Category:Solution characterization
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The classification that we propose for switching decisions is based on insight from Pontryagin's maximum principle <bibref>Pontryagin1962</bibref> 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, <bibref>Srinivasan2003</bibref>, 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.
