M. Rungger and O. Stursberg, “Comparing Approximations of the Value Function for Exit Time Optimal Control,” in 18th IFAC World Congress, ., Ed. Amsterdam: Elsevier, 2011, pp. 8607–8613.



A fundamental quantity of the solution of an optimal control problem is the value function, i. e., the optimal cost-to-go function. In the general case, the function is not known exactly, but need to be approximated numerically. Most approaches to numerical approximation of the value function follow a procedure of three steps: first, the original continuous problem formulation is fully discretized; second , the discretized finite optimal control problem is solved by a shortest-path algorithm, and as third step, the solution is projected back from the finite space onto the continuous state space by using an interpolating function. This paper investigates the differences of discretization schemes and interpolating functions in this context. The performanc eof the computed approximations is evaluated in terms of an a-posteriori error, which is obtained from the approximating value functions. The convergence of the approximations to the true value function is proved for all considered schemes for the case that the discretization parameters are decreased to zero.



  author = {M. Rungger and O. Stursberg},
  title = {{Comparing Approximations of the Value Function for Exit Time Optimal Control}},
  booktitle = {$18^{th}$ IFAC World Congress},
  year = {2011},
  pages = {8607-8613},
  comment = {noch nicht gemeldet, ISBN: ?, ? Normseiten}