No abstract

a b s t r a c tThere 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.

No abstract

We propose a mathematical model to study the water usage for the irrigation of given farmland to guarantee that the field crop is kept in a good state of preservation. This problem is formulated as an optimal control problem. The lack of analytic solution leads us to turn to numerical methods to solve the problem numerically. We then apply necessary conditions of optimality to validate the numerical solution. To deal with the high degree of unpredictability of water inflow due to weather, we further propose a replan strategy and we implement it.

No 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.

In this paper, a daily plan model to the irrigation of a crop field using optimal control was developed. This daily plan model have in consideration: weather data (temperatures, rainfall, wind speed), the type of crop, the location, humidity in the soil at the initial time, the type of soil and the type of irrigation. The aim is to minimise the water used in the irrigation systems ensuring that the field crop is kept in a good state of preservation. MATLAB was used to develop our mathematical model and obtain its output. Its results were compared with experimental ones obtained from a real farm field of grass in Portugal. This comparison not only allowed us to validate our model, but also allowed us to conclude that, using optimal control considerable savings in water resources, while keeping the crop safe are obtained. Some real test cases were simulated and the comparison between the optimised water to be used by the irrigation system (calculated by software) and the real amount of water used in irrigation site (on-off control system for irrigation) produced water savings above 10%.

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.