Optimal synthesis in grid schemes for quasi-convex approximation functions

✍ Scribed by N.V Mel'nikova; A.M Taras'yev

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 556 KB
• Volume: 62
• Category: Article
• ISSN: 0021-8928
• DOI: 10.1016/s0021-8928(98)00070-7

✦ Synopsis

A single grid algorithm which constructs the value function and the optimal synthesis, based on a local quasi-differential approximations of the Hamilton-Jacobi equation, is considered. The optimal synthesis is generated by the method of extremal translation in the direction of generalized gradients. The quasi-convex approximation functions, for which it is possible to use a linear dependence of the space-time steps for correct interpolation of the nodal optimal control values, thus substantially reducing the amount of computation, simplifying the finite-difference formulae and permitting the use of simple operators involving constructions of the method of least squares, are investigated.