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Markov Chain Approximations for Deter- Ministic Control Problems with Aane Dynamics and Quadratic Cost In
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fleming, Wendell H. Soner, Halil Mete Souganidis, Panagiotis E. Dupuis, Paul |
| Copyright Year | 1998 |
| Abstract | An optimal control formulation and related numerical methods for a problem in shape reconstruction, Annals of Applied Probability, 4 (1994), pp. 287{346. 36 surface z(x; y) = (1=4) sin(7 4 x) sin(7 4 y): The approximate controls are computed on a grid with spacing h = 0:025, and the trajectories are integrated by a simple Euler method with linear interpolation. In Figure 7b, we show the value function computed with h = 0:025 for the corresponding control problem, illustrating the fairly complex structure of the regions of strong regularity. Since we do not know the exact solution for this problem, it is not possible for us to present a numerical measure of accuracy for the approximate geodesics in Figure 7a. However, Theorem 5.5 guarantees that for initial conditions in a region of strong regularity, the approximations will converge to the correct geodesics as h ! 0. Being that a more reened grid does not result in discernible changes to the paths indicated in Figure 7a, we conclude that these are, in fact, good approximations to the exact geodesic curves. |
| File Format | PDF HTM / HTML |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
