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The solution of riccati's equation asthe hessian of bellman's function

✍ Scribed by M.I. Zelikin

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
387 KB
Volume
68
Category
Article
ISSN
0021-8928

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✦ Synopsis

The problem of optimal control with separated conditions for the ends is investigated. It is assumed that for the manifold of left ends (and also for the manifold of right ends) a field of extremals including the given extremal exists. A criterion, which gives the necessary and sufficient conditions for optimality in terms of these two fields, is proved. The positive definiteness of the difference of the solutions of the corresponding Riccati matrix equations serves as the sufficient condition, and its non-negativity serves as the necessary condition. The formula relating the solution of Riccati's equation to the Hessian of Bellman's function plays a key role in the proof of the criterion.

πŸ“œ SIMILAR VOLUMES

Riccati equation-based generalization of
Riccati equation-based generalization of Dawson's integral function
✍ R. Messina; M. A. Jivulescu; A. Messina; A. Napoli πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 111 KB

## Abstract A new generalization of Dawson's integral function based on the link between a Riccati nonlinear differential equation and a second‐order ordinary differential equation is reported. The MacLaurin expansion of this generalized function is built up and to this end an explicit formula for