Category:Solution characterization

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 ${\displaystyle \omega (\cdot )}$, denoted by ${\displaystyle \alpha (\cdot )\in [0,1{]}^{n_{\omega }}}$. 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

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