Abstract
For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this paper we propose a new constraint qualification under which a nondegenerate maximum principle is validated. In contrast with existing results, our constraint qualification is of an integral type. An advantage of the proposed constraint qualification is that it is verified on a larger class of problems with nonsmooth data and convex velocity sets.

Abstract
There has been a longstanding interest in deriving conditions under which dynamic optimization problems are normal, that is, the necessary conditions of optimality (NCO) can be written with a nonzero multiplier associated with the objective function. This paper builds upon previous results on nondegenerate NCO for trajectory constrained optimal control problems to provide even stronger, normal forms of the conditions. The NCO developed may address problems with nonsmooth, less regular data. The particular case of calculus of variations problems is here explored to show a favorable comparison with existent results.

Abstract
In a previous study, the authors developed the planning of the water used in the irrigation systems of a given farmland in order to ensure that the field cultivation is in a good state of preservation. This planning was modelled and tackled as an optimal control problem: minimize the water flow (control) so that the extent water amount in the soil (trajectory) fulfils the cultivation water requirements. In this paper, we characterize the solution of our problem guaranteeing the existence of the solution and applying the necessary and sufficient conditions of optimality. We validate the numerical results obtained previously, comparing the analytical and numerical solutions.

Abstract
The main purpose of necessary conditions of optimality (NCO) is to identify a 'small' set of candidates to minimizers among the overall set of admissible solutions. However, for certain optimal control problems with state constraints, it might happen that the set of all admissible solutions coincides with the set of candidates satisfying the NCO. This phenomenon is known as the degeneracy phenomenon and there has been some literature proposing stronger forms of NCO that can be informative in such cases: The so-called nondegenerate NCO. The nondegenerate NCO proposed here are valid under a different set of hypothesis and under a constraint qualification of an integral-type that, in relation to some previous literature, is easier to verify. © 2007 EUCA.

Abstract
The focus of this paper is on optimal control problems with mixed state and control inequality constraints. We identify a class of problems which can be associated with an auxiliary problem with both regular mixed constraints and pure state constraints. For that class of problems we derive a new set of necessary conditions of optimality. © 2007 EUCA.