Sofia Oliveira Lopes

An integral-type constraint qualification to guarantee nondegeneracy of the maximum principle for optimal control problems with state constraints

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.

Irrigation planning: an optimal control approach

We aim to plan the water usage in the irrigation of a given farmland keeping, at same time, the field cultivation in a good state of preservation. This problem is modeled and tackled as an optimal control problem: minimize the water flow (control) so that the extent water amount in the soil (trajectory) fulfills the cultivation water requirements. To estimate rainfall, we consider two models: one based on the average monthly rainfall of the last 10 years in Lisbon area and another which considers the best linear combination of average monthly rainfall from the last 10 years and the amount of rainfall in the previous month. We study the behavior of the solutions under different weather scenarios and we compare the solutions obtained using our model of rainfall with solutions obtained having a prior knowledge of the rainfall.

Optimal Control Applied to an Irrigation Planning Problem

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.

Optimal control for an irrigation planning problem: characterisation of solution and validation of the numerical results

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.

Irrigation planning: replanning and numerical solution

A model to optimize the water use in the irrigation of a farm field via optimal control (water flow) that take into account the evapotranspiration, rainfall, and losses by filtration and runoff was developed in [1]. Here we improve the previous model to take into account real data of rainfall. Model predictive control is applied to replan. We test and compare different nonlinear constrained optimization techniques for solving the nonlinear constrained optimization problem that arises from the discretization of the proposed optimal control problem. Furthermore, we test different time discretization steps.

Optimal Control Applied to an Irrigation Planning Problem : a real case study in Portugal

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%.

Optimal Control for an Irrigation Problem with Several Fields and Common Reservoir

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. In this paper, we introduce a model to minimize the water flowing into a reservoir that supplies different fields with different types of crops. This model is described as an optimal control problem where the water flow from a tap and the water used in the fields are the controls. The trajectories are described as the humidity in the soil and the amount of water in the reservoir.

A Scheduling Application to a Molding Injection Machine: A Challenge Addressed on the 109th European Study Group with Industry

This paper addresses a scheduling optimization problem applied to a molding injection machine. This optimization problem was posed as a challenge to the mathematical community present at the 109th European Study Group with Industry (ESGI), held in Portugal in 2015. We propose a mathematical model for the scheduling optimization problem, which was coded in a widely known modeling language. The model is validated through a set of numerical results obtained with a state-of-the-art solver.

Tau deletion triggers age-dependent sciatic nerve morphofunctional deficits and motor impairment

Background: Trans-synaptic spread of tau pathology is AD is generally accepted but the process is poorly understood. We have recently reported that most synaptic tau is c-terminal truncated, and have also demonstrated depolarization-induced release of total tau from AD but not aged control synapses. Release of tau from synapses is a presumed major source of CSF tau, which is a core CSF biomarker for AD and other neurodegenerative diseases, including traumatic brain injury. The importance of extracellular tau is highlighted by a recent literature documenting success with tau immunotherapy; however a lack of clarity about the precise species of tau peptide that is released presents a significant barrier with respect to tau immunotherapeutic approaches. Methods: We examined the supernatants from depolarized synaptosomes to categorize the peptide species of tau and investigate release of exosomes in a series of normal and AD cases. Release experiments used cryopreserved synaptosomes prepared from samples with a post-mortem interval less than 12h; synaptosomes were depolarized in a 5 min incubation in Kreb’s Ringer buffer containing 50mM KCl. Results: In the present experiments, tau release supernatants were probed with an antibody directed against the intact C-terminus of tau, and demonstrated a 6-fold increase in release of intact C-terminal tau by depolarization in AD samples (79.25 vs. 494 RFU, p<0.002); no significant depolarization-induced release was observed in aged control synaptosomes. An antibody directed against caspase-cleaved tau (TauC3 antibody; D421) did not reveal differential release. Release of exosomes into tau release supernatants was probed with the exosome-associated protein Alix (PDCD61P), an auxillary ESCRT protein that supportes viral budding. Alix is detected as aw75 kDa protein in tau release supernatants, but shows only a trend for depolarization-induced release in the control samples. Conclusions: These results demonstrate robust depolarization-induced release of tau from cryopreserved postmortemAD synaptic terminals, and indicate release of multiple tau peptide species along with synaptic release of exosomal markers. Because C-terminal truncated tau is associated with increased aggregation, release of tau with an intact C terminal may follow from retention of fragmented tau in intraterminal aggregates.

On the Relation Between Inward Pointing Velocity Conditions

Inward pointing velocity conditions are important in the study of whether trajectories remain within sets (the so‐called invariance or viability) and also to establish constraint qualifications (CQ) under which necessary conditions of optimality for control problem can be guaranteed to be nondegenerate NCO or normal. In our research on nondegenerate NCO we have studied different types of CQs in the form of inward pointing velocity (IPV) conditions, and, in particular, in which situation one type implies other type of IPV. Such findings are reported in the article.