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- W98364855 abstract "A time scale quadratic problem J with piecewise right-dense continuous coecien ts and one varying endpoint is considered. Such problems are hybrid, since they include mixing of continuous- and discrete-time problems. A new notion of a generalized conjugate point involving dynamic (hybrid) systems and comprising as special cases those known for the continuous- and discrete-time settings is introduced. A type of a strengthened Legendre condition is identied and used to establish characterizations of the nonnegativity and positivity of J in terms of (i) the nonexistence of such conjugate points, (ii) the natural conjoined basis of the associated time scale Jacobi equation, and (iii) a solution of the corresponding time scale Riccati equation. These results furnish second order necessary optimality conditions for a nonlinear time scale variational problem. Furthermore, we present an example of an optimal impulsive control problem and we show how this problem can be reduced to a variational problem over a time scale. AMS (MOS) Subject Classication. 39A12, 49K99." @default.
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- W98364855 date "2007-09-01" @default.
- W98364855 modified "2023-09-23" @default.
- W98364855 title "LEGENDRE, JACOBI, AND RICCATI TYPE CONDITIONS FOR TIME SCALE VARIATIONAL PROBLEM WITH APPLICATION" @default.
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