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.

Toward optimal display of physiologic status in critical care: I. Recreating bedside displays from archived physiologic data

BACKGROUND: Physiologic data display is essential to decision making in critical care. Current displays echo first-generation hemodynamic monitors dating to the 1970s and have not kept pace with new insights into physiology or the needs of clinicians who must make progressively more complex decisions about their patients. The effectiveness of any redesign must be tested before deployment. Tools that compare current displays with novel presentations of processed physiologic data are required. Regenerating conventional physiologic displays from archived physiologic data is an essential first step. OBJECTIVES: The purposes of the study were to (1) describe the SSSI (single sensor single indicator) paradigm that is currently used for physiologic signal displays, (2) identify and discuss possible extensions and enhancements of the SSSI paradigm, and (3) develop a general approach and a software prototype to construct such "extended SSSI displays" from raw data. RESULTS: We present Multi Wave Animator (MWA) framework-a set of open source MATLAB (MathWorks, Inc., Natick, MA, USA) scripts aimed to create dynamic visualizations (eg, video files in AVI format) of patient vital signs recorded from bedside (intensive care unit or operating room) monitors. Multi Wave Animator creates animations in which vital signs are displayed to mimic their appearance on current bedside monitors. The source code of MWA is freely available online together with a detailed tutorial and sample data sets.

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.

Vibrations, Posture, and the Stabilization of Gaze: An Experimental Study on Impedance Control

Vibrations, Posture, and the Stabilization of Gaze: An Experimental Study on Impedance Control R. KREDEL, A. GRIMM & E.-J. HOSSNER University of Bern, Switzerland Introduction Franklin and Wolpert (2011) identify impedance control, i.e., the competence to resist changes in position, velocity or acceleration caused by environmental disturbances, as one of five computational mechanisms which allow for skilled and fluent sen-sorimotor behavior. Accordingly, impedance control is of particular interest in situa-tions in which the motor task exhibits unpredictable components as it is the case in downhill biking or downhill skiing. In an experimental study, the question is asked whether impedance control, beyond its benefits for motor control, also helps to stabi-lize gaze what, in turn, may be essential for maintaining other control mechanisms (e.g., the internal modeling of future states) in an optimal range. Method In a 3x2x4 within-subject ANOVA design, 72 participants conducted three tests on visual acuity and contrast (Landolt / Grating and Vernier) in two different postures (standing vs. squat) on a platform vibrating at four different frequencies (ZEPTOR; 0 Hz, 4 Hz, 8 Hz, 12 Hz; no random noise; constant amplitude) in a counterbalanced or-der with 1-minute breaks in-between. In addition, perceived exertion (Borg) was rated by participants after each condition. Results For Landolt and Grating, significant main effects for posture and frequency are re-vealed, representing lower acuity/contrast thresholds for standing and for higher fre-quencies in general, as well as a significant interaction (p < .05), standing for in-creasing posture differences with increasing frequencies. Overall, performance could be maintained at the 0 Hz/standing level up to a frequency of 8 Hz, if bending of the knees was allowed. The fact that this result is not only due to exertion is proved by the Borg ratings showing significant main effects only, i.e., higher exertion scores for standing and for higher frequencies, but no significant interaction (p > .40). The same pattern, although not significant, is revealed for the Vernier test. Discussion Apparently, postures improving impedance control not only turn out to help to resist disturbances but also assist in stabilizing gaze in spite of these perturbations. Con-sequently, studying the interaction of these control mechanisms in complex unpre-dictable environments seems to be a fruitful field of research for the future. References Franklin, D. W., & Wolpert, D. M. (2011). Computational mechanisms of sensorimotor control. Neuron, 72, 425-442.

Economic efficiency analysis of different strategies to control post-weaning multi-systemic wasting syndrome and porcine circovirus type 2 subclinical infection in 3-weekly batch system farms.

The study assessed the economic efficiency of different strategies for the control of post-weaning multi-systemic wasting syndrome (PMWS) and porcine circovirus type 2 subclinical infection (PCV2SI), which have a major economic impact on the pig farming industry worldwide. The control strategies investigated consisted on the combination of up to 5 different control measures. The control measures considered were: (1) PCV2 vaccination of piglets (vac); (2) ensuring age adjusted diet for growers (diets); (3) reduction of stocking density (stock); (4) improvement of biosecurity measures (bios); and (5) total depopulation and repopulation of the farm for the elimination of other major pathogens (DPRP). A model was developed to simulate 5 years production of a pig farm with a 3-weekly batch system and with 100 sows. A PMWS/PCV2SI disease and economic model, based on PMWS severity scores, was linked to the production model in order to assess disease losses. This PMWS severity scores depends on the combination post-weaning mortality, PMWS morbidity in younger pigs and proportion of PCV2 infected pigs observed on farms. The economic analysis investigated eleven different farm scenarios, depending on the number of risk factors present before the intervention. For each strategy, an investment appraisal assessed the extra costs and benefits of reducing a given PMWS severity score to the average score of a slightly affected farm. The net present value obtained for each strategy was then multiplied by the corresponding probability of success to obtain an expected value. A stochastic simulation was performed to account for uncertainty and variability. For moderately affected farms PCV2 vaccination alone was the most cost-efficient strategy, but for highly affected farms it was either PCV2 vaccination alone or in combination with biosecurity measures, with the marginal profitability between 'vac' and 'vac+bios' being small. Other strategies such as 'diets', 'vac+diets' and 'bios+diets' were frequently identified as the second or third best strategy. The mean expected values of the best strategy for a moderately and a highly affected farm were £14,739 and £57,648 after 5 years, respectively. This is the first study to compare economic efficiency of control strategies for PMWS and PCV2SI. The results demonstrate the economic value of PCV2 vaccination, and highlight that on highly affected farms biosecurity measures are required to achieve optimal profitability. The model developed has potential as a farm-level decision support tool for the control of this economically important syndrome.