Difference between revisions of "Category:Solution characterization"
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| − | The classification that we propose for switching decisions is based on insight from Pontryagin's maximum principle < | + | The classification that we propose for switching decisions is based on insight from Pontryagin's maximum principle <bib id="Pontryagin1962" /> applied here only to the relaxation of the binary control functions <math>\omega(\cdot)</math>, denoted by <math>\alpha(\cdot) \in [0,1]^{n_\omega}</math>. In the analysis of linear control problems one distinguishes three cases: bang-bang arcs, sensitivity-seeking arcs, and path-constrained arcs, <bib id="Srinivasan2003" />, where an arc is defined to be a nonzero time-interval. Of course a problem's solution can show two or even all three behaviors at once on different time arcs. |
Additionally we characterize solutions, whenever chattering or sliding mode behavior occurs. | Additionally we characterize solutions, whenever chattering or sliding mode behavior occurs. | ||
Revision as of 18:54, 20 January 2016
The classification that we propose for switching decisions is based on insight from Pontryagin's maximum principle [Pontryagin1962]Address: Chichester
Author: Pontryagin, L.S.; Boltyanski, V.G.; Gamkrelidze, R.V.; Miscenko, E.F.
Publisher: Wiley
Title: The Mathematical Theory of Optimal Processes
Year: 1962
applied here only to the relaxation of the binary control functions 
, denoted by ![\alpha(\cdot) \in [0,1]^{n_\omega}](https://mintoc.de/images/math/6/d/4/6d44af77747bea2951d669a09e98b55d.png)
. In the analysis of linear control problems one distinguishes three cases: bang-bang arcs, sensitivity-seeking arcs, and path-constrained arcs, [Srinivasan2003]Author: Srinivasan, B.; Palanki, S.; Bonvin, D.
Journal: Computers \& Chemical Engineering
Pages: 1--26
Title: Dynamic Optimization of Batch Processes: I. Characterization of the Nominal Solution
Volume: 27
Year: 2003, where an arc is defined to be a nonzero time-interval. Of course a problem's solution can show two or even all three behaviors at once on different time arcs.
Additionally we characterize solutions, whenever chattering or sliding mode behavior occurs.
References
<bibreferences/>
Subcategories
This category has the following 5 subcategories, out of 5 total.
