- Tytuł:
- Second order conditions for periodic optimal control problems
- Autorzy:
-
Allwright, J.
Vinter, R. - Powiązania:
- https://bibliotekanauki.pl/articles/970564.pdf
- Data publikacji:
- 2005
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
równanie Riccatiego
programowanie dynamiczne
second order conditions
periodic optimal control
Riccati equations
dynamic programming - Opis:
- This paper concerns second order sufficient conditions of optimality, involving the Riccati equation, for optimal control problems with periodic boundary conditions. The problems considered involve no pathwise constraints and are 'regular', in the sense that the strengthened Legendre-Clebsch condition is assumed to be satisfied. A well-known sufficient, condition, which we refer to as the Riccati sufficient condition, requires the existence of a global solution to the Riccati equation whose endpoint values satisfy a certain inequality. A sharper condition, named the extended sufficient, condition, takes the form of an inequality involving the solutions of a Riccati equation and two additional linear matrix equations. We highlight the superiority of the extended Riccati sufficient condition and develop a number of equivalent formulations of this condition. Not only does the extended Riccati sufficient, condition supply more information about, minimizers, but it is the basis of simpler numerical tests for assessing whether an extremal is a minimizer, at least in a local sense. The Riccati and also the extended Riccati sufficient conditions are applied to a variant of Speyer's 'sailboat' problem, involving parameters. It is found that the extended Riccati sufficient condition identifies a much larger set of points on parameter space for which a nominal control is optimal, in comparison to the Riccati sufficient condition.
- Źródło:
-
Control and Cybernetics; 2005, 34, 3; 617-643
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł