A new approach for modeling and control of nonlinear systems via norm-bounded linear differential inclusions

A systematic approach to model nonlinear systems using norm-bounded linear differential inclusions (NLDIs) is proposed in this paper. The resulting NLDI model is suitable for the application of linear control design techniques and, therefore, it is possible to fulfill certain specifications for the underlying nonlinear system, within an operating region of interest in the state-space, using a linear controller designed for this NLDI model. Hence, a procedure to design a dynamic output feedback controller for the NLDI model is also proposed in this paper. One of the main contributions of the proposed modeling and control approach is the use of the mean-value theorem to represent the nonlinear system by a linear parameter-varying model, which is then mapped into a polytopic linear differential inclusion (PLDI) within the region of interest. To avoid the combinatorial problem that is inherent of polytopic models for medium- and large-sized systems, the PLDI is transformed into an NLDI, and the whole process is carried out ensuring that all trajectories of the underlying nonlinear system are also trajectories of the resulting NLDI within the operating region of interest. Furthermore, it is also possible to choose a particular structure for the NLDI parameters to reduce the conservatism in the representation of the nonlinear system by the NLDI model, and this feature is also one important contribution of this paper. Once the NLDI representation of the nonlinear system is obtained, the paper proposes the application of a linear control design method to this representation. The design is based on quadratic Lyapunov functions and formulated as search problem over a set of bilinear matrix inequalities (BMIs), which is solved using a two-step separation procedure that maps the BMIs into a set of corresponding linear matrix inequalities. Two numerical examples are given to demonstrate the effectiveness of the proposed approach.

Phase-Locked loops lock-in range in Frequency Modulated-Atomic Force Microscope nonlinear control system

Since the mid 1980s the Atomic Force Microscope is one the most powerful tools to perform surface investigation, and since 1995 Non-Contact AFM achieved true atomic resolution. The Frequency-Modulated Atomic Force Microscope (FM-AFM) operates in the dynamic mode, which means that the control system of the FM-AFM must force the micro-cantilever to oscillate with constant amplitude and frequency. However, tip-sample interaction forces cause modulations in the microcantilever motion. A Phase-Locked loop (PLL) is used to demodulate the tip-sample interaction forces from the microcantilever motion. The demodulated signal is used as the feedback signal to the control system, and to generate both topographic and dissipation images. As a consequence, a proper design of the PLL is vital to the FM-AFM performance. In this work, using bifurcation analysis, the lock-in range of the PLL is determined as a function of the frequency shift (Q) of the microcantilever and of the other design parameters, providing a technique to properly design the PLL in the FM-AFM system. (C) 2011 Elsevier B.V. All rights reserved.

An extension of the invariance principle for dwell-time switched nonlinear systems

In this paper, we propose an extension of the invariance principle for nonlinear switched systems under dwell-time switched solutions. This extension allows the derivative of an auxiliary function V, also called a Lyapunov-like function, along the solutions of the switched system to be positive on some sets. The results of this paper are useful to estimate attractors of nonlinear switched systems and corresponding basins of attraction. Uniform estimates of attractors and basin of attractions with respect to time-invariant uncertain parameters are also obtained. Results for a common Lyapunov-like function and multiple Lyapunov-like functions are given. Illustrative examples show the potential of the theoretical results in providing information on the asymptotic behavior of nonlinear dynamical switched systems. (C) 2012 Elsevier B.V. All rights reserved.

Facies associations and controls on the evolution from a coastal bay to a lagoon system, Santa Catarina Coast, Brazil

The diverse Holocene morphological features along the south coast of the state of Santa Catarina include lagoons and residual lakes, a barrier, a delta (constructed by the Tubarao River), and pre-existing incised valleys that have flooded and filled. This scenario contains the sedimentary record of the transition from a bay to a lagoon system, which occurred during the rise and subsequent semi-stabilisation of the relative sea-level during the Holocene. The geomorphological evolution of this area was investigated using a combination of morphology, stratigraphic analysis of rotary push cores, vibracores and trenches with radiocarbon dating, taxonomic determination and taphonomic characterisation of Holocene fossil molluscs. Palaeogeographic maps were constructed to illustrate how the bay evolved over the last 8000 years. The relative sea-level rise and local sedimentary processes were the prime forcing factors determining the depositional history and palaeogeographic changes. The Holocene sedimentary succession began between 8000 and 5700 cal BP with the deposits of transgressive sandsheets. These deposits correspond to the initial marine flooding surface that was formed while the relative sea-level rose at a higher rate than the input of sediments, prior to the formation of the coastal barrier. The change from a bay to a lagoon system occurred around 5700 and 2500 cal BP during the mid-Holocene highstand with the formation of the barrier and with the achievement of a balance between sea-level rise and sedimentary supply. Until 2500 cal BP, the presence of this barrier, the following gentle decline in sea level and the initial emergence of back-barrier features restricted the hydro-dynamic circulation inside the bay and favoured an increase in the Tubarao River delta progradation rate. The final stage, during the last 2500 years, was marked by the increasing back-barrier width, with the establishment of salt marshes, the arrival of the delta in the back-barrier, and the advance of aeolian dunes along the outer lagoon margins. This study shed light on the mechanisms of coastal bay evolution in a setting existed prior to the beginning of barrier lagoon sedimentation. (C) 2012 Elsevier B.V. All rights reserved.

Optimization of Large-Scale Hydrothermal System Operation

This paper presents the development of a mathematical model to optimize the management and operation of the Brazilian hydrothermal system. The system consists of a large set of individual hydropower plants and a set of aggregated thermal plants. The energy generated in the system is interconnected by a transmission network so it can be transmitted to centers of consumption throughout the country. The optimization model offered is capable of handling different types of constraints, such as interbasin water transfers, water supply for various purposes, and environmental requirements. Its overall objective is to produce energy to meet the country's demand at a minimum cost. Called HIDROTERM, the model integrates a database with basic hydrological and technical information to run the optimization model, and provides an interface to manage the input and output data. The optimization model uses the General Algebraic Modeling System (GAMS) package and can invoke different linear as well as nonlinear programming solvers. The optimization model was applied to the Brazilian hydrothermal system, one of the largest in the world. The system is divided into four subsystems with 127 active hydropower plants. Preliminary results under different scenarios of inflow, demand, and installed capacity demonstrate the efficiency and utility of the model. From this and other case studies in Brazil, the results indicate that the methodology developed is suitable to different applications, such as planning operation, capacity expansion, and operational rule studies, and trade-off analysis among multiple water users. DOI: 10.1061/(ASCE)WR.1943-5452.0000149. (C) 2012 American Society of Civil Engineers.

Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrodinger flow

In a previous work El et al. (2006) [1] exact stable oblique soliton solutions were revealed in two-dimensional nonlinear Schrodinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. (C) 2012 Elsevier B.V. All rights reserved.

Linear and nonlinear measures of fetal heart rate patterns evaluated on very short fetal magnetocardiograms

We analyzed the effectiveness of linear short- and long-term variability time domain parameters, an index of sympatho-vagal balance (SDNN/RMSSD) and entropy in differentiating fetal heart rate patterns (fHRPs) on the fetal heart rate (fHR) series of 5, 3 and 2 min duration reconstructed from 46 fetal magnetocardiograms. Gestational age (GA) varied from 21 to 38 weeks. FHRPs were classified based on the fHR standard deviation. In sleep states, we observed that vagal influence increased with GA, and entropy significantly increased (decreased) with GA (SDNN/RMSSD), demonstrating that a prevalence of vagal activity with autonomous nervous system maturation may be associated with increased sleep state complexity. In active wakefulness, we observed a significant negative (positive) correlation of short-term (long-term) variability parameters with SDNN/RMSSD. ANOVA statistics demonstrated that long-term irregularity and standard deviation of normal-to-normal beat intervals (SDNN) best differentiated among fHRPs. Our results confirm that short-and long-term variability parameters are useful to differentiate between quiet and active states, and that entropy improves the characterization of sleep states. All measures differentiated fHRPs more effectively on very short HR series, as a result of the fMCG high temporal resolution and of the intrinsic timescales of the events that originate the different fHRPs.

Odd homoclinic orbits for a second order Hamiltonian system

The aim of this paper is to find an odd homoclinic orbit for a class of reversible Hamiltonian systems. The proof is variational and it employs a version of the concentration compactness principle of P. L. Lions in a lemma due to Struwe.

Remarks on Parametric Surface Waves in a Nonlinear and Non-Ideally Excited Tank

We studied free surface oscillations of a fluid in a cylinder tank excited by an electric motor with limited power supply. We investigated the possibility of parametric resonance in this system, showing that the excitation mechanism can generate chaotic response. Numerical experiments are carried out to present the existence of several types of regular and chaotic attractors. For the first time powers (power of the motor, power consumed by the damping force under fluid free surface oscillations, and a total power) are calculated, investigated, and shown for different regimes, regular and chaotic ones for parametric resonance interactions. [DOI: 10.1115/1.4005844]

Bifurcation analysis of an aeroelastic system with concentrated nonlinearities

Analytical and numerical analyses of the nonlinear response of a three-degree-of-freedom nonlinear aeroelastic system are performed. Particularly, the effects of concentrated structural nonlinearities on the different motions are determined. The concentrated nonlinearities are introduced in the pitch, plunge, and flap springs by adding cubic stiffness in each of them. Quasi-steady approximation and the Duhamel formulation are used to model the aerodynamic loads. Using the quasi-steady approach, we derive the normal form of the Hopf bifurcation associated with the system's instability. Using the nonlinear form, three configurations including supercritical and subcritical aeroelastic systems are defined and analyzed numerically. The characteristics of these different configurations in terms of stability and motions are evaluated. The usefulness of the two aerodynamic formulations in the prediction of the different motions beyond the bifurcation is discussed.

Analysis of nonlinear dynamics of vocal folds using high-speed video observation and biomechanical modeling

Primary voice production occurs in the larynx through vibrational movements carried out by vocal folds. However, many problems can affect this complex system resulting in voice disorders. In this context, time-frequency-shape analysis based on embedding phase space plots and nonlinear dynamics methods have been used to evaluate the vocal fold dynamics during phonation. For this purpose, the present work used high-speed video to record the vocal fold movements of three subjects and extract the glottal area time series using an image segmentation algorithm. This signal is used for an optimization method which combines genetic algorithms and a quasi-Newton method to optimize the parameters of a biomechanical model of vocal folds based on lumped elements (masses, springs and dampers). After optimization, this model is capable of simulating the dynamics of recorded vocal folds and their glottal pulse. Bifurcation diagrams and phase space analysis were used to evaluate the behavior of this deterministic system in different circumstances. The results showed that this methodology can be used to extract some physiological parameters of vocal folds and reproduce some complex behaviors of these structures contributing to the scientific and clinical evaluation of voice production. (C) 2010 Elsevier Inc. All rights reserved.

Classical bifurcation in a quadrupolar NMR system

The Josephson junction model is applied to the experimental implementation of classical bifurcation in a quadrupolar nuclear magnetic resonance system. There are two regimes, one linear and one nonlinear, which are implemented by the radio-frequency and the quadrupolar terms of the Hamiltonian of a spin system, respectively. These terms provide an explanation of the symmetry breaking due to bifurcation. Bifurcation depends on the coexistence of both regimes at the same time in different proportions. The experiment is performed on a lyotropic liquid crystal sample of an ordered ensemble of 133Cs nuclei with spin I = 7/2 at room temperature. Our experimental results confirm that bifurcation happens independently of the spin value and of the physical system. With this experimental spin scenario, we confirm that a quadrupolar nuclei system could be described analogously to a symmetric two-mode Bose-Einstein condensate.