients of) the forcing term. Then the minimization problem becomes purely algebraic, and can be solved by standard methods of constrained optimization, e.g. with Lagrange multipliers. We provide an application of this algorithm to the restricted three body problem in order to study the planning of low thrust transfer orbits.