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In this paper, we introduce a novel entropy-based metric to characterize the fault-induced delayed voltage recovery (FIDVR) phenomenon. In particular, we make use of Kullback-Leibler (KL) divergence to determine both the rate and the level of voltage recovery following a fault or disturbance. The computation of the entropy-based measure relies on voltage time-series data and is independent of the underlying system model used to generate the voltage time-series. The proposed measure provides quantitative information about the degree of WECC voltage performance violation for FIDVR phenomenon. The quantitative measure for violation allows one to compare the voltage responses of different buses to various contingencies and to rank order them, based on the degree of violation.

Multidrug resistant (MDR) Klebsiella pneumoniae an increasing cause of neonatal sepsis in India. This observational study was designed to monitor temporal change in prevalence of K. pneumoniae as a causative organism for neonatal sepsis and its sensitivity pattern. The time period was divided into four time frames of six months each (designated A (1/10/2006-31/03/2007) to D (1/04/2008-30/09/2008)). K. pneumoniae isolation in all cultures sent from neonatal intensive care units doubled in time frame D (6.3%) compared to time frame A (3.0). Similarly, the percentage of total positive cultures in the neonatal intensive care unit that were K. pneumoniae also doubled (27.8% in A to 55.6% in D). K. pneumoniae sepsis tripled in inborn neonates (15.4% in A to 47.1% in D). Incidence of MDR K. pneumoniae increased from 0% in time frame A to 76.5% in time frame D. Resistance against ampicillin and third generation cephalosporins (cefotaxime and ceftazidime) remained 100% in all time frames. Carbapenem (meropenem and imipenem) resistance increased from 0% in time frame A and B to 41.2% in time frame D. Death due to K. pneumoniae sepsis showed brisk resurgence in time frame D (17.6%) compared to time frame C (10%). Lower gestational age and birth weight were associated with higher mortality. MDR K. pneumoniae is emerging as a more frequent cause of neonatal sepsis. There is an dincreasing threat of combined quinolone and carbapenem resistant MDR K. pneumoniae.

Congenital diaphragmatic hernia (CDH) is a rare condition. The reported incidence of intrathoracic renal ectopia due to CDH is also rare. A right-sided thoracic kidney is much less common due to the location of the liver. Isolated intrathoracic kidney is usually asymptomatic and diagnosed incidentally on chest imaging. The authors report on a 21days old female infant with late-presenting right sided congenital diaphragmatic hernia associated with intrathoracic ectopic kidney and adrenal gland. Prenatal ultrasound showed no pathology. A female baby was investigated for silent tachypnoea, a chest x-ray confirmed the diagnosis of congenital diaphragmatic hernia, the postnatal ultrasound revealed a right-sided kidney herniation. On computed tomography (CT) scan intrathoracic ectopic kidney was diagnosed. CDH is an delivery room emergency. This case had complex anatomy of right side CDH and intrathoracic kidney and presentation was only tachypnoea. Hence we are reporting this case.

This paper investigates modeling a heterogeneous group of Thermostatically Controlled Loads (TCLs) as a discrete-time discrete-state Markov model. Details of the Markov model development process using a statistical learning technique with full parameter heterogeneity are described and evaluated. The learning process is based on a training data sets which are obtained via Monte Carlo simulation of individual end-users' devices. The performance of various Markov models is evaluated under different initial conditions to determine representative models that can approximates the TCLs dynamics for the short-term and long-term applications. A detailed analysis of the model's eigenvalues is used to derive an accurate distribution of the TCL devices during steady-state conditions. This distribution is validated and tested against the actual devices' simulation. The study is applied to a group of 10,000 heterogeneous air-conditioning devices and the simulations are performed using MATLAB (R2015a).

Classification is at the very center of the supervised learning. In this work, we propose a novel algorithm to classify the test data set with the aid of a vector field, emanating from the training data set. In particular, the vector field is constructed such that the location of each training data point becomes a local minimum of the potential. The test data points are allowed to evolve under the influence of the velocity field, generated by the training data set, and thereby would be converging to the domain of attractions of different classes. The proposed approach avoids explicit computation of the separating hyper-plane like Support Vector Machine, which becomes difficult, if the structure of the separating hyper-plane is nonlinear. The proposed method is specially suited for online learning problems, as the model training does not involve any additional time. Comparative simulation studies are presented over data sets coming from three practical Machine Learning benchmark problems.

In this paper, we demonstrate the fragility of decentralized load-side frequency algorithms proposed in [1] against stochastic parametric uncertainty in power network model. The stochastic parametric uncertainty is motivated through the presence of renewable energy resources in power system model. We show that relatively small variance value of the parametric uncertainty affecting the system bus voltages cause the decentralized load-side frequency regulation algorithm to become stochastically unstable. The critical variance value of the stochastic bus voltages above which the decentralized control algorithm become mean square unstable is computed using an analytical framework developed in [2], [3]. Furthermore, the critical variance value is shown to decrease with the increase in the cost of the controllable loads and with the increase in penetration of renewable energy resources. Finally, simulation results on IEEE 68 bus system are presented to verify the main findings of the paper.

In this paper, we propose a new definition of information transfer in a discrete dynamical system. The information transfer is based on how much entropy (uncertainty) is transferred from state x to state y, as the dynamical system evolves in time. In our previous work, we had provided an axiomatic definition of information transfer where we had considered absolute entropy to define the transfer. Our new definition can be viewed as a natural generalization of directed information from information theory to dynamical systems and is based on transfer of conditional entropy. This new definition also satisfies the properties of a) zero transfer, b) transfer asymmetry and c) information conservation. We start with a definition of one-step information transfer and then generalize this definition to n-step information transfer and average information transfer over infinite time step. We also provide analytical expressions for information transfer for linear systems. Some basic examples are provided to understand the physical meaning of information transfer and how this can be used to infer causality and influence in dynamical system setting.

Preterm birth survivors are at a higher risk of growth and developmental disabilities compared to their term counterparts. Development of strategies to lower the complications of preterm birth forms the rising need of the hour. Appropriate nutrition is essential for the growth and development of preterm infants. Early administration of optimal nutrition to preterm birth survivors lowers the risk of adverse health outcomes and improves cognition in adulthood. A group of neonatologists, pediatricians, and nutrition experts convened to discuss and frame evidence-based recommendations for optimizing nutrition in preterm low birth weight (LBW) infants. The following were the primary recommendations of the panel: (1) enteral feeding is safe and may be preferred to parenteral nutrition due to the complications associated with the latter; however, parenteral nutrition may be a useful adjunct to enteral feeding in some critical cases; (2) early, fast, or continuous enteral feeding yields better outcomes compared to late, slow, or intermittent feeding, respectively; (3) routine use of nasogastric tubes is not advisable; (4) preterm infants can be fed while on ventilator or continuous positive airway pressure; (5) routine evaluation of gastric residuals and abdominal girth should be avoided; (6) expressed breast milk (EBM) is the first choice for feeding preterm infants due to its beneficial effects on cardiovascular, neurological, bone health, and growth outcomes; the second choice is donor pasteurized human milk; (7) EBM or donor milk may be fortified with human milk fortifiers, without increasing the osmolality of the milk, to meet the high protein requirements of preterm infants; (8) standard fortification is effective and safe but does not fulfill the high protein needs; (9) use of targeted and adjustable fortification, where possible, helps provide optimal nutrition; (10) optimizing weight gain in preterm infants prevents long-term cardiovascular complications; (11) checking for optimal weight and sucking/swallowing ability is essential prior to discharge of preterm infants; and (12) appropriate counseling and regular follow-up and monitoring after discharge will help achieve better long-term health outcomes. This consensus summary serves as a useful guide to clinicians in addressing the challenges and providing optimal nutrition to preterm LBW infants.

Summary In this paper, we study the problem of control of discrete time nonlinear systems in Lure form over erasure channels at the input and output. The input and output channel uncertainties are modeled as Bernoulli random variables. The main results of this paper provide sufficient condition for the mean square exponential stability of the closed loop system expressed in terms of statistics of channel uncertainty and plant characteristics. We also provide synthesis method for the design of observer-based controller that is robust to channel uncertainty. To prove the main results of this paper, we discover a stochastic variant of the well-known positive real lemma and the principle of separation for stochastic nonlinear system. Application of the results for the stabilization of system in Lure form over packet-drop network is discussed. Finally, a result for state feedback control of a Lure system with a general multiplicative uncertainty at actuation is discussed. Copyright © 2014 John Wiley & Sons, Ltd.

Numerical solutions for the optimal feedback stabilization of discrete time dynamical systems is the focus of this technical note. Set-theoretic notion of almost everywhere stability introduced by the Lyapunov measure, weaker than conventional Lyapunov function-based stabilization methods, is used for optimal stabilization. The linear Perron-Frobenius transfer operator is used to pose the optimal stabilization problem as an infinite dimensional linear program. Set-oriented numerical methods are used to obtain the finite dimensional approximation of the linear program. We provide conditions for the existence of stabilizing feedback controls and show the optimal stabilizing feedback control can be obtained as a solution of a finite dimensional linear program. The approach is demonstrated on stabilization of period two orbit in a controlled standard map.

We prove a necessary and sufficient condition for the existence of Lyapunov density for a system of coupled autonomous ordinary differential equations. In particular, we characterize the kinds of couplings that preserve almost everywhere uniform stability of the origin provided the isolated systems have an almost everywhere uniformly stable equilibrium point at the origin.

This paper, for the first time, explores the use of data-driven method to model the traffic dynamics of an interstate highway system with high resolution probe data. The dynamic mode decomposition and spatio-temporal pattern network were used to analyze traffic patterns on a 290 mile interstate highway across Iowa. The results show the data-driven methods can effectively detect the changes in traffic system dynamics during different time of day. Traffic dynamics during morning peak hours, evening peak hours and off-peak were very different on the studied road. In contrast, the trends over multiple months were similar during the same time periods. The study also found that inclement weather had a significant impact on the system dynamics. In future, the proposed methodology can be used to gain insights in the system dynamics of a traffic network. These models will be instrumental in optimal traffic control, traffic sensor placement and other policy decisions affecting the capacity of the network.

In this paper, we show through examples, how the existing definitions of information transfer, namely directed information and transfer entropy fail to capture true causal interaction between states in control dynamical system. Furthermore, existing definitions are shown to be too weak to have any implication on two of the most fundamental concepts in system theory, namely controllability and observability. We propose a new definition of information transfer, based on the ideas from dynamical system theory, and show that this new definition can not only capture true causal interaction between states, but also have implication on system controllability and observability properties. In particular, we show that non-zero transfer of information from input-to-state and state-to-output implies structural controllability and observability properties of the control dynamical system respectively. Analytical expression for information transfer between state-to-state, input-to-state, state-to-output, and input-to-output are provided for linear system. There is a natural extension of our proposed definition to define information transfer over n time steps and average information transfer over infinite time step. We show that the average information transfer in feedback control system between plant output and input is equal to the entropy of the open loop dynamics thereby re-deriving the Bode fundamental limitation results using the proposed definition of transfer.

Accurate and rapid monitoring of indoor air quality is critical to ensure occupant safety in the built environment. This is especially important in events where hazardous substances are released, and prompt estimation of contaminant distribution will facilitate quick evacuation and control response. The built environment is usually equipped with a finite set of sensors that measure local concentration of contaminants. The goal is to use this streaming dataset to estimate the contaminant concentration distribution in the complete domain. We accomplish this by integrating two powerful concepts. We utilize an operator theoretic approach – specifically the Perron-Frobenius (P-F) operator – to model the contaminant transport. Previous work has shown that the PF approach is a fast, effective, and accurate paradigm for sensor placement and contaminant transport prediction. The PF approach is integrated with an Ensemble Kalman Filter to rapidly estimate contaminant distribution under unknown release scenarios, given minimal sensor data. The framework is illustrated for two scenarios: a 2D problem involving an office space, and a 3D problem involving a furnished hotel room. Both examples show that the contaminant distribution is accurately predicted within a few sensor measurement cycles. The general applicability of the framework is illustrated by testing the framework for multiple, unknown release locations. This approach provides a unified, extendable framework for rapid contaminant estimation.

Gastrocolic Fistula is, in the majority of cases the pathological communication between stomach and transverse colon. It occurs mostly in adults, but they can be present in infants, as well, as a result of congenital abnormalities or iatrogenic procedures (i.e. migration of naso gastric tube that placed before). We report a case of 10 days old full term, male neonate, was on naso gastric tube feeds, had clinical features of necrotizing enterocolitis (NEC), diagnosed to have gastrocolic fistula on barium enema study and confirmed on CT abdomen. Intraoperatively, baby had multiple perforations with gastrocolic fistula. Histopathological examination was suggestive of NEC. We searched literature, we could find seven case reports.

Heating ventilation and air conditioning (HVAC) systems in residential and commercial buildings make up 16% of the United States energy consumption. Utilizing natural ventilation strategies is a low energy solution to reduce the energy used by building environmental control systems. Design of effective natural ventilation strategies is challenging because of inherent stochasticity in interior (machine loads, number of people) and exterior conditions (wind load, outside temperature). However, by exploiting the natural dynamics of building systems, efficient design and control seems possible. We explore this idea by introducing a stochastic approach to analyze the natural dynamics of building systems (under natural ventilation) by explicitly incorporating the effects of stochastic wind speeds and stochastic internal loads. We show that complex dynamics in the form of bi-stable behavior emerges when considering a single zone building with stochastic inputs. We show that neglecting these complex stochastic dynamics leads to inaccurate predictions in the thermal response, especially for natural ventilation. We compute the sensitivity of the system with respect to various system parameters which provide insight into developing robust design guidelines. The techniques presented aid in the design process, and are a step toward adaptive, efficient, robust control of natural ventilation systems.

In this technical note, we study the problem of state observation of nonlinear systems over an erasure channel. The notion of mean square exponential stability is used to analyze the stability property of observer error dynamics. The main results of this technical note prove, fundamental limitation arises for mean square exponential stabilization of the observer error dynamics, expressed in terms of probability of erasure, and positive Lyapunov exponents of the system. Positive Lyapunov exponents are a measure of average expansion of nearby trajectories on an attractor set for nonlinear systems. Hence, the dependence of limitation results on the Lyapunov exponents highlights the important role played by nonequilibrium dynamics on the attractor set in observation over an erasure channel. The limitation on observation is also related to measure-theoretic entropy of the system, which is another measure of dynamical complexity. The limitation result for the observation of linear systems is obtained as a special case, where Lyapunov exponents are shown to emerge as the natural generalization of eigenvalues from linear systems to nonlinear systems.

SUMMARY In this paper, we study the problem of control of discrete-time linear time varying systems over uncertain channels. The uncertainty in the channels is modeled as a stochastic random variable. We use exponential mean square stability of the closed-loop system as a stability criterion. We show that fundamental limitations arise for the mean square exponential stabilization for the closed-loop system expressed in terms of statistics of channel uncertainty and the positive Lyapunov exponent of the open-loop uncontrolled system. Our results generalize the existing results known in the case of linear time invariant systems, where Lyapunov exponents are shown to emerge as the generalization of eigenvalues from linear time invariant systems to linear time varying systems. Simulation results are presented to verify the main results of this paper. Copyright © 2012 John Wiley & Sons, Ltd.

There is increased research trend towards the use of Phasor Measurement Units (PMUs) for real-time stability monitoring and active feedback control of power system. In this paper, we address the problem of control of inter-area oscillations when the measurements from Phasor Measurement Units (PMUs) are corrupted with noise. Unlike existing results, we assume that the noise enters multiplicatively in system measurements. We provide systematic procedure based on the solution of Linear Matrix Inequalities (LMI) for the mean square stochastic stability verification of power system with measurement uncertainties. Furthermore, an optimization-based procedure is proposed for the synthesis of measurement-based feedback controller robust to wide area measurement noise. Finally, simulation results are provided to demonstrate the application of the developed framework on WSCC 9 bus system.

We study synchronization in scalar nonlinear systems connected over a linear network with stochastic uncertainty in their interactions. We provide a sufficient condition for the synchronization of such network systems expressed in terms of the parameters of the nonlinear scalar dynamics, the second and largest eigenvalues of the mean interconnection Laplacian, and the variance of the stochastic uncertainty. The sufficient condition is independent of network size thereby making it attractive for verification of synchronization in a large size network. The main contribution of this paper is to provide analytical characterization for the interplay of roles played by the internal dynamics of the nonlinear system, network topology, and uncertainty statistics in network synchronization. We show there exist important tradeoffs between these various network parameters necessary to achieve synchronization. We show for nearest neighbor networks with stochastic uncertainty in interactions there exists an optimal number of neighbors with maximum margin for synchronization. This proves in the presence of interaction uncertainty, too many connections among network components is just as harmful for synchronization as the lack of connection. We provide an analytical formula for the optimal gain required to achieve maximum synchronization margin thereby allowing us to compare various complex network topology for their synchronization property.

In this technical note, we study the mean square stability based analysis of stochastic continuous-time linear networked systems. The stochastic uncertainty is assumed to enter multiplicatively in system dynamics through input and output channels of the plant. Necessary and sufficient conditions for mean square exponential stability are expressed in terms of the input–output property of deterministic or nominal system dynamics captured by the mean square system norm and variance of channel uncertainty. The stability results can also be interpreted as a small-gain theorem for continuous-time stochastic systems. Linear matrix inequalities based optimization formulation is provided for the computation of mean square system norm for the stability analysis. For a special case of single-input channel uncertainty, we also prove a fundamental limitation result that arises in the mean square exponential stabilization of the continuous-time linear system. Overall, the contributions in this technical note generalize the existing results on stability analysis from discrete-time linear systems to continuous-time linear systems with multiplicative uncertainty. Simulation results are presented for Western System Coordinating Council 9-bus power system to demonstrate the application of the developed framework.

In this paper, we study the synchronization of identical nonlinear systems over large-scale network with uncertainty in the interconnections. We consider a special class of nonlinear systems which have a dissipative nonlinearity and the stability of such systems can be analyzed using absolute stability theory tools like the Positive Real Lemma, Bounded Real Lemma and dissipativity theory. We extend this analysis to the stochastic setting over a network where the interconnection weights are drive by Wiener process with given mean and variance. To capture the stability of the synchronized state, we study the notion of mean square stability from stochastic stability theory and formulate a network size-independent sufficient condition based on the theory of stochastic dissipative systems. We also compute a heuristic margin of synchronization for the networked systems to indicate the tolerance to stochastic uncertainty in interconnection links.

We study the problem of actuator and sensor placement in a linear advection partial differential equation (PDE). The problem is motivated by its application to actuator and sensor placement in building systems for the control and detection of a scalar quantity such as temperature and contaminants. We propose a gramian based approach to the problem of actuator and sensor placement. The special structure of the advection PDE is exploited to provide an explicit formula for the controllability and observability gramian in the form of a multiplication operator. The explicit formula for the gramian, as a function of actuator and sensor location, is used to provide test criteria for the suitability of a given sensor and actuator location. Furthermore, the solution obtained using gramian based criteria is interpreted in terms of the flow of the advective vector field. In particular, the almost everywhere stability property of the advective vector field is shown to play a crucial role in deciding the location of actuators and sensors. Simulation results are performed to support the main results of this paper.

In this paper, we study the stabilization problem of a scalar nonlinear system over a packet-drop channel. We consider moment stability notions adopted from the ergodic theory of dynamical systems. The main result of this paper proves that q -moment exponential stability requires a minimal quality of service from the communications link. The necessary conditions presented in the paper relate the positive Lyapunov exponent of the open loop system and the largest probability of erasure. For the first time, the dependence on the Lyapunov exponent highlights the important role played by the global non-equilibrium dynamics in nonlinear stabilization over networks.

In our recent work [1], we introduced Lyapunov measure as a new tool to verify weaker set-theoretic notion of almost everywhere stability of stochastic nonlinear systems. A Linear transfer Perron-Frobenius operator for stochastic systems was used to provide an explicit formula for the Lyapunov measure, verifying almost everywhere almost sure stability of stochastic systems. The focus of this paper is on the computational aspect of the Lyapunov measure for stochastic systems. We used set-oriented numerical methods for the finite dimensional approximation of the linear operator and the Lyapunov measure. Stability results in the finite dimensional approximation space are also presented. In particular, we show the finite dimensional approximation leads to a further weaker notion of stability referred to as coarse stability.

In this paper, we derive results for the stochastic stability analysis and controller synthesis for continuous-time stochastic system. The important feature considered here is the multiplicative nature of the stochastic uncertainty in system dynamics. We generalize the existing small-gain type results for stability of discrete-time system with stochastic uncertainty in feedback loop to continuous-time dynamics. Further, LMI-based computable necessary and sufficient conditions are provided for the mean square stability of feedback system. The proposed stability analysis results are used for the synthesis of dynamic robust stabilizing feedback controller with stochastic uncertainty in the feedback loop between the plant and the controller. Fundamental limitation result for the mean square stabilization of system over stochastic channels is presented. Finally, we demonstrate the proposed framework on pendulum on a cart system.

Online monitoring of rotor angle stability in wide area power systems is an important task to avoid out-of-step instability conditions. In recent years, the installation of phasor measurement units (PMUs) on the power grids has increased significantly and, therefore, a large amount of real-time data is available for online monitoring of system dynamics. This paper proposes a PMU-based application for online monitoring of rotor angle stability. A technique based on Lyapunov exponents is used to determine if a power swing leads to system instability. The relationship between rotor angle stability and maximal Lyapunov exponent (MLE) is established. A computational algorithm is developed for the calculation of MLE in an operational environment. The effectiveness of the monitoring scheme is illustrated with a three-machine system and a 200-bus system model.

This paper is concerned with computational methods for Lyapunov-based stabilization of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is used for these purposes. The paper poses and solves the co-design problem of jointly obtaining a control Lyapunov measure and a state feedback controller. The computational framework employs set-oriented numerical techniques. Using these techniques, the resulting co-design problem is shown to lead to a finite number of linear inequalities. These inequalities determine the feasible set of the solutions to the co-design problem. A particular solution can be efficiently obtained using methods of linear programming.

Extrauterine growth retardation is a major clinical problem in preterm infants. Aggressive nutritional interventions may play an important role to fight this prevalent problem. Parenteral nutrition is almost indispensable part of aggressive nutritional approach in neonates, because of certain limitations of enteral route during first few days of life. Formidable research work done in developed world has resolved certain important issues like dosage regimens. However, still we need to resolve quite a few unanswered queries. This is especially true for Indian context where we deal with a different population of neonates than the developed world. In this article we will discuss both the resolved and unresolved issues regarding neonatal parenteral nutrition and the research priorities for us.

Bubble continuous positive airway pressure (BCPAP) is a low-cost nasal CPAP delivery system with potential benefits for developing nations. The objective of the study was to compare the efficacy and safety of BCPAP with ventilator CPAP (VCPAP) in preterm neonates with moderate respiratory distress.In a pilot randomized controlled trial, 30 preterm neonates (gestation37 weeks) with Silverman-Anderson score between 5 to 7 and oxygen requirement30% within first 6 h of life were randomly allocated to BCPAP or VCPAP after informed parental consent. Proportion of neonates with success or failure, while using the allocated mode of CPAP delivery (primary outcome) was compared.The success rate was comparable [VCPAP: 80% (12/15) vs. BCPAP: 87% (13/15)] between the two groups. Dislodgement was commonest problem with equal frequency [10/15, (67%)] in each group.BCPAP appears to be a promising method of CPAP delivery in preterm neonates with moderate respiratory distress.

This paper is concerned with the analysis and computational methods for verifying global stability of an attractor set of a nonlinear dynamical system. Based upon a stochastic representation of deterministic dynamics, a Lyapunov measure is proposed for these purposes. This measure is shown to be a stochastic counterpart of stability (transience) just as an invariant measure is a counterpart of the attractor (recurrence). It is a dual of the Lyapunov function and is useful for the study of more general (weaker and set-wise) notions of stability. In addition to the theoretical framework, constructive methods for computing approximations to the Lyapunov measures are presented. These methods are based upon set-oriented numerical approaches. Several equivalent descriptions, including a series formula and a system of linear inequalities, are provided for computational purposes. These descriptions allow one to carry over the intuition from the linear case with stable equilibrium to nonlinear systems with globally stable attractor sets. Finally, in certain cases, the exact relationship between Lyapunov functions and Lyapunov measures is also given.

Motivated by the problem of microfluidic mixing, optimal control of advective mixing in Stokes fluid flows is considered. The velocity field is assumed to be induced by a finite set of spatially distributed force fields that can be modulated arbitrarily with time, and a passive material is advected by the flow. To quantify the degree of mixedness of a density field, we use a Sobolev space norm of negative index. We frame a finite-time optimal control problem for which we aim to find the modulation that achieves the best mixing for a fixed value of the action (the time integral of the kinetic energy of the fluid body) per unit mass. We derive the first-order necessary conditions for optimality that can be expressed as a two-point boundary value problem (TPBVP) and discuss some elementary properties that the optimal controls must satisfy. A conjugate gradient descent method is used to solve the optimal control problem and we present numerical results for two problems involving arrays of vortices. A comparison of the mixing performance shows that optimal aperiodic inputs give better results than sinusoidal inputs with the same energy.

Air quality has been an important issue in public health for many years. Sensing the level and distributions of impurities help in the control of building systems and mitigate long term health risks. Rapid detection of infectious diseases in large public areas like airports and train stations may help limit exposure and aid in reducing the spread of the disease. Complete coverage by sensors to account for any release scenario of chemical or biological warfare agents may provide the opportunity to develop isolation and evacuation plans that mitigate the impact of the attack. All these scenarios involve strategic placement of sensors to promptly detect and rapidly respond. This paper presents a data driven sensor placement algorithm based on a dynamical systems approach. The approach utilizes the finite dimensional Perron-Frobenius (PF) concept. The PF operator (or the Markov matrix) is used to construct an observability gramian that naturally incorporates sensor accuracy, location constraints, and sensing constraints. The algorithm determines the response times, sensor coverage maps, and the number of sensors needed. The utility of the procedure is illustrated using four examples: a literature example of the flow field inside an aircraft cabin and three air flow fields in different geometries. The effect of the constraints on the response times for different sensor placement scenarios is investigated. Knowledge of the response time and coverage of the multiple sensors aides in the design of mechanical systems and response mechanisms. The methodology provides a simple process for place sensors in a building, analyze the sensor coverage maps and response time necessary during extreme events, as well as evaluate indoor air quality. The theory established in this paper also allows for future work in topics related to construction of classical estimator problems for the sensors, real-time contaminant transport, and development of agent dispersion, contaminant isolation/removal, and evacuation strategies., Highlights • A robust sensor placement algorithm is developed that is capable of covering all possible release scenarios. • Placement algorithm includes constraints on sensing accuracy, placement constraints, and sensing constraints. • The algorithm provides sensor coverage maps, response times, and number of sensors for different scenarios. • Show applications involving indoor air quality, transmission of infectious diseases, and chemical and biological warfare.

Proportionate sharing of load changes in a microgrid without communication among the generators is a difficult problem. In this paper an exact power sharing algorithm is developed that uses an optimization-based technique to minimize the exchange of state information among the generators. To demonstrate the application of the developed framework we present simulation results for a system constructed using the data obtained from IEEE 14 bus system. Simulation results reveal that power sharing can be achieved using relatively few communication links among the generators.

In this paper, we present results for the vulnerability analysis of a power network to stochastic link failure attacks. We assume a network links are subjected to attacks where the link-based attack is modeled as stochastic perturbation to link weight. The objective is to determine which links in the network can tolerate the least amount of stochastic perturbation to maintain stochastic stability of a power network. We develop a system theoretical-based, analytical, and computation framework that allows us to rank links in the order of their critical importance to maintain stochastic stability of the network. The computational approach relies on solving a Linear Matrix Inequality (LMI). The developed framework is applied to a structure preserving model of the power network. The structure preserving model allows for the representation of original network topology, thereby identifying critical links connecting generators and load buses. Simulations are performed on IEEE 14 bus system to demonstrate the application of the developed framework.

We consider the problem of controllability degradation in dynamical networks subjected to malicious attacks. Attacks on the networks are assumed to be in the form of the removal of interconnection links. We formulate an optimization problem that seeks sets of links whose removal causes maximal degradation in the rank of the controllability gramian. We apply the alternating direction method of multipliers and sequential convex programming to find local solutions to this combinatorial optimization problem. We provide illustrative examples to demonstrate the utility of our results.

In this paper, we study controllability of two-dimensional integrable twist maps with bounded area-preserving time-dependent (control) perturbations. In contrast to the time-independent perturbation case of the Kolmogorov–Arnold–Moser theorem, there are no invariant sets other than the whole phase space if the perturbation is made a function of time. We give necessary and sufficient conditions for global controllability of these maps.

Active controllers that allow the compressor to operate safely at its peak pressure rise point by preventing surge and controlling entry into rotating stall need to be globally stabilizing. Bifurcation methods have emerged as a useful tool for the analysis of global stability and control of nonlinear dynamical systems such as the axial compressor. In this paper we show how bifurcation analysis can be used effectively to obtain answers to questions of global stability of the compressor dynamics. Since the bifurcation method does not directly provide information on transient behaviour, we demonstrate how bifurcation results need to be carefully interpreted to be of use when dealing with practical systems. We then present a novel nonlinear bifurcation-based stall/surge controller that is globally stabilizing. With such a controller, it becomes possible to avoid surge entirely and to prevent abrupt entry into rotating stall. The controller also eliminates the hysteresis between entry into and recovery from a rotating stall, and maintains system stability under all perturbations, small and large.

In this paper, we investigate the behaviour of networked systems under two different nonlinear protocols: 1) Pitchfork bifurcation nonlinearity in absolute flow 2) Hopf bifurcation nonlinearity in disagreement flow. The former one is an extension of the results proposed in [13] for the case when individual agents are free to choose a parameter that defines their own dynamics. Based on the eigenvalues of the linearized system, we characterize the set of equilibria that can be achieved under the above protocols. Furthermore, we provide sufficient conditions to achieve consensus for both protocols. Finally, we show that varying the values of the parameter leads to bifurcation for the entire network. For each protocol, we analyze system with two and three agents, and present a characterization of the steady-state behaviour of the entire system.

We study the vulnerability of large-scale linear dynamical networks to coordinated attacks. We consider scenarios in which an attacker can tamper with the links connecting the network components and can also manipulate input injections at the nodes. When these two types of attacks take place simultaneously, the attack is referred to as a coordinated attack. We assume that network links are attacked with a certain probability and that malicious data is injected at the input ports. We employ Markov jump linear systems to model link-based attacks and the system input matrix to model data injection attacks. System theoretic vulnerability metrics developed in earlier work are used to analyze network vulnerability to coordinated attacks. These measures of vulnerability allow us to characterize the impact of coordinated attacks and the difficulty associated with detecting them. Finally, we analyze the vulnerability of coordinated attacks on the New England 39 bus power network.

We develop a model-free approach for the short-term voltage stability monitoring of a power system. Finite time Lya-punov exponents are used as the certificate of stability. The time-series voltage data from phasor measurement units (PMU) are used to compute the Lyapunov exponent to predict voltage stability in real time. Issues related to practical implementation of the proposed method, such as phasor measurement noise, communication delay, and the finite window size for prediction, are also discussed. Furthermore, the stability certificate in the form of Lyapunov exponents is also used to determine the stability/instability contributions of the individual buses to the overall system stability and for computation of critical clearing time. Simulation results are provided for the IEEE 162-bus system to demonstrate the application of the developed method.

Aeroelastic flutter is a dynamic instability of fluid-structural system in which the structure exhibits a sustained, often diverging oscillation. Flutter behavior is self-feeding and destructive. Nonlinearities such as freeplay in rigid-body rotational stiffness of the structural system can have an effect on the onset of flutter and its amplitude. In particular there is experimental evidence that as the amount of freeplay increases, the freestream velocity at which the flutter instability occurs decreases. In this paper, we develop a modeling framework that allows us to predict this dependence of flutter velocity on the freeplay parameter. We model the airfoil system with freeplay nonlinearity as a feedback interconnection of linear system and sector bounded nonlinearity. Freeplay in stiffness is practically approximated as a hyperbola nonlinearity. Eigenvalue analysis at equilibrium points is used to predict onset of flutter and characterize a Hopf bifurcation of the system from stable to limit cycle behavior. Spectral analysis us used to characterize the limit cycle behavior. This analysis indicates the flutter onset velocity to be a function of freeplay region length. Follow-on research correlating recently obtained wind tunnel results to a three-dimensional extension of the model is outlined.

Existing sensing solutions facilitating continuous condition assessment of wind turbine blades are limited by a lack of scalability and clear link signal-to-prognosis. With recent advances in conducting polymers, it is now possible to deploy networks of thin film sensors over large areas, enabling low cost sensing of large-scale systems. Here, we propose to use a novel sensing skin consisting of a network of soft elastomeric capacitors (SECs). Each SEC acts as a surface strain gage transducing local strain into measurable changes in capacitance. Using surface strain data facilitates the extraction of physics-based features from the signals that can be used to conduct condition assessment. We investigate the performance of an SEC network at detecting damages. Diffusion maps are constructed from the time series data, and changes in point-wise diffusion distances evaluated to determine the presence of damage. Results are benchmarked against time-series data produced from off-the-shelf resistive strain gauges. This paper presents data from a preliminary study. Results show that the SECs are promising, but the capability to perform damage detection is currently reduced by the presence of parasitic noise in the signal.