Numerical solution of optimal control problems with constant control delays

We investigate a class of optimal control problems that exhibit constant exogenously given delays in the control in the equation of motion of the differential states. Therefore, we formulate an exemplary optimal control problem with one stock and one control variable and review some analytic properties of an optimal solution. However, analytical considerations are quite limited in case of delayed optimal control problems. In order to overcome these limits, we reformulate the problem and apply direct numerical methods to calculate approximate solutions that give a better understanding of this class of optimization problems. In particular, we present two possibilities to reformulate the delayed optimal control problem into an instantaneous optimal control problem and show how these can be solved numerically with a stateof- the-art direct method by applying Bock’s direct multiple shooting algorithm. We further demonstrate the strength of our approach by two economic examples.

An Actor-Critic based controller for glucose regulation in type 1 diabetes

A novel adaptive approach for glucose control in individuals with type 1 diabetes under sensor-augmented pump therapy is proposed. The controller, is based on Actor-Critic (AC) learning and is inspired by the principles of reinforcement learning and optimal control theory. The main characteristics of the proposed controller are (i) simultaneous adjustment of both the insulin basal rate and the bolus dose, (ii) initialization based on clinical procedures, and (iii) real-time personalization. The effectiveness of the proposed algorithm in terms of glycemic control has been investigated in silico in adults, adolescents and children under open-loop and closed-loop approaches, using announced meals with uncertainties in the order of ±25% in the estimation of carbohydrates. The results show that glucose regulation is efficient in all three groups of patients, even with uncertainties in the level of carbohydrates in the meal. The percentages in the A+B zones of the Control Variability Grid Analysis (CVGA) were 100% for adults, and 93% for both adolescents and children. The AC based controller seems to be a promising approach for the automatic adjustment of insulin infusion in order to improve glycemic control. After optimization of the algorithm, the controller will be tested in a clinical trial.

Consensus Document of the International Union of Angiology (IUA)-2013. Current concept on the management of arterio-venous management

Arterio-venous malformations (AVMs) are congenital vascular malformations (CVMs) that result from birth defects involving the vessels of both arterial and venous origins, resulting in direct communications between the different size vessels or a meshwork of primitive reticular networks of dysplastic minute vessels which have failed to mature to become 'capillary' vessels termed "nidus". These lesions are defined by shunting of high velocity, low resistance flow from the arterial vasculature into the venous system in a variety of fistulous conditions. A systematic classification system developed by various groups of experts (Hamburg classification, ISSVA classification, Schobinger classification, angiographic classification of AVMs,) has resulted in a better understanding of the biology and natural history of these lesions and improved management of CVMs and AVMs. The Hamburg classification, based on the embryological differentiation between extratruncular and truncular type of lesions, allows the determination of the potential of progression and recurrence of these lesions. The majority of all AVMs are extra-truncular lesions with persistent proliferative potential, whereas truncular AVM lesions are exceedingly rare. Regardless of the type, AV shunting may ultimately result in significant anatomical, pathophysiological and hemodynamic consequences. Therefore, despite their relative rarity (10-20% of all CVMs), AVMs remain the most challenging and potentially limb or life-threatening form of vascular anomalies. The initial diagnosis and assessment may be facilitated by non- to minimally invasive investigations such as duplex ultrasound, magnetic resonance imaging (MRI), MR angiography (MRA), computerized tomography (CT) and CT angiography (CTA). Arteriography remains the diagnostic gold standard, and is required for planning subsequent treatment. A multidisciplinary team approach should be utilized to integrate surgical and non-surgical interventions for optimum care. Currently available treatments are associated with significant risk of complications and morbidity. However, an early aggressive approach to elimiate the nidus (if present) may be undertaken if the benefits exceed the risks. Trans-arterial coil embolization or ligation of feeding arteries where the nidus is left intact, are incorrect approaches and may result in proliferation of the lesion. Furthermore, such procedures would prevent future endovascular access to the lesions via the arterial route. Surgically inaccessible, infiltrating, extra-truncular AVMs can be treated with endovascular therapy as an independent modality. Among various embolo-sclerotherapy agents, ethanol sclerotherapy produces the best long term outcomes with minimum recurrence. However, this procedure requires extensive training and sufficient experience to minimize complications and associated morbidity. For the surgically accessible lesions, surgical resection may be the treatment of choice with a chance of optimal control. Preoperative sclerotherapy or embolization may supplement the subsequent surgical excision by reducing the morbidity (e.g. operative bleeding) and defining the lesion borders. Such a combined approach may provide an excellent potential for a curative result. Conclusion. AVMs are high flow congenital vascular malformations that may occur in any part of the body. The clinical presentation depends on the extent and size of the lesion and can range from an asymptomatic birthmark to congestive heart failure. Detailed investigations including duplex ultrasound, MRI/MRA and CT/CTA are required to develop an appropriate treatment plan. Appropriate management is best achieved via a multi-disciplinary approach and interventions should be undertaken by appropriately trained physicians.

Hyperaldosteronism in pregnancy

Aldosterone is a key regulator of electrolyte and water homeostasis and plays a central role in blood pressure regulation. Hormonal changes during pregnancy, among them increased progesterone and aldosterone production, lead to the required plasma volume expansion of the maternal body as an accommodation mechanism for fetus growth. This review discusses the regulation of aldosterone production by aldosterone synthase (CYP11B2); the impact on aldosterone secretion due to the presence of a chimeric gene originating from a crossover between CYP11B1 and CYP11B2 in glucocorticoid remediable aldosteronism (GRA) - the inherited form of hypertension; enhanced aldosterone production in aldosterone-producing adenoma (APA); and idiopathic hyperaldosteronism (IHA). Features of hyperaldosteronism are also found in patients with apparent mineralocorticoid excess (AME), in which glucocorticoids exacerbate activation of the mineralocorticoid receptor (MR) because of a defect in the 11beta-hydroxysteroid dehydrogenase type 2 enzyme. Regulation of aldosterone production and tissue-specific activation of the mineralocorticoid receptor are prerequisites for optimal control of body fluids and blood pressure during pregnancy and contribute largely to the wellbeing of the mother-to-be.

Adaptive Algorithms for Personalized Diabetes Treatment

Dynamic systems, especially in real-life applications, are often determined by inter-/intra-variability, uncertainties and time-varying components. Physiological systems are probably the most representative example in which population variability, vital signal measurement noise and uncertain dynamics render their explicit representation and optimization a rather difficult task. Systems characterized by such challenges often require the use of adaptive algorithmic solutions able to perform an iterative structural and/or parametrical update process towards optimized behavior. Adaptive optimization presents the advantages of (i) individualization through learning of basic system characteristics, (ii) ability to follow time-varying dynamics and (iii) low computational cost. In this chapter, the use of online adaptive algorithms is investigated in two basic research areas related to diabetes management: (i) real-time glucose regulation and (ii) real-time prediction of hypo-/hyperglycemia. The applicability of these methods is illustrated through the design and development of an adaptive glucose control algorithm based on reinforcement learning and optimal control and an adaptive, personalized early-warning system for the recognition and alarm generation against hypo- and hyperglycemic events.

Optimization of Schwinger pair production in colliding laser pulses

Recent studies of Schwinger pair production have demonstrated that the asymptotic particle spectrum is extremely sensitive to the applied field profile. We extend the idea of the dynamically assisted Schwinger effect from single pulse profiles to more realistic field configurations to be generated in an all-optical experiment searching for pair creation. We use the quantum kinetic approach to study the particle production and employ a multi-start method, combined with optimal control theory, to determine a set of parameters for which the particle yield in the forward direction in momentum space is maximized. We argue that this strategy can be used to enhance the signal of pair production on a given detector in an experimental setup.

The inverse problem for Schwinger pair production

The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism) depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

Optimal Scheduling of Work-Content-Constrained Projects

The execution of a project requires resources that are generally scarce. Classical approaches to resource allocation assume that the usage of these resources by an individual project activity is constant during the execution of that activity; in practice, however, the project manager may vary resource usage over time within prescribed bounds. This variation gives rise to the project scheduling problem which consists in allocating the scarce resources to the project activities over time such that the project duration is minimized, the total number of resource units allocated equals the prescribed work content of each activity, and various work-content-related constraints are met. We formulate this problem for the first time as a mixed-integer linear program. Our computational results for a standard test set from the literature indicate that this model outperforms the state-of-the-art solution methods for this problem.

Constrained pattern of viral evolution in acute and early HCV infection limits viral plasticity

Cellular immune responses during acute Hepatitis C virus (HCV) and HIV infection are a known correlate of infection outcome. Viral adaptation to these responses via mutation(s) within CD8+ T-cell epitopes allows these viruses to subvert host immune control. This study examined HCV evolution in 21 HCV genotype 1-infected subjects to characterise the level of viral adaptation during acute and early HCV infection. Of the total mutations observed 25% were within described CD8+ T-cell epitopes or at viral adaptation sites. Most mutations were maintained into the chronic phase of HCV infection (75%). The lack of reversion of adaptations and high proportion of silent substitutions suggests that HCV has structural and functional limitations that constrain evolution. These results were compared to the pattern of viral evolution observed in 98 subjects during a similar phase in HIV infection from a previous study. In contrast to HCV, evolution during acute HIV infection is marked by high levels of amino acid change relative to silent substitutions, including a higher proportion of adaptations, likely reflecting strong and continued CD8+ T-cell pressure combined with greater plasticity of the virus. Understanding viral escape dynamics for these two viruses is important for effective T cell vaccine design.

Genetic diversity in an indigenous horse breed: implications for mating strategies and the control of future inbreeding

The Franches-Montagnes is an indigenous Swiss horse breed, with approximately 2500 foalings per year. The stud book is closed, and no introgression from other horse breeds was conducted since 1998. Since 2006, breeding values for 43 different traits (conformation, performance and coat colour) are estimated with a best linear unbiased prediction (BLUP) multiple trait animal model. In this study, we evaluated the genetic diversity for the breeding population, considering the years from 2003 to 2008. Only horses with at least one progeny during that time span were included. Results were obtained based on pedigree information as well as from molecular markers. A series of software packages were screened to combine best the best linear unbiased prediction (BLUP) methodology with optimal genetic contribution theory. We looked for stallions with highest breeding values and lowest average relationship to the dam population. Breeding with such stallions is expected to lead to a selection gain, while lowering the future increase in inbreeding within the breed.

Control of ventricular unloading using an electrocardiogram-synchronized Thoratec paracorporeal ventricular assist device

OBJECTIVE: Current pulsatile ventricular assist devices operate asynchronous with the left ventricle in fixed-rate or fill-to-empty modes because electrocardiogram-triggered modes have been abandoned. We hypothesize that varying the ejection delay in the synchronized mode yields more precise control of hemodynamics and left ventricular loading. This allows for a refined management that may be clinically beneficial. METHODS: Eight sheep received a Thoratec paracorporeal ventricular assist device (Thoratec Corp, Pleasanton, Calif) via ventriculo-aortic cannulation. Left ventricular pressure and volume, aortic pressure, pulmonary flow, pump chamber pressure, and pump inflow and outflow were recorded. The pump was driven by a clinical pneumatic drive unit (Medos Medizintechnik AG, Stolberg, Germany) synchronously with the native R-wave. The start of pump ejection was delayed between 0% and 100% of the cardiac period in 10% increments. For each of these delays, hemodynamic variables were compared with baseline data using paired t tests. RESULTS: The location of the minimum of stroke work was observed at a delay of 10% (soon after aortic valve opening), resulting in a median of 43% reduction in stroke work compared with baseline. Maximum stroke work occurred at a median delay of 70% with a median stroke work increase of 11% above baseline. Left ventricular volume unloading expressed by end-diastolic volume was most pronounced for copulsation (delay 0%). CONCLUSIONS: The timing of pump ejection in synchronized mode yields control over left ventricular energetics and can be a method to achieve gradual reloading of a recoverable left ventricle. The traditionally suggested counterpulsation is not optimal in ventriculo-aortic cannulation when maximum unloading is desired.

Cardiovascular risk factor control and outcomes in peripheral artery disease patients in the Reduction of Atherothrombosis for Continued Health (REACH) Registry

OBJECTIVES: To examine differences in risk factor (RF) management between peripheral artery disease (PAD) and coronary artery (CAD) or cerebrovascular disease (CVD), as well as the impact of RF control on major 1-year cardiovascular (CV) event rates. METHODS: The REACH Registry recruited >68000 outpatients aged >/=45 years with established atherothrombotic disease or >/=3 RFs for atherothrombosis. The predictors of RF control that were evaluated included: (1) patient demographics, (2) mode of PAD diagnosis, and (3) concomitant CAD and/or CVD. RESULTS: RF control was less frequent in patients with PAD (n=8322), compared with those with CAD or CVD (but no PAD, n=47492) [blood pressure; glycemia; total cholesterol; smoking cessation (each P<0.001)]. Factors independently associated with optimal RF control in patients with PAD were male gender (OR=1.9); residence in North America (OR=3.5), Japan (OR=2.5) or Latin America (OR=1.5); previous coronary revascularization (OR=1.3); and statin use (OR=1.4); whereas prior leg amputation was a negative predictor (OR=0.7) (P<0.001). Optimal RF control was associated with fewer 1-year CV ischemic symptoms or events. CONCLUSIONS: Patients with PAD do not achieve RF control as frequently as individuals with CAD or CVD. Improved RF control is associated with a positive impact on 1-year CV event rates.