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We consider the output-feedback state consensus problem for a homogeneous multi-agent system consisting of one leader agent and $N$ follower agents. The dynamics of each of these agents is governed by a single-input single-output regular linear system (RLS), with the input to the leader agent being zero at all times. The transfer function of this RLS has all its poles in the closed left-half of the complex-plane, with only a finite number of them lying on the imaginary axis. Each follower agent can access the relative output of all its neighboring agents and some of the follower agents can access the relative output of the leader. The communication graph associated with the exchange of relative outputs is directed. Under this setting, we first establish that a controller solves the above leader-follower consensus problem if and only if it can simultaneously stabilize $N$ regular linear systems. We then adapt a recently developed frequency-domain technique to construct a stable finite-dimensional output-feedback controller which solves the simultaneous stabilization problem, and hence the consensus problem. We demonstrate the efficacy of our controller design technique using a numerical example.

One of the main issues related to integral control is windup, which occurs when, possibly due to a fault, the input signal u of the plant reaches a value outside the allowed input range U. This paper presents an integral controller with anti-windup, called saturating integrator, for a single-input single-output nonlinear plant having a curve of locally exponentially stable equilibrium points that correspond to constant inputs in U. A closed-loop system is formed by connecting the saturating integrator in feedback with the plant. The control objective is to make the output signal y of the plant track a constant reference r, while not allowing its input signal u to leave U. Using singular perturbation methods, we prove that, under reasonable assumptions, the equilibrium point of the closed-loop system is exponentially stable, with a “large” region of attraction. Moreover, when the state of the closed-loop system converges to this equilibrium point, then the tracking error tends to zero. A step-by-step procedure is presented to perform the closed-loop stability analysis, by finding separately a Lyapunov function for the reduced (slow) model and a Lyapunov function for the boundary-layer (fast) system. Afterwards, a Lyapunov function for the closed-loop system is built as a convex combination of the two previous ones, and an upper bound on the controller gain is found such that closed-loop stability is guaranteed. Finally, we show that if certain stronger conditions hold, then the domain of attraction of the stable equilibrium point of the closed-loop system can be made large by choosing a small controller gain.

A methodology for capturing resonance in a continuous-casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beams is proposed. The mechanism of the mold motion distortion generation in the mold oscillator is clearly delineated. Nontrivial damped natural frequency and resonance frequency calculations are carried out. Then, for a finite-difference analytical beam model approximation, a discovery of monotonic dependence on spatial approximation accuracy of the beam resonance frequency under the fixed mass and of the mass under the fixed resonance frequency is demonstrated numerically. Based on these findings, a novel beam parameters selection procedure for the precise attainment of the desired resonance and damped natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the beam model parameters to match the actual resonance frequencies exhibited by thin and thick slab casting mold oscillators at, respectively, the Nucor Decatur and the AK Steel Dearborn steel mills, is demonstrated. The resulting resonance frequency value for the latter is then used to guide the internal-model-principle-based controller design for resonance suppression in the software testbed for the AK Steel caster mold oscillator.

Self-supervised pretraining followed by supervised fine-tuning has seen success in image recognition, especially when labeled examples are scarce, but has received limited attention in medical image analysis. This paper studies the effectiveness of self-supervised learning as a pretraining strategy for medical image classification. We conduct experiments on two distinct tasks: dermatology skin condition classification from digital camera images and multi-label chest X-ray classification, and demonstrate that self-supervised learning on ImageNet, followed by additional self-supervised learning on unlabeled domain-specific medical images significantly improves the accuracy of medical image classifiers. We introduce a novel Multi-Instance Contrastive Learning (MICLe) method that uses multiple images of the underlying pathology per patient case, when available, to construct more informative positive pairs for self-supervised learning. Combining our contributions, we achieve an improvement of 6.7% in top-1 accuracy and an improvement of 1.1% in mean AUC on dermatology and chest X-ray classification respectively, outperforming strong supervised baselines pretrained on ImageNet. In addition, we show that big self-supervised models are robust to distribution shift and can learn efficiently with a small number of labeled medical images.

We consider the problem of stabilizing PDE-ODE cascade systems in which the input is applied to the PDE system whose output drives the ODE system. We also consider the dual problem of constructing an observer for ODE-PDE cascade systems in which the output of the ODE system drives the PDE system, whose output is measured. The PDE in these problems is stable and the ODE is unstable. While the ODE system models the plant in both the problems, the PDE system models the actuator in the stabilization problem and the sensor in the dual problem. In the literature, these problems have been solved for specific PDE models using the backstepping approach. In contrast, in the present work we consider these problems in an abstract framework by letting the PDE system be any regular linear system. Using a state transformation obtained by solving a Sylvester equation with unbounded operators, we first diagonalize the state operator corresponding to the cascade systems. We then solve the stabilization problem and the dual estimation problem, provided they are solvable, by solving certain finite-dimensional counterparts. We also derive necessary and sufficient conditions for verifying the solvability of these problems. We show that the controller which solves the stabilization problem is robust to certain unbounded perturbations. We illustrate our theory by designing a stabilizing controller for a PDE-ODE cascade in which the PDE is a 1D diffusion equation and an observer for a ODE-PDE cascade in which the PDE is a 1D wave equation., 26 pages, 3 figures, in review

We consider the following question: Given n distinct non-negative frequencies {ω 1 , ω 2 , ... ω n }, does there always exist a stable real nth-order transfer function (TF) with a desired phase at these frequencies? For n even, we prove that the answer is yes and propose a numerical algorithm for obtaining such TFs. For n > 1 odd, we conjecture that the answer is no. These results are useful for designing lower-order output feedback compensators that solve the multi-agent consensus problem for high-order linear agent dynamics.

Synchronverters are inverters that mimic the behavior of synchronous generators. In this paper, we propose five modifications to the synchronverter algorithm from the paper “Synchronverters: Inverters that mimic synchronous generators,” ( IEEE Trans. Ind. Electron. , vol. 58, no. 4, pp. 1259–1267, Apr. 2011), to improve its stability and performance. These modifications are implemented in software and do not require any changes in the inverter hardware. The first two modifications concern the control of the virtual field current in the synchronverter so that it is more robust to faults. We prove the stability of the grid-connected synchronverter with this improved field current controller. The third modification is to increase the effective size of the filter inductors virtually. This is motivated using results from the stability analysis of a constant field current synchronous generator connected to an ac power grid and also by practical considerations. Simulations and experiments show that this leads to a much better response to changes in grid frequency, voltage, or to imbalance in the grid. The fourth modification is to change the formula for the (virtual) nominal active mechanical torque to take into account the (virtual) losses in the output impedance of the converter. This makes the tracking of the desired active power much more accurate. The fifth modification is to introduce virtual capacitors in series with the inverter outputs to filter spurious dc components from the current supplied to the grid.

Background: A variety of techniques have been utilized to improve the accuracy of pedicle screw instrumentation. Recently, a novel handheld computerized drill system, IntelliSense Drill Technology, has been used in orthopedic trauma to improve drilling accuracy and reduce radiation and iatrogenic injury. The specialized drill technology detects changes in cortical density to prevent inadvertent cortical violation. The aim of this study is to assess the ability of this system to identify pedicle trajectories in the thoracic and lumbar spine compared to a standard freehand technique. Methods: Two spine surgeons, including 1 senior-level and 1 junior-level attending drilled pedicle screw tracts using a freehand technique and computerized drill technology in 4 cadaveric spines from T2 to S1. A total of 134 pedicle screws were placed, including 70 by the senior surgeon and 64 by the junior surgeon. Cortical violations were assessed using computed tomography after instrumenting each pedicle tract, and procedure time for insertion of pedicle screws was recorded. Results: A total of 15 (22.4%) and 12 (18.2%) pedicle violations were noted using the freehand and computerized drill technique, respectively (P = .767). Perforations using the computerized drill decreased from 31.1% in the first attempt to 5.9% in the second attempt (P = .027). Mean drill time per pedicle using the freehand and computerized drill techniques were comparable (12.2 ± 8.4 versus 12.1 ± 13.2, P = .871), and both surgeons had an improvement in procedure time using the computerized drill (surgeon 1: 12.3 ± 13.7–5.7 ± 3.8 [SD], P = .059; surgeon 2: 20.3 ± 20.0–10.4 ± 5.6 [SD], P = .063). Conclusions: We demonstrate the use of a novel drill technology for placement of pedicle screws in the thoracic and lumbar spine. After an initial learning curve, this technology is comparable to use of a freehand technique by both a senior-level and a junior-level attending surgeon in a cadaveric model. Further investigation is needed to identify the clinical role of this technology in spine surgery.

We investigate the exact controllability of a nonlinear plant described by the equation x˙(t)=Ax(t)+Bu(t)+BNN(x(t),t), where t ≥ 0. Here A is the infinitesimal generator of a strongly continuous group T on a Hilbert space X, B and BN, defined on Hilbert spaces U and UN, respectively, are admissible control operators for T and the function N:X×[0,∞)↦UN is continuous in t and Lipschitz in x, with Lipschitz constant LN independent of t. Thus, B and BN can be unbounded as operators from U and UN to X, in which case the nonlinear term BNN(x(t),t) in the plant is in general not Lipschitz in x. We assume that there exist linear operators F and Fb such that the triples (A,[BBN],F) and (-A,[BBN],Fb) are regular and A + BFΛ and −A + BFb, Λ are generators of operator semigroups Tf and Tb on X such that ∥Ttf∥·∥Ttb∥ decays to zero exponentially. We prove that if LN is sufficiently small, then the nonlinear plant is exactly controllable in some time τ > 0. Our proof is constructive, i.e. given an initial state ...

BACKGROUND Closed reduction of pediatric fractures is commonly performed by orthopaedic residents using conscious sedation in the emergency department (ED). The purpose of this study was to determine the rate of satisfactory reductions as performed by residents, and to determine the outcomes of these procedures. METHODS A retrospective review was performed of all fractures that underwent closed reduction under conscious sedation in the ED of a level 1 pediatric trauma center between January 1, 2010 and November 30, 2014. Initial and subsequent radiographs were reviewed and a determination was made as to whether the initial reduction was satisfactory, based on predetermined criteria for angulation and displacement. If a second reduction attempt in the operating room was necessary, this was noted. Chart notes were reviewed until a documented endpoint was reached, such as uneventful healing, malunion, nonunion, or growth arrest. RESULTS A total of 838 subjects were identified. The upper extremity was involved in 85% of the fractures. Of the initial 838 fracture reductions performed, 39 (4.7%) were unsatisfactory. Residents on their first pediatric orthopaedic rotation had a higher unsatisfactory reduction rate compared with more experienced residents (7.0% vs. 3.4%, P=0.01). A second reduction was performed for 94 of 749 (12.6%) fractures. Of these, 35 (37.2%) required an open procedure to accomplish a satisfactory reduction. Fractures with initially satisfactory reductions were significantly less likely to require a second reduction attempt than those with initially unsatisfactory reductions (9.2% vs. 80.0%, P

Design of reduced-order distributed controllers for solving the output feedback state consensus problem in a homogeneous multi-agent network is the topic of this paper. The dynamics of each agent in this network is governed by a marginally unstable single-input single-output linear system and each agent can access the relative output of its neighboring agents. Recognizing, possibly for the first time, the similarities between the feedback structures appearing in a well-known low-gain controller design approach for solving the consensus problem and the low-gain approach to the output regulation of stable linear plants, we propose a novel controller design technique for solving the consensus problem. Our technique is frequency-domain based, unlike most of the techniques in the literature which are state–space based. Combining our technique with a recent result on the existence of stable p th -order transfer functions with a desired phase at p given frequencies, we design controllers whose order is significantly lower than the order of the controllers proposed in the consensus literature. The techniques developed in this work can be applied equally to design reduced-order controllers for solving the aforementioned consensus problem in the presence of known, uniform and arbitrarily large communication and input delays in the network.

We study the global asymptotic behavior of a grid-connected constant field current synchronous generator (SG). The grid is regarded as an "infinite bus", i.e. a three-phase AC voltage source. The generator does not include any controller other than the frequency droop loop. This means that the mechanical torque applied to this generator is an affine function of its angular velocity. The negative slope of this function is the frequency droop constant. We derive sufficient conditions on the SG parameters under which there exist exactly two periodic state trajectories for the SG, one stable and another unstable, and for almost all initial states, the state trajectory of the SG converges to the stable periodic trajectory (all the angles are measured modulo $2\pi$). Along both periodic state trajectories, the angular velocity of the SG is equal to the grid frequency. Our sufficient conditions are easy to check computationally. An important tool in our analysis is an integro-differential equation called the {\em exact swing equation}, which resembles a forced pendulum equation and is equivalent to our fourth order model of the grid-connected SG. Apart from our objective of providing an analytical proof for a global asymptotic behavior observed in a classical dynamical system, a key motivation for this work is the development of synchronverters which are inverters that mimic the behavior of SGs. Understanding the global dynamics of SGs can guide the choice of synchronverter parameters and operation. As an application we find a set of stable nominal parameters for a 500 kW synchronverter., Comment: submitted in October 2015, waiting for reviews, 37 pages

Synchronverters are inverters that mimic the behavior of synchronous generators. In this paper, we propose modifications to the synchronverter algorithm to improve its stability and performance. The proposed modifications are implemented in software and do not require any changes in the inverter hardware. The first two modifications concern the control of the virtual field current in the synchronverter to make it more robust to faults. The next modification is to increase the effective size of the filter inductors virtually. This is well-motivated theoretically, using results from the stability analysis of synchronous generators connected to a AC power grid, and also by practical considerations: it dramatically improves the response of converter to an imbalance in the grid. This modification necessitates a change in the formula for the (virtual) nominal active mechanical torque. The third modification is to split the frequency droop loop into a low-pass and a high-pass branch, with a saturation on the low-pass branch, to ensure that the synchronverter is not required to supply or absorb active power exceeding physically possible values. We demonstrate the efficacy of our modifications using both simulations and experiments.

Consider a nonlinear distributed parameter system (DPS) described by ẋ (t) = Ax(t)+Bu(t)+B N N(x(t), t) for all t ≥ 0. Here A is the infinitesimal generator of a strongly continuous group of operators 𝕋 on a Hilbert space X, B and B N , defined on Hilbert spaces U and U N , respectively, are admissible control operators for 𝕋 and N : X × [0,∞) ↦ U N is continuous in t and Lipschitz in x, with Lipschitz constant L N independent of t. Thus B and B N can be unbounded as operators from U and U N to X, in which case the nonlinear term B N N(x(t), t) in the DPS is in general not a Lipschitz map from X ×[0,∞) to the state space X. Our goal is to find conditions under which this DPS is exactly controllable in some time τ, which means that for any initial state x(0) ∈ X, we can steer the final state x(τ) of the DPS to any chosen point in X by using an appropriate input function u ∈ L2([0, τ];U). We suppose that there exist linear operators F and F b such that (A, [B B N ], F) and (−A; [B B N ], F b ) are regular triples and A + BF Λ and −A + BF b,Λ are generators of strongly continuous semigroups 𝕋f and 𝕋b on X such that ∥𝕋 t f∥ · ∥𝕋 t b∥ decays to zero exponentially. We prove that if L N is sufficiently small, then the nonlinear DPS is exactly controllable in some time τ > 0. Our proof is constructive and provides a numerical algorithm for approximating the required control signal. We illustrate our approach using a simple example.

This paper is about the state feedback regulator problem for infinite-dimensional linear systems. The plant, assumed to be an exponentially stable regular linear system, is driven by a linear (possibly infinite-dimensional) exosystem via a disturbance signal. The exosystem has its spectrum in the closed right half-plane and also generates the reference signal for the plant output. The regulator problem is to design a controller that, while guaranteeing the stability of the closed-loop system without the exosystem, drives the tracking error to zero. A particular version of this problem is the state feedback regulator problem in which the states of the exosystem and the plant are known to the controller. Under suitable assumptions, we show that the latter problem is solvable if and only if a pair of algebraic equations, called the regulator equations, is solvable. We derive conditions, in terms of the transfer function of the plant and eigenvalues of the exosystem, for the solvability of the regulator equations. Three examples illustrating the theory are presented.

Adaptive observers using projection-operator-based parameter update laws are considered for a class of linear infinite-dimensional systems with bounded input operator and full state measurement and subject to time-varying matched uncertainties and disturbances. The L1 adaptive control architecture, introduced recently for finite-dimensional plants to provide guaranteed transient performance via fast adaptation, is then extended to this class using the proposed observers. Existence and uniqueness of solutions for the resulting closed loop system and uniform boundedness of the observation error are established first. Then, provided certain assumptions on the plant transfer function and the solution of a Lyapunov inequality hold, uniform guaranteed transient performance bounds on the plant state and control signal under the L1 architecture are derived. Two examples satisfying the assumptions-control of a heat equation and a wave equation-are presented. Reference input tracking simulation results for the heat equation under the L1 adaptive control subject to time-varying matched uncertainties and disturbances are presented in support of the theory.

We investigate the state feedback regulator problem for exponentially stable plants belonging to the class of regular linear systems. The plant is driven by a linear completely unstable exosystem via a disturbance signal. The exosystem also generates the reference signal for the plant output. The state feedback regulator problem is to design a controller that has access to the states of the exosystem and the plant and which, while guaranteeing the stability of the closed-loop system without the exosystem, drives the tracking error to zero. We show that, under suitable assumptions, this problem is solvable if and only if a pair of algebraic equations, called the regulator equations, is solvable. We present an example that illustrates our theory.

This paper is about the nonlinear local error feedback regulator problem. The plant is a nonlinear finite-dimensional system with a single control input and a single output and it is locally exponentially stable around the origin. The plant is driven, via a separate disturbance input, by a Lyapunov stable exosystem whose states are nonwandering. The reference signal that the plant output must track is a nonlinear function of the exosystem state. The local error feedback regulator problem is to design a dynamic feedback controller, with the tracking error as its input, such that (i) the closed-loop system of the plant and the controller is locally exponentially stable, and (ii) the tracking error tends to zero for all sufficiently small initial conditions of the plant, the controller and the exosystem. Under the assumption that the above regulator problem is solvable, we propose a nonlinear controller whose order is relatively small - typically equal to the order of the exosystem, and which solves the regulator problem. The emphasis is on the low order of the controller. The stability assumption on the plant (which can be relaxed to some extent) is crucial for making it possible to design a low order controller. We will show, under certain assumptions, that our proposed controller is of minimal order. Three examples are presented - the first illustrates our controller design procedure using an exosystem whose trajectories are periodic even though the state operator of the linearized exosystem contains a nontrivial Jordan block. The second example is more involved, and shows that sometimes a nontrivial immersion of the exosystem is needed in the design. The third example, based on output voltage regulation for a boost power converter, shows how the regulator equations may reduce to a first order PDE with no given boundary conditions, but which nevertheless has a locally unique solution., Comment: 33 pages, 6 figures

This paper considers a nonlinear infinite-dimensional system Σ N obtained by the feedback interconnection of a well-posed linear system Σ P with a globally Lipschitz (memoryless) nonlinear feedback operator N. First, under mild assumptions, we establish the global existence and uniqueness of a state trajectory and an output function for Σ N , for any initial state in its state space X and any input signal of class. Then we investigate the behavior of Σ N when it is driven by a nonlinear time-invariant exosystem with well defined dynamics forward and backward in time. Under the assumption that Σ P is exponentially stable, denoting the state space of the exosystem by W , we find that there exists a continuous map Π : W → X such that regardless of initial states lim t →∞ ‖Π w (t) – x ( t )‖ = 0, where w ( t ) is the state of the exosystem and x ( t ) is the state of Σ N. In particular, when w is T -periodic, then the state of the interconnection tends to a T -periodic limit cycle. The construction of Π can be viewed as an extension of the famous center manifold theorem, which lies at the basis of nonlinear regulator theory, to a class of infinite-dimensional systems.

BACKGROUND The Joint Commission on Accreditation of Healthcare Organizations specifically mandates the dual interpretation of musculoskeletal radiographs by a radiologist in addition to the orthopaedist in all hospital-based orthopaedic clinics. Previous studies have questioned the utility of this practice. The purpose of this study was to further investigate the clinical significance of having the radiologist provide a second interpretation in a hospital-based pediatric orthopaedic clinic. METHODS A retrospective review was performed of all patients who had plain radiographs obtained in the pediatric orthopaedic clinic at an academic children's hospital over a 4-month period. For each radiographic series, the orthopaedist's note and the radiology interpretation were reviewed and a determination was made of whether the radiology read provided new clinically useful information and/or a new diagnosis, whether it recommended further imaging, or if it missed a diagnosis that was reflected in the orthopaedist's note. The hospital charges associated with the radiology read for each study were also quantified. RESULTS The charts of 1570 consecutive clinic patients who were seen in the pediatric orthopaedic clinic from January to April, 2012 were reviewed. There were 2509 radiographic studies performed, of which 2264 had both a documented orthopaedist's note and radiologist's read. The radiologist's interpretation added new, clinically important information in 1.0% (23/2264) of these studies. In 1.7% (38/2264) of the studies, it was determined that the radiologist missed the diagnosis or clinically important information that could affect treatment. The total amount of the professional fees charged for the radiologists' interpretations was $87,362. On average, the hospital charges for each occurrence in which the radiologist's read provided an additional diagnosis or clinically important information beyond the orthopaedist's note were $3798. CONCLUSIONS The results of this study suggest that eliminating the requirement to have the radiologist interpret radiographs in the pediatric orthopaedic clinic would have few clinical consequences. LEVEL OF EVIDENCE Level III-This is a diagnostic retrospective cohort study.

PI controllers are the most widespread type of controllers and there is an intuitive understanding that if their gains are sufficiently small and of the correct sign, then they always work. In this paper we try to give some rigorous backing to this claim, under specific assumptions. Let $\bf P$ be a nonlinear system described by $\dot x=f(x,u)$, $y=g(x)$, where the state trajectory $x$ takes values in $R^n$, $u$ and $y$ are scalar and $f,g$ are of class $C^1$. We assume that there is a Lipschitz function $��:[u_{min},u_{max}]\rightarrow R^n$ such that for every constant input $u_0\in[u_{min},u_{max}]$, $��(u_0)$ is an exponentially stable equilibrium point of $\bf P$. We also assume that $G(u)=g(��(u))$, which is the steady state input-output map of $\bf P$, is strictly increasing. Denoting $y_{min}=G(u_{min})$ and $y_{max}=G(u_{max})$, we assume that the reference value $r$ is in $(y_{min},y_{max})$. Our aim is that $y$ should track $r$, i.e., $y\rightarrow r$ as $t\rightarrow\infty$, while the input of $P$ is only allowed to be in $[u_{min},u_{max}]$. For this, we introduce a variation of the integrator, called the saturating integrator, and connect it in feedback with $\bf P$ in the standard way, with gain $k>0$. We show that for any small enough $k$, the closed-loop system is (locally) exponentially stable around an equilibrium point $(Xi(u_r),u_r)$, with a large region of attraction $X_T\subset R^n\times[u_{min},u_{max}]$. When the state $(x(t),u(t))$ of the closed-loop system converges to $(��(u_r),u_r)$, then the tracking error $r-y$ tends to zero. The compact set $X_T$ can be made larger by choosing a larger parameter $T>0$, resulting in smaller $k$., submitted in July 2016, 8 pages in IEEE 2-column format

Output regulation for a class of nonlinear infinite-dimensional systems, called regular nonlinear systems (RNS), is the subject of this work. For the plants in this class, the linearization at the origin is an exponentially stable regular linear system (RLS). The plants are driven by a control input and a disturbance signal. Well-posedness of the plants for small initial states, control inputs and disturbance signals is established and it is shown that if the control input and the disturbance signal for a plant are T-periodic, then so are its state and output (asymptotically). On the basis of this characterization, an approximate local output regulator problem for multi-input multi-output (MIMO) plants in the RNS class is addressed. Given a plant, the regulation objective is to ensure that a finite number of harmonics of a T-periodic reference signal and the plant output are identical whenever the reference signal, the T-periodic disturbance signal for this plant and the initial state are small. An internal model based output feedback control scheme is proposed for an exponentially stable RLS for tracking reference signals, which are a finite sum of functions that are a product of a sinusoid and a polynomial in time. This scheme merely uses the transfer function gains of the RLS at the poles of the Laplace transform of the reference signal and practically requires no other data. Using the proposed control scheme, a linear finite-dimensional controller is designed for a MIMO nonlinear plant in the RNS class using minimal plant information. The resulting closed-loop system is rigorously analyzed to establish that the controller achieves the regulation objective. The efficacy of the control design is illustrated numerically using the model of a cable coupled to a point mass via a nonlinear spring.

Disturbance is a pervasive source of uncertainty in most applications. This paper presents model reference adaptive control (MRAC) laws for uncertain multiagent networks with a disturbance rejection capability. The algorithms proposed can also be viewed as the extension of the robust model reference adaptive control (MRAC) laws with disturbance rejection recently derived for systems described by parabolic and hyperbolic partial differential equations (PDEs) with spatially-varying parameters under distributed sensing and actuation to heterogeneous multiagent networks characterized by parameter uncertainty. The latter extension is carried out using partial difference equations (PdEs) on graphs that preserve parabolic and hyperbolic like cumulative network behavior. Unlike in the PDE case, only boundary input is specified for the reference model. The algorithms proposed directly incorporate this boundary reference input into the reference PdE to generate the distributed admissible reference evolution profile followed by the agents. The agent evolution thus depends only on the interaction with the adjacent agents, making the system fully decentralized. Numerical examples are presented as well. The resulting PdE MRAC laws inherit the robust linear structure of their PDE counterparts.

In a recent work, the authors presented an extension of robust model reference adaptive control (MRAC) laws for spatially varying partial differential equations (PDEs) proposed by them earlier for the decentralized adaptive control of heterogeneous multiagent networks with agent parameter uncertainty using the partial difference equations (PdEs) on graphs framework. The examples provided demonstrated the capabilities of this approach under the assumption that individual vehicles executing coordinated maneuvers were fully actuated and characterized by linear dynamics. However, detailed models for autonomous vehicles–whether terrestrial, aerial, or aquatic–are often underactuated and strongly nonlinear. Using this approach, but assuming the plant parameters to be known, this work presents the model reference (MR) control laws without adaptation for the coordination of underactuated aquatic vehicles modeled individually in terms of strongly nonlinear dynamic equations arising from ideal planar hydrodynamics. The case of unknown plant parameters for this class of underactuated agents with complex dynamics is an open problem. The paper is based on an invited talk on adaptive control presented at the 2008 World Congress of Nonlinear Analysts.

We reviewed the effects of obesity and long-term weight loss on nononcological urological disease, particularly urinary stone formation, erectile dysfunction, female sexual dysfunction, voiding dysfunction and urinary incontinence.A literature search was conducted using Ovid's MEDLINE, accessed through Emory University's Health Sciences Library web site. The subject headings obesity, weight loss surgery, urolithiasis, sexual dysfunction, erectile dysfunction, benign prostatic hyperplasia and urinary incontinence were used as indices for the search. Articles published earlier than 10 years before the literature review (performed in summer of 2007) were not used.There is ample evidence to support an increased risk of urolithiasis in obese patients. However, the effects of long-term weight loss on urinary stone formation have not been studied as extensively in the literature. It is unclear whether the decreased food intake after surgical weight loss procedures may negate the associated risk of malabsorption and decrease the risk of urolithiasis in the long term. The incidence and severity of erectile dysfunction in men increase with obesity. Female sexual dysfunction also appears to be positively correlated with obesity, although the literature is less clear as to the extent to which this is true. Despite a scarcity of relevant data, preliminary evidence indicates that weight loss improves sexual function in men and women. Obesity is associated with an increased incidence of benign prostatic hyperplasia and subsequent lower urinary tract symptoms in men, as well as an increased incidence of stress urinary incontinence in women. Despite a lack of relevant data, there is preliminary evidence that stress urinary incontinence and benign prostatic hyperplasia may be reversible after weight loss.Despite the abundant evidence that indicates a correlation between obesity and several urological diseases, there is a paucity of data regarding the effects of long-term weight loss on these conditions. However, the preliminary data indicate that the detrimental effects of obesity are reversible, and that long-term weight loss may decrease the incidence and severity of urological disease. Therefore, further research is needed to elucidate the impact of long-term surgical and medical weight loss on urolithiasis, lower urinary tract symptoms and incontinence, and sexual dysfunction.

Robust globally stable model reference adaptive control (MRAC) laws recently derived for systems described by parabolic and hyperbolic partial differential equations (PDEs) with spatially-varying coefficients under distributed sensing and actuation are extended to heterogeneous multiagent networks characterized by parameter uncertainty. The extension is carried out using partial difference equations (PdEs) on graphs that preserve parabolic- and hyperbolic-like cumulative network behavior. Unlike in the PDE case, only boundary input is specified for the reference model. The algorithms proposed directly incorporate this boundary reference input into the reference PdE to generate the distributed admissible reference evolution profile followed by the agents. The agent evolution thus depends only on the interaction with the adjacent agents, making the system fully decentralized. Numerical examples are presented as well, including the case of the switched topology associated with a sudden loss of an agent. The resulting PdE MRAC laws inherit the robust linear structure of their PDE counterparts.

A methodology for development of high fidelity control-oriented continuous casting mold oscillator software testbed incorporating two coupled hydraulically actuated Timoshenko beam models is proposed. Nontrivial damped natural frequency calculation is carried out. For a finite-difference approximation of analytical model, monotonic dependence on spatial approximation accuracy of the resonance frequency under the fixed mass and of the mass under the fixed resonance frequency is discovered. Based on these findings, a novel beam parameter selection procedure for precise attainment of the desired resonance and damped natural frequencies by analytical and numerical models under the relevant boundary conditions and runtime constraints is developed. Using this procedure, fitting of the model parameters to resonance frequencies exhibited by thin and thick slab casting mold oscillators at the Nucor Decatur and Severstal Dearborn steel mills, respectively, is demonstrated. Assessment of controller efficacy in suppression of the undesirable oscillations in the software testbed fitted to Severstal caster is shown.

The importance of pushing the performance envelope of disk drives continues to grow, not just in the server market but also in numerous consumer electronics products. One of the most fundamental factors impacting disk drive design is the heat dissipation and its effect on drive reliability, since high temperatures can cause off-track errors, or even head crashes. Until now, drive manufacturers have continued to meet the 40% annual growth target of the internal data rates (IDR) by increasing RPMs, and shrinking platter sizes, both of which have counter-acting effects on the heat dissipation within a drive. As this paper will show, we are getting to a point where it is becoming very difficult to stay on this roadmap. This paper presents an integrated disk drive model that captures the close relationships between capacity, performance and thermal characteristics over time. Using this model, we quantify the drop off in IDR growth rates over the next decade if we are to adhere to the thermal envelope of drive design.We present two mechanisms for buying back some of this IDR loss with Dynamic Thermal Management (DTM). The first DTM technique exploits any available thermal slack, between what the drive was intended to support and the currently lower operating temperature, to ramp up the RPM. The second DTM technique assumes that the drive is only designed for average case behavior, thus allowing higher RPMs than the thermal envelope, and employs dynamic throttling of disk drive activities to remain within this envelope.

We derive conditions for the almost global asymptotic stability of a system, modeling a constant rotor current synchronous generator connected to an infinite bus, in terms of the system parameters.

This paper is about the nonlinear error feedback regulator problem. The plant is a nonlinear finite-dimensional single-input-single-output system and it is locally exponentially stable around the origin. It is driven by a linear exosystem with simple eigenvalues on the imaginary axis. The reference signal that the plant output must track is obtained from the state of the exosystem, in a nonlinear way. The regulator problem is to design a dynamic feedback controller, with the tracking error as its input and the control input to the plant as its output, such that (i) the closed-loop system of the plant and the controller is locally exponentially stable and (ii) the tracking error tends to zero for all sufficiently small initial conditions of the plant, the controller and the exosystem. Under the assumption that the regulator problem is solvable, i.e., there exists a solution to the so-called nonlinear regulator equations, we propose a nonlinear controller of order equal to that of the exosystem to solve the regulator problem. In contrast, previous results on the regulator problem have typically proposed controllers of a larger order. The motivation for the nonlinear controller designed in this work is the structure of a linear controller that solves the regulator problem for the plant linearized around the origin, when the reference and disturbance signals are linear functions of the exosystem state. The nonlinear controller has the same state and control operators as the linear controller and the linearization of its (possibly nonlinear) observation operator is the observation operator of the linear controller. An example and a counterexample illustrating the theory are presented.

We design an error feedback controller using the regulator theory for stabilizing a boost converter, subject to disturbances, around a desired equilibrium point. The input voltage to the converter is a constant whose nominal value is known; but its actual value is not known. The difference between the nominal and actual values of the input voltage is modeled as a constant unknown disturbance. In addition, the converter is also subject to a sinusoidal disturbance current. According to the regulator theory, we derive the nonlinear regulator equations for our model of the converter. We show that these equations reduce to an equivalent first order quasilinear PDE without boundary conditions, which nevertheless has a locally unique solution. We solve this PDE via a semi-analytic approach. Finally, following a recently proposed technique for designing minimal order controllers using the solution to the regulator equations, we design an error feedback controller that stabilizes the boost converter. Simulation results demonstrating the efficacy of our approach are presented. A key contribution of this work is the solution of the regulator equations for the boost converter, which provides insights into the nature of such equations.

We consider a grid connected synchronous generator (SG), having a constant field current and driven by a prime mover with constant torque. The grid is regarded as an “infinite bus”, i.e., a three-phase AC voltage source. The problem of interest is verifying if, for a given set of SG parameters, the angular velocity of the SG rotor converges to the angular velocity of the grid, irrespectively of the SG initial conditions. We pose this problem as a question of almost global asymptotic stability of a fourth order nonlinear system. In a recent work, we derived an integro-differential equation, which resembles the forced pendulum equation, and showed that the fourth order system is almost globally asymptotically stable if and only if the same holds for this equation. In this paper, it is shown that this equation is almost globally asymptotically stable if a real-valued nonlinear map defined on a finite interval is a contraction. For any given set of SG parameters, it is straight forward to check numerically if this map is a contraction. An example demonstrating our results is included.

We consider the control system x=Ax+Bu, where A generates a strongly continuous semigroup T on the Hilbert space X and the control operator B maps into the dual of D(A*), but it is not necessarily admissible for T. We prove that if the pair (A;B) is both forward and backward optimizable (our definition of this concept is slightly more general than the one in the literature), then the system is exactly controllable. This is a generalization of a well-known result called Russell's principle. Moreover the usual stabilization by state feedback u = Fx, where F is an admissible observation operator for the closed-loop semigroup, can be replaced with a more complicated periodic (but still linear) controller. The period τ of the controller has to be chosen large enough to satisfy an estimate. This controller can improve the exponential decay rate of the system to any desired value, including -∞ (dead-beat control). The corresponding control signal u, generated by alternately solving two exponentially stable homogeneous evolution equations on each interval of length τ, back and forth in time, will still be in L2. The better the decay rate that we want to achieve, the more iterations the controller needs to perform, but (unless we want to achieve -∞) the number of iterations needed on each period is finite.

Adaptive observers with projection operator based parameter update laws are considered for a class of linear infinite dimensional systems with bounded input operator and full state measurement under constant and time-varying matched uncertainties. The L 1 adaptive control architecture, introduced recently for finite dimensional plants to provide guaranteed transient performance via fast adaptation, is then extended to this class. Existence and uniqueness of solution to the closed loop system and asymptotic decay of the observation error are established. Under certain assumptions on the transfer function and on the solution to the Lyapunov inequality, the L 1 architecture is analyzed and uniform bounds on the state and control signal are established. Two examples, a heat equation and a wave equation, satisfying the assumptions are presented.

Cooperation between nodes is essential for the functionality of a mobile ad-hoc network (MANET). However, since the nodes in a MANET are generally resource limited, some nodes could refuse service to other nodes to conserve their resources, thereby exhibiting selfish behavior. Also, since a MANET is often deployed in uncontrolled environments, some nodes could be compromised by an adversary and directed to act maliciously. A trust management framework in a MANETis useful to infer if nodes behave in a selfish or malicious manner, so that appropriate action could be taken, in order to maximize network performance. In this paper, we propose a scalable trust management scheme to partition and store an information network of trust metadata of nodes in a MANET. The simplicity of our scheme for trust metadata propagation and retrieval and its robustness to node failures, membership changes and mobility, make it a promising choice for trust management in a MANET. Simulation results that evaluate our scheme based on the trust management metrics we have defined demonstrate its performance benefits.

A trust management framework is useful to ensure proper functioning of a mobile ad-hoc network (MANET). Trust metadata created by individual nodes, based on their observation of the behavior of other nodes in their vicinity, is required to be accessible to a trust authority (TA) (e.g., the network administrator) for prompt decision making (e.g., revoking malicious nodes). In this work, for security and scalability reasons, we propose a secure semantics-aware trust metadata management scheme to partition and store an information network of trust metadata of nodes in a MANET. That is, trust metadata is securely propagated to and stored at certain geographic locations inside the network itself, based on its semantics. The TA can send queries of various types in the network to obtain the trust metadata of its interest. This scheme is robust to several security attacks that attempt to disrupt the availability of trust metadata in the network. Our analysis shows that the proposed scheme provides desirable security and functionality properties with low query overhead.

An application-motivated system class - nonlinearly perturbed regular linear systems (NPRLS) - is considered, and the response of the latter to periodic inputs is characterized. A recently proposed robust control scheme for tracking bandlimited periodic signals by uncertain exponentially stable regular linear systems (RLS) is then applied to an uncertain system belonging to the NPRLS class, whose linearization is an exponentially stable RLS, to reject internally generated sinusoids from the system output. Assuming the uncertain NPRLS to be unknown, but its gain at the frequency of interest known and bounded away from zero, and using the aforementioned characterization, the stability and disturbance rejection of the resulting topology are shown to be guaranteed for sufficiently small nonlinearity.

In a Delay-Tolerant Network (DTN), data originating from a source node may be delivered to the destination node, despite the non-existence of end-to-end connectivity between them at all times. In an adversarial environment such as a battlefield, DTN nodes could be compromised to launch Denial-of-Service (DoS) attacks by generating excess data, to cause an overflow of the limited resources of the legitimate nodes, hence decreasing the network throughput. A node may also display selfish behavior by generating more data than allowed, to increase its throughput and to decrease the latency of its data packets. In this paper, we term such a DoS attack and selfish data generation behavior, a resource-misuse attack. We study two types of resource-misuse attacks, breadth attacks and depth attacks. Accordingly, we propose different schemes to detect these attacks. Trace-driven simulations using both a synthetic and a real-world trace show that our detection schemes have low average detection latency and additionally, probabilistic detection of the depth attack has low false positive and false negative rates.

Assuming no knowledge of closed-loop dynamics other than being that of a stable nonlinearly perturbed linear system and the forward path gain at the frequency of interest being known and non-zero, a control approach is proposed that rejects a sinusoidal disturbance of known frequency from the system output. The approach consists in partitioning the feedback path of a stable closed-loop system into two weighted paths and inserting between them a loop containing an internal model based filter. The approach is supported by two theorems ascertaining internal stability, that guarantee the rejection of the unwanted sinusoid under the augmentation proposed, with no closed-loop stability loss. The efficacy of the approach is demonstrated through simulations on a model of a servo system consisting of a beam with an electro-hydraulic actuator attached at one end and a mass at the other, and through experiments on the corresponding physical testbed. Robustness of the approach is briefly discussed. A relative non-intrusiveness of the augmentation procedure, a virtual lack of a modeling necessity, and simplicity of estimating the unaugmented forward path gain via experiment on the stable closed-loop system make the approach proposed well suited for industrial use.

A robust control scheme for tracking of periodic signals, consisting of a finite number of sinusoids, by uncertain exponentially stable infinite dimensional linear systems is presented. The scheme consists in constructing a cascade interconnection of the stable linear system and a partitioning filter and augmenting this cascade system with a simple internal model based filter. The stable system model is presumed to be unknown, but its transfer function gain at the frequencies to be tracked is assumed to be known and non-zero. A theorem guaranteeing the robust stability and performance of this scheme while tracking a sinusoidal reference is proved. The general theorem for tracking periodic signals is stated and can be established analogously. A discussion on quantitatively estimating the robustness of this scheme is presented. The efficacy of the scheme is demonstrated via simulation of an example. The simplicity of the proposed scheme, its quantitatively ascertainable robustness and a virtual lack of modeling requirements make it well suited for industrial applications.