# Category:Solution characterization

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 . 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

[Pontryagin1962] | Pontryagin, L.S.; Boltyanski, V.G.; Gamkrelidze, R.V.; Miscenko, E.F. (1962): The Mathematical Theory of Optimal Processes. (%edition%). Wiley, Chichester, %pages% | |

[Srinivasan2003] | Srinivasan, B.; Palanki, S.; Bonvin, D. (2003): Dynamic Optimization of Batch Processes: I. Characterization of the Nominal Solution. Computers \& Chemical Engineering, 27, 1--26 |

## Subcategories

This category has the following 5 subcategories, out of 5 total.