Continuous Hands-off Control by CLOT Norm Minimization

In this paper, we consider hands-off control via minimization of the C LOT (Combined L -One and Two) norm. The maximum hands-off control is the L 0 -optimal (or the sparsest) control among all feasible controls that are bounded b y a specified value and transfer the state from a given initial state to the origin within a fixed time dura tion. In general, the maximum hands-off control is a bang-off-bang control taking value s of ± 1 and 0. For many real applications, such discontinuity in the control is not desirable. To ob tain a continuous but still relatively sparse control, we propose to use the CLOT norm, a conv ex combination of L 1 and L 2 norms. We show by numerical simulation that the CLOT control is con tinuous and much sparser (i.e. has longer time duration on which the control takes 0) than the conventional EN (elastic net) control, which is a convex combination of L 1 and squared L 2 norms

Sparsity Methods for Systems and Control

The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control

Locally deforming continuation method based on a shooting method for a class of optimal control problems

This paper proposes a new continuation method for solving optimal control problems. The proposed method is based on a shooting method. In the proposed method, a cost function of an optimal control problem is locally deformed to find the solution of the problem in a stable way. This paper also analyses a relationship between the variation of the continuation parameter and the proximity of the solutions before and after a deformation in the proposed method. The obtained relation provides guidance on how to deform the continuation parameter. The effectiveness of this method is confirmed through numerical examples

Computer Simulation of a Nitric Oxide-Releasing Catheter with a Novel Stable Convection-Diffusion Equation Solver and Automatic Quantification of Lung Ultrasound Comets by Machine Learning

Biological transport processes often involve a boundary acting as separation of flow, most commonly in transport involving blood-contacting medical devices. The separation of flow creates two different scenarios of mass transport across the interface. No flow exists within the medical device and diffusion governs mass transport; both convection and diffusion exist when flow is present. The added convection creates a large concentration gradient around the interface. Computer simulation of such cases prove to be difficult and require proper shock capturing methods for the solutions to be stable, which is typically lacking in commercial solvers. In this thesis, we propose a second-order accurate numerical method for solving the convection-diffusion equation by using a gradient-limited Godunov-type convective flux and the multi-point flux approximation (MPFA) L-Method for the diffusion flux. We applied our solver towards simulation of a nitric oxide-releasing intravascular catheter. Intravascular catheters are essential for long-term vascular access in both diagnosis and treatment. Use of catheters are associated with risks for infection and thrombosis. Because infection and thrombosis lead to impaired flow and potentiality life threatening systemic infections, this leads to increased morbidity and mortality, requiring catheters to be replaced among other treatments for these complications. Nitric oxide (NO) is a potent antimicrobial and antithrombotic agent produced by vascular endothelial cells. The production level in vivo is so low that the physiological effects can only be seen around the endothelial cells. The catheter can incorporate a NO source in two major ways: by impregnating the catheter with NO-releasing compounds such as S-nitroso-N-acetyl penicillamine (SNAP) or using electrochemical reactions to generate NO from nitrites. We applied our solver to both situations to guide the design of the catheter. Simulations revealed that dissolved NO inside the catheter is depleted after 12 minutes without resupplying, and electrochemical release of NO requires 10.5 minutes to reach steady state. Lung edema is often present in patients with end-stage renal disease due to reduced filtration functions of the kidney. These patients require regular dialysis sessions to manage their fluid status. The clinical gold standard to quantify lung edema is to use CT, which exposes patients to high amounts of radiation and is not cost efficient. Fluid management in such patients becomes very challenging without a clear guideline of fluid to be removed during dialysis sessions. Hypotension during dialysis can limit fluid removal, even in the setting of ongoing fluid overload or congestive heart failure. Accurate assessment of the pulmonary fluid status is needed, so that fluid overload and congestive heart failure can be detected, especially in the setting of hypotension, allowing dialysis to be altered to improve fluid removal. Recently, reverberations in ultrasound signals, referred to as ``lung comets'' have emerged as a potential quantitative way to measure lung edema. Increased presence of lung comets is associated with higher amounts of pulmonary edema, higher mortality, and more adverse cardiac events. However, the lung comets are often counted by hand by physicians with single frames in lung ultrasound and high subjectivity has been found to exist among the counting by physicians. We applied image processing and neural network techniques as an attempt to provide an objective and accurate measurement of the amount of lung comets present. Our quantitative results are significantly correlated with diastolic blood pressure and ejection fraction.PHDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163182/1/micw_1.pd

Analysis of the Interlimb similarity of motor patterns for improving stroke assessment and neurorehabilitation

Stroke is the leading cause of adult disability, with upper limb hemiparesis being one of the most common consequences. Regaining voluntary arm movement is one of the major goals of rehabilitation. However, even with intensive rehabilitation, approximately 30% of patients remain permanently disabled and only 5 to 20% of them recover full independence. Hence, there is an increasing interest in incorporating the latest advances in neuroscience, medicine and engineering to improve the efficacy of conventional therapies. In the last years, a variety of promising targets have been identified to improve rehabilitation. However, there is no consensus on which measure should be applied as a gold standard to study functional recovery. This fact dramatically hinders the development of new interventions since it turns difficult to compare different clinical trials and draw consistent conclusions about therapeutic efficiency. In addition, available scales are subjective, qualitative and often lead to incongruent outcomes. Indeed, there is increasing suspicion that the lack of optimal assessment measures hampers the detection of benefits of new therapies. Moreover, existing scales totally ignore the neuromuscular state of the patient masking the ongoing recovery processes. In consequence, making appropriate clinical decisions in such environment is almost impossible. In light of all these facts, the need for new objective biomarkers to develop effective therapies is undeniable. To give response to these demands we have organized this thesis into two main branches. On the one hand, we have developed an innovative physiological scale that reveals the neuromuscular state of the patient and is able to discriminate between motor impairment levels. The innovation here resides in the concept of interlimb similarity (ILS). Based on the latest findings about the modular organization of the motor system and taking into account that stroke provokes unilateral motor damage, we propose comparing the control structure of the unaffected arm with the control structure of the paretic arm to quantify motor impairment. We have defined the control structure as the set of muscle synergies and activation coefficients needed to complete a task. The advantage of this approach is not only its capacity to provide neuromuscular information about the patient, but also that the ILS is personalized to each patient and can purposely guide rehabilitation based on the patient¿s own physiological patterns. This supposes a huge advance taking into account the heterogeneity of stroke pathogenesis. On other hand, we have characterized the therapeutic potential of Visual Feedback (VF) as a tool to purposely induce neuroplastic changes. We have chosen VF among the various interventions proven to improve motor performance, because VF is a cheap strategy that can be implemented in almost any rehabilitation center. We demonstrate that VF is able to modulate the human control structure. In healthy subjects, it seems that VF makes accessible the refined dominant motor programs for the nondominant hemisphere giving rise to an increased interlimb similarity of the control structure. Interestingly, in stroke patients VF is able to manipulate the ILS of upper-limb kinematics in favor of finer motor control but a single training session seems not to be enough to fix those changes in the neuromuscular system of a damaged brain. Overall, these findings offer a new promising framework to develop and assess an effective intervention to guide the restoration of the original neuromuscular patterns and avoid unwanted maladaptive neuroplasticity. In conclusion, this thesis seeks moving forward in the understanding of human motor recovery processes and their relationship with neuroplasticity. In this sense, it provides important advances in the design of a new biomarker of motor impairment and tests the power of VF to modulate the neuromuscular control of patients with stroke.L'ictus és la principal causa de discapacitat en adults, essent l'hemiparèsia del membre superior una de les conseqüències més comunes. Els programes de rehabilitació tenen com a objectiu fonamental restituir la mobilitat del braç afectat. No obstant això, es calcula que només entre el 5 i el 20% dels pacients aconsegueixen recuperar la seva independència mentre que el 30% queden incapacitats permanentment. En front d'aquest escenari es fa necessari incorporar els últims avenços de la neurociència, la medicina i l'enginyeria en aquesta àrea. En els darrers anys s'han identificat diversos aspectes clau per intentar millorar la rehabilitació. El problema, però, és que no hi ha consens per definir una mesura com a "gold estàndard" per avaluar la recuperació funcional, motiu pel qual, el desenvolupament de noves teràpies queda profundament afectat, ja que esdevé impossible poder comparar diferents assajos clínics i extreure conclusions consistents sobre la seva eficiència terapèutica. A més, les diverses mesures que s'utilitzen són subjectives, qualitatives i sovint donen resultats incongruents. De fet, se sospita que la manca de mesures d'avaluació òptimes dificulta la detecció dels beneficis de noves teràpies. A tot això se li ha d'afegir que les mesures actuals no consideren l'estat neuromuscular del pacient, emmascarant els processos reparadors subjacents. Així doncs, prendre les decisions clíniques adequades sota aquestes condicions esdevé pràcticament impossible. En aquestes circumstàncies, no es pot ignorar el requeriment de nous biomarcadors que proporcionin dades objectives per catalitzar el disseny de teràpies efectives. Per donar resposta a aquesta situació, la tesi s'ha estructurat en dues parts. Per una banda, s'ha desenvolupat una innovadora escala fisiològica que revela l'estat neuromuscular del pacient i és capaç de discriminar entre diferents nivells d'incapacitat motora. La innovació rau en el concepte de similitud entre membres (ILS, en anglès). Així, basant-nos en els darrers descobriments sobre l'organització modular del sistema motor, i en el fet que l'ictus provoca dany unilateral, proposem comparar l'estructura de control del braç no-afectat amb l'estructura de control del braç parètic per quantificar la incapacitat motora. L'estructura de control l'hem definida com el conjunt de sinergies musculars i coeficients d'activació que es necessiten per a dur a terme una tasca. L'avantatge d'aquesta proposta és doble, ja que proporciona informació sobre l'estat neuromuscular del pacient i en ser personalitzable, pot guiar la rehabilitació d'acord amb els patrons fisiològics propis de cada pacient. Això suposa un enorme avenç en aquesta àrea, donada la immensa heterogeneïtat de la patogènesi d'aquest trastorn. D'altra banda, s'ha caracteritzat el potencial terapèutic del feedback visual (VF) per induir canvis neuroplàstics. Aquesta és una eina molt interessant perquè a més de millorar el control motor, és assequible per gairebé qualsevol centre de rehabilitació. S'ha demostrat que el VF és capaç de modular l'estructura de control. Concretament, el VF sembla transferir els programes motors de l'hemisferi dominant al costat no dominant augmentant així el ILS dels subjectes sans. En pacients amb ictus, el VF és capaç d'augmentar el ILS cinemàtic afavorint patrons de control més fins. En conclusió, l'objectiu d'aquesta tesi és aprofundir en la comprensió dels processos de recuperació motora i la seva relació amb la neuroplasticitat. La tesi ofereix un nou i prometedor marc per desenvolupar i avaluar procediments efectius per guiar la restauració dels patrons neuromusculars originals i evitar que el cervell pateixi canvis neuroplàstics indesitjables. Així, la tesi proporciona avanços importants en el disseny d'un biomarcador per quantificar la incapacitat motora i avaluar el potencial del VF per modular el control neuromuscular de pacients amb ictus.Postprint (published version