The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.
@article{bwmeta1.element.bwnjournal-article-amcv11i2p391bwm, author = {Jacewicz, Edyta}, title = {An algorithm for construction of $\epsilon$-value functions for the Bolza control problem}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {11}, year = {2001}, pages = {391-428}, zbl = {0974.49016}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv11i2p391bwm} }
Jacewicz, Edyta. An algorithm for construction of ε-value functions for the Bolza control problem. International Journal of Applied Mathematics and Computer Science, Tome 11 (2001) pp. 391-428. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv11i2p391bwm/
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