Search

This paper is about the strong stabilization of small amplitude gravity water waves in a vertical rectangle. The control imposes the horizontal acceleration of the water along one vertical boundary segment, as a multiple of a scalar input function u, times a function h of the position along the active boundary. The state z of the system is a vector with two components: one is the water level ζ along the top boundary and the other is its time derivative ζ. We prove that for suitable functions h, there exists a bounded feedback functional F such that the feedback u = Fz leads to a strongly stable closed-loop system. Moreover, for initial states in the domain of the semigroup generator, the norm of the solution decays like (1 + t) − 1/6. Our approach uses careful estimates on certain partial Dirichlet to Neumann and Neumann to Neumann operators associated to the rectangular domain, as well as non-uniform stabilization results due to Chill, Paunonen, Seifert, Stahn and Tomilov (2019).

Virtual synchronous machines (VSM) are inverters that behave towards the power grid like synchronous generators. One popular way to realize such inverters are synchronverters, whose control algorithm has evolved over time, but both theoretical analysis and practical observations show that the output currents of a synchronverter are very sensitive to grid voltage measurement errors and processing delay, as well imprecisions in the PWM process. To overcome this problem (of excessive sensitivity), we propose in this paper to use a different type of control to realize a VSM, that includes a fast current controller as the internal control loop of the inverter. Our simulations and experiments show that this results in a dramatic reduction of the sensitivity of the VSM to various kinds of measurement errors, noise and imprecision, and hence to the proper operation of such inverters. In particular, it leads to a large reduction of the total harmonic distortion of the grid currents.

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.

This paper develops systematically the output feedback exponential stabilization for a one-dimensional unstable/anti-stable wave equation where the control boundary suffers from both internal nonlinear uncertainty and external disturbance. Using only two displacement signals, we propose a disturbance estimator that not only can estimate successfully the disturbance in the sense that the error is in L2(0, ∞) but also is free high-gain. With the estimated disturbance, we design a state observer that is exponentially convergent to the state of original system. An observer-based output feedback stabilizing control law is proposed. The disturbance is then canceled in the feedback loop by its approximated value. The closed-loop system is shown to be exponentially stable and it can be guaranteed that all internal signals are uniformly bounded.

We solve the output regulator problem for a system described by a Neumann boundary controlled anti-stable one-dimensional Schrodinger equation by the backstepping approach. The output to be controlled is not required to be measured and its observation operator is assumed to be admissible for a certain Co-semigroup that is related to the original system, while the measurements used for control are located at the boundary First we show that the open-loop system is well-posed. Then we find a state feedback control law to solve the output regulator problem by the backstepping method. We design a finite-dimensional reference observer and an infinite-dimensional disturbance observer. Based on this observer, we propose an output feedback controller to achieve output regulation.

We consider the mathematical model of a rigid ball moving in a viscous incompressible fluid occupying a bounded domain Ω, with an external force acting on the ball. We investigate in particular the case when the external force is what would be produced by a spring and a damper connecting the center of the ball h to a fixed point h 1 ∈ Ω . If the initial fluid velocity is sufficiently small, and the initial h is sufficiently close to h 1 , then we prove the existence and uniqueness of global (in time) solutions for the model. Moreover, in this case, we show that h converges to h 1 , and all the velocities (of the fluid and of the ball) converge to zero. Based on this result, we derive a control law that will bring the ball asymptotically to the desired position h 1 even if the initial value of h is far from h 1 , and the path leading to h 1 is winding and complicated. Now, the idea is to use the force as described above, with one end of the spring and damper at h , while other end is jumping between a finite number of points in Ω, that depend on h (a switching feedback law).

We revisit a by now well known stability result for power networks containing several synchronous generators, due to F. Dorfler and F. Bullo, SIAM Journal on Control and Optimization, 2012. The approximate (or reduced) model that we work with is called the network reduced power system (NRPS) model. The mentioned result from 2012 is that under certain conditions, the state trajectory of the NRPS model is close to the trajectory of the corresponding Kuramoto model (that is obtained by setting the inertias of the generators to zero), if both start from the same initial angles. The Kuramoto model is locally exponentially stable, so that this gives us useful indications on the behavior of the power network. We show that the mentioned result can be generalized and strengthened in several aspects. For instance, we show that the Kuramoto model has a unique asymptotically stable equilibrium point and we give an explicit characterization of its domain of attraction. We also characterize the region in the state space of the NRPS model where the asymptotic approximation by the state trajectories of the Kuramoto model is valid. We also significantly enlarge the class of NRPS models for which the result applies, and we prove the local exponential stability of the NRPS model for small enough inertia constants. We briefly indicate how this result can be useful for analyzing the stability of microgrids containing virtual synchronous machines.

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

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 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 Young men who have sex with men (YMSM) continue to be at elevated risk for substance use; however, models explaining this phenomenon have often focused on a limited array of explanatory constructs. This study examined the longitudinal relationship of contextual risk factors, social cognitive processes, mental health, and health protective behavior to identify key mechanisms of illicit drug use of YMSM as they aged through emerging adulthood. Methods Our sample included an ethnically diverse cohort of 487 YMSM recruited through venue based probability sampling in Los Angeles. We used latent growth curve modeling to understand relationships between environmental risk factors, changing individual and social process variables, health protective behavior, psychological distress, and illicit drug use outcomes among YMSM. Results Age, ethnicity, violence and discrimination, depression, and previous histories of illicit drug use were key elements of risk for future illicit drug use among YMSM. During this theoretically distinct time period, health as a value, self-efficacy, and social support are vital social cognitive processes for promoting self-change among YMSM, and YMSM have independent growth within each process. Health as a value, self-efficacy, and social support were dynamic social cognitive processes, which served as key mechanisms by which risk factors were converted into health promotion strategies or psychological distress, and ultimately illicit drug use. Conclusions The efficacy of prevention interventions aimed at reducing illicit drug use among YMSM can be enhanced by addressing social cognitive processes for this underserved portion of the male population.

We demonstrate that deterministic sea wave prediction (DSWP) combined with constrained optimal control can dramatically improve the efficiency of sea wave energy converters (WECs), while maintaining their safe operation. We focus on a point absorber WEC employing a hydraulic/electric power take-off system. Maximizing energy take-off while minimizing the risk of damage is formulated as an optimal control problem with a disturbance input (the sea elevation) and with both state and input constraints. This optimal control problem is non-convex, which prevents us from using quadratic programming algorithms for the optimal solution. We demonstrate that the optimum can be achieved by bang–bang control. This paves the way to adopt a dynamic programming (DP) algorithm to resolve the on-line optimization problem efficiently. Simulation results show that this approach is very effective, yielding at least a two-fold increase in energy output as compared with control schemes which do not exploit DSWP. This level of improvement is possible even using relatively low precision DSWP over short time horizons. A key finding is that only about 1 second of prediction horizon is required, however, the technical difficulties involved in obtaining good estimates necessitate a DSWP system capable of prediction over tens of seconds.

We study a time-varying well-posed system resulting from the additive perturbation of the generator of a time-invariant well-posed system. The associated generator family has the form A+G(t), where G(t) is a bounded operator on the state space and G(·) is strongly continuous. We show that the resulting time-varying system (the perturbed system) is well-posed and we investigate its properties. In the particular case when the unperturbed system is scattering passive, we derive an energy balance inequality for the perturbed system. If the operators G(t) are dissipative, then the perturbed system is again scattering passive. We illustrate this theory by using it to formulate the system corresponding to a conductor moving in an electromagnetic field described by Maxwell's equations.

Permanent magnet synchronous motors (PMSMs) are widely used as high-performance variable-speed drives. Ripple in the electric torque of such motors is often a source of vibration and tracking errors, especially at low speeds. In this paper we study the torque characteristics of PMSMs and propose a method to minimize the torque ripple. First, we establish a model for the motor to cover all dynamics without any assumptions on the signals. Next, we present a Fourier analysis of the torque ripple, caused by non-sinusoidal EMF and cogging torque. We propose a controller based on the internal model principle, and we prove the stability of the (non-linear) closed-loop, based on the passivity of the motor model. Finally, simulation results are given to verify the concept.

We consider coupled systems consisting of an infinite-dimensional part (a PDE system) and a finite-dimensional part (an ODE system) connected in feedback, such as for example the well-known SCOLE system (a beam with a rigid body attached at one end). The external world interacts with the coupled system via the finite-dimensional part, which receives the external input and sends out the output. The infinite-dimensional part is assumed to be a system node. Under several assumptions, we derive well-posedness and exact controllability results for such coupled systems. The first main result concerns the case when the input signal of the finite-dimensional part is the difference between the external input and the feedback signal. The second main result allows a more general structure for the finite-dimensional part. We also prove a result for the approximate controllability of the coupled system.

We examined the prevalence and patterns of alcohol use within a large, ethnically diverse sample of young men who have sex with men (YMSM) and identified psychosocial correlates of these alcohol-use patterns. A sample of 526 YMSM (ages 18-24 years) was recruited in Los Angeles, CA using a venue-based, stratified probability sampling design. Based on criteria used by previous research with young adults, participants were assigned to one of four alcohol-use/non-use groups according to frequency and number of drinks per sitting in the last 30 days. Findings revealed a high prevalence of alcohol use (91%) within the sample, with 21% reporting binge drinking; of binge drinkers, 40% reported frequent binge drinking. Multinomial logistic regression analyses revealed that race/ethnicity, gay bar attendance, depression, sensation seeking, peer risk behaviors, and age of alcohol initiation significantly differentiated between non-/light users from frequent and binge drinkers. Results also indicated unique psychosocial profiles among frequent/binge drinkers. The heterogeneity of predictors associated with different patterns of alcohol use highlights the need to consider unique risk profiles and alcohol-use trajectories according to exposure to different risk and protective factors.

Background In recent years, the World Health Organization in general, and Israel in particular, have dealt with mass casualty events (MCEs) resulting from terrorism. Children are the casualties in many of these events—a reality that forces hospitals to prepare to deal with such a scenario. A literature review designed to identify unique recommendations regarding pediatric MCEs highlights both a lack of existing training programs and uncertainty on the part of health care staff when dealing with these events. Objectives The purpose of the study was to examine the preparedness level of emergency department staff to deal with MCEs involving pediatric casualties. The study included 104 physicians and nurses working in, or responding to, the emergency department at a hospital in Israel. Method The study included a 41-item questionnaire examining perception, approaches, and staff knowledge regarding dealing with pediatric MCEs versus those involving adults. The reliability of all sections of the questionnaire ranged between Chronbach's α coefficient 0.6 α-0.94. Results The preparedness levels for MCEs involving children were found to be low. Study participants ranked the likelihood of a pediatric MCE lower than one involving adults, while ranking significantly higher ( P = .000) their ability to cope mentally and the knowledge and skills required when treating adults involved in MCEs. While nurses ranked higher than physicians regarding their knowledge and skills in dealing with pediatric MCE casualties, the level of knowledge for MCEs involving children was low in all subjects. Staff agreement for the parent of an MCE victim to be present during treatment was medium-low. Implications On the basis of these findings, additional research involving a larger number of individuals and hospitals is indicated to determine if these results are consistent throughout the region.

Purpose To describe the range of health and mental health problems for which young men who have sex with men (YMSM) may be at risk. Methods An audio-computer-assisted survey was administered to a large, ethnically diverse sample of 526 YMSM (aged 18–24 years) recruited from bars, clubs, and other social venues using a venue-based probability sampling method. Results Subjects reported a range of health and mental health problems, and involvement in health-compromising behaviors, such as overweight/obesity, depression, and suicidal thoughts/attempts, and many were found to have high rates of sexually transmitted infections. Moreover, many reported not having insurance coverage and/or limited access to care. Conclusions Many of the health concerns and risks reported by these young men are preventable and can be addressed by any number of sectors, including health care and social service providers, religious organizations, schools, and employers.

In this paper we solve the tracking and disturbance rejection problem for infinite-dimensional linear systems, with reference and disturbance signals that are finite superpositions of sinusoids. We explore two approaches, both based on the internal model principle. In the first approach, we use a low gain controller, and here our results are a partial extension of results by Hamalainen and Pohjolainen. In their papers, the plant is required to have an exponentially stable transfer function in the Callier-Desoer algebra, while in this paper we only require the plant to be well-posed and exponentially stable. These conditions are sufficiently unrestrictive to be verifiable for many partial differential equations in more than one space variable. Our second approach concerns the case when the second component of the plant transfer function (from control input to tracking error) is positive. In this case, we identify a very simple stabilizing controller which is again an internal model, but which does not require low gain. We apply our results to two problems involving systems modeled by partial differential equations: the problem of rejecting external noise in a model for structure/acoustics interactions, and a similar problem for two coupled beams.

We solve the quadratic optimal control problem on an infinite time interval for a class of linear systems whose state space is a Hilbert space and whose operator semigroup is unitary. The difficulty is that the systems in this class, having unbounded control and observation operators, may be ill-posed. We show that there is a surprisingly simple solution to the problem (the optimal feedback turns out to be output feedback). Our approach is to use a change of variables which transforms the system into a one which, according to recent research, is known to be conservative. We show that, under a mild assumption, the transfer function of this conservative system is inner, and then it follows that the optimal control of this conservative system is trivial. We give an example with the wave equation on an n-dimensional domain, with Neumann control and Dirichlet observation of the velocity.

We derive necessary conditions for exact controllability of infinite-dimensional systems described by x=Ax+Bu, where the generator A has a Riesz basis of eigenvectors and the input space is finite-dimensional. These conditions are in terms of the eigenvalues of A and the degree of unboundedness of B, but no further information about B is needed. Our results easily imply lack of exact controllability for a wide range of distributed parameter systems. It is known from partial differential equation (PDE) examples that the addition of damping into an exactly controllable second order system can destroy exact controllability. We discuss the effect of damping on such systems using our general conditions. We also give simple new proofs for results about the lack of exact controllability of hyperbolic systems in more than one space dimension.

In many engineering problems, periodic signals which should be either tracked (reference signals) or rejected (disturbances) occur. A successful way of solving such problems is repetitive control, a well-known technique based on the internal model principle. Here, we extend repetitive control theory to plants with several outputs, of which only some have to track reference signals. The other outputs are used to supply additional information to the controller. We analyze stability, robustness and give estimates of the size of the error in such a feedback system. Our approach to this analysis is new, based on the recent theory of regular linear systems. We introduce a correction to the amount of delay used in the internal model and this leads to a significant improvement in performance (i.e., to a smaller error).

Let X be a Hilbert space and let T = (T1),,, be a C, semigroup of linear operators on X, with generator A. The aim of this paper is to show how information about the behavior of T, for large t can be obtained from information about the behavior of the resolvent (slA)-’ for s with large imaginary part, and vice versa. In particular, the type of U can easily be determined if we know on which vertical lines in the complex plane the resolvent is bounded. We start by defining a sequence of numbers (oU,), which give information about the behavior of the semigroup for large t.

We characterize the admissible unbounded input elements for diagonal semigroups on l 2 . The result verifies the necessity of a condition whose sufficience was previously established by L.F. Ho and D.L. Russell.

THE NOISE GENERATED BY A STREAM OF TRAFFIC IS CONSIDERED USING AS A MODEL, A STREAM OF SIMPLE ACOUSTIC SOURCES. IN CONTRAST TO AN EARLIER ANALYSIS, THE POSSIBILITY OF A NEGATIVE EXPONENT HEADWAY DISTRIBUTION BETWEEN SUCCESSIVE CARS IS ALLOWED. THE MODEL IS SHOWN TO BE EQUIVALENT TO A SHOT PROCESS, AND THE CUMULANTS ARE READILY CALCULATED. IF TRAFFIC CONSISTS OF SEVERAL TYPES OF VEHICLES, EACH TYPE GENERATING NOISE OF A DIFFERENT INTENSITY, THEN IN THE LOW DENSITY REGIME THE TRAFFIC CAN BE REPRESENTED BY A SUPERPOSITION OF NONINTERACTING ACOUSTIC SOURCES. MODIFICATIONS OF THE SHOT NOISE MODEL CAN BE MADE TO TAKE INTO ACCOUNT SURFACE GRADIENTS OR SOUND-ABSORBING SURFACES BY A SUITABLE DISTRIBUTION OF ACOUSTIC SOURCES. /AUTHOR/

The general problem discussed is the optimal addition of an internal ring road to a circular city with a circumferential ring road. It is assumed that both the origins and destinations have circular symmetry, and that speed in any direction is a function of radial position only. Routes are chosen so as to minimize journey times. For plausible models of destination distributions and speed vs. radius relationship it is shown that optimal positioning of the internal ring road is insensitive to the ratio of speed at the city center to speed at a distance infinitely far from the city center. Furthermore, the benefit in improved journey time does not depend strongly on positioning of the internal ring road. /Author/