Comparing Mathematical Programming Algorithms Based on Lagrangian Functions for Solving Optimal Control Problems

Finite‐difference gradients versus error‐quadrature gradients in the solution of parameterized optimal control problems

“…Two customary alternatives for generating these partial derivatives are: (1) difference schemes, e.g.…”

“…The state variables are defined by the following set of ordinary differential equations given in a trajectory system. 1 t= ~ (Tcosr-D)-ysiny…”

“…Find the control functions u(t) and the design parameters v which minimize the scalar functional @(x( 1 )? v) (1) subject to the differential constraints [ro, z,] a.e., and parameters v E RP. The interval [ z, , z,] of the actual independent variable z is normalized to [0,1] by t = (z -t,)/~~.…”