Normality and Nondegeneracy for Optimal Control Problems with State Constraints
In this paper, we investigate normal and nondegenerate forms of the maximum principle for optimal control problems with state constraints. We propose new constraint qualifications guaranteeing nondegeneracy and normality that have to be checked on smaller sets of points of an optimal trajectory than those in known sufficient conditions. In fact, the constraint qualifications proposed impose the existence of an inward pointing velocity just on the instants of time for which the optimal trajectory has an outward pointing velocity.
KeywordsOptimal control Maximum principle State constraints Constraint qualifications Normality Degeneracy Nonsmooth analysis Oriented distance
Mathematics Subject Classification49K15
The partial supports of projects FP7-ITN-264735-SADCO “Sensitivity Analysis for Deterministic Controller Design” and FCT/FEDER Project PTDC/EEA-CRO/116014/2009 “Optimal Control in Constrained and Hybrid Nonlinear Systems”, PTDC/EEI-AUT/1450/2012 “Optimal Control: Health, Energy and Robotics Applications” are gratefully acknowledged.
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