β Scribed by A.J. Koivo
No coin nor oath required. For personal study only.
The solution to an optimum control problem is often determined by ful$lling necessary conditions for the optimality. It usually amounts to solving a two-point-boundary-value problem. Most computational schemes used for the solution are based on the first-order variation of performance index (PI). In order to obtain a more accurate improvement, and hence a quicker convergence to the optimal solution, the second-order variation of the PI can be introduoed in the algorithm. This leads to computing the solution of a set of linear differenceequations. The equations result from the perturbation of the system equations, which may be nonlinear.
In this paper recurrence relations for determining the solution to the perturbation equations are developed. An algorithm for improving the control sequence from one iteration to the next is constructed. The optimal solution is obtained fast, although the number of mathematical opera:ions is large. The advantages and drawbaelcs of this second-order variational scheme are discussed. An example demonstrates the applicability of the algorithm.
π SIMILAR VOLUMES
We investigate explicit higher order time discretizations of linear second order hyperbolic problems. We study the even order (2m) schemes obtained by the modified equation method. We show that the corresponding CFL upper bound for the time step remains bounded when the order of the scheme increases