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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク DNSS Points ： ウィキペディア英語版 DNSS point DNSS points arise in optimal control problems that exhibit multiple optimal solutions. A DNSS point$-$named alphabetically after Deckert and Nishimura, Sethi, and Skiba$-$is an indifference point in an optimal control problem such that starting from such a point, the problem has more than one different optimal solutions. A good discussion of such points can be found in Grass et al.〔Grass, D., Caulkins, J.P., Feichtinger, G., Tragler, G., Behrens, D.A. (2008). ''Optimal Control of Nonlinear Processes: With Applications in Drugs, Corruption, and Terror''. Springer. ISBN 978-3-540-77646-8.〕 == Definition == Of particular interest here are discounted infinite horizon optimal control problems that are autonomous.〔Sethi, S.P. and Thompson, G.L. (2000). ''Optimal Control Theory: Applications to Management Science and Economics''. Second Edition. Springer. ISBN 0-387-28092-8 and ISBN 0-7923-8608-6. Slides are available at http://www.utdallas.edu/~sethi/OPRE7320presentation.html〕 These problems can be formulated as : $$ \max_\int_0^ e^ \varphi\left(x(t), u(t)\right)dt s.t. : $$ \dot(t) = f\left(x(t), u(t)\right), x(0) = x_, where $\backslash rho\; >\; 0$ is the discount rate, $x(t)$ and $u(t)$ are the state and control variables, respectively, at time $t$, functions $\backslash varphi$ and $f$ are assumed to be continuously differentiable with respect to their arguments and they do not depend explicitly on time $t$, and $\backslash Omega$ is the set of feasible controls and it also is explicitly independent of time $t$. Furthermore, it is assumed that the integral converges for any admissible solution $\backslash left(x(.),\; u(.)\backslash right)$. In such a problem with one-dimensional state variable $x$, the initial state $x\_$ is called a ''DNSS point'' if the system starting from it exhibits multiple optimal solutions or equilibria. Thus, at least in the neighborhood of $x\_0$, the system moves to one equilibrium for $x\; >\; x\_0$ and to another for . In this sense, $x\_0$ is an indifference point from which the system could move to either of the two equilibria. For two-dimensional optimal control problems, Grass et al.〔 and Zeiler et al.〔Zeiler, I., Caulkins, J., Grass, D., Tragler, G. (2009). Keeping Options Open: An Optimal Control Model with Trajectories that Reach a DNSS Point in Positive Time. ''SIAM Journal on Control and Optimization'', Vol. 48, No. 6, pp. 3698-3707.| doi =10.1137/080719741 |〕 present examples that exhibit DNSS curves. Some references on the application of DNSS points are Caulkins et al. and Zeiler et al.〔I. Zeiler, J. P. Caulkins, and G. Tragler. When Two Become One: Optimal Control of Interacting Drug. ''Working paper, ''Vienna University of Technology, Vienna, Austria〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「DNSS point」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.