Continuous Time Systems

In epidemiological models of infectious diseases the basic reproduction number ${\mathcal{R}_0}$ is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for ${\mathcal{R}_0}$ can be obtained from the digraphs in the reduction process.

We introduce explicitly the effort as a choice variable in a continuous time utility maximisation framework of an executive who is partly compensated with stock options. We solve the model in the case where the executive is not allowed to trade in the company's stock but is able to achieve a partial insurance through trading in a correlated market portfolio. We define the executive's value of the options through a certainty equivalence approach both in the case of European call options and nonstandard capped stock options and study the behaviour of the reservation price as relevant parameters change.

We examine the relationship between volatility and past and future returns using high-frequency aggregate equity index data. Consistent with a prolonged “leverage” effect, we find the correlations between absolute high-frequency returns and current and past high-frequency returns to ...

This paper presents an adaptive position control scheme for DC motors based on an on-line closed loop continuous-time identiflcation method. A fast, non-asymptotic, algebraic identiflcation method is used to estimate simultaneously the unknown sys- tem parameters and the unmeasured states to update an adaptive position control scheme.

This paper contains a brief overview of the infinitedimensional sampled-data Kalman filter (ISKF) derivation [1]. The ISKF is essentially a mathematical extension of the (finitedimensional) sampled-data Kalman filter that applies to a larger class of problems that satisfy the strongly continuous semigroup property which includes certain partial and delay differential equations.

The adoption of a common formalism for describing planning domains fosters far greater reuse of research and allows more direct comparison of systems and approaches, and therefore supports faster progress in the field. A common formalism is a compromise between expressive power (in which development is strongly driven by potential applications) and the progress of basic research (which encourages development from well-understood foundations). The role of a common formalism as a communication medium for exchange demands that it is provided with a clear semantics. This paper describes extensions of PDDL2.1 (used in the 3rd International Planning Competition) that support the modelling of continuous time-dependent effects and illustrates why they can play a critical role in modelling real domains.

A new approach for robust fixed-order H∞ controller design by convex optimization is proposed. Linear timeinvariant single-input single-output systems represented by a finite set of complex values in the frequency domain are considered. It is shown that the H∞ robust performance condition can be approximated by a set of linear or convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Multimodel and frequency-domain uncertainty can be directly considered in the proposed approach by increasing the number of constraints. The proposed method is compared with the standard H∞ control problem. It is shown by an example that for an unstable uncertain model, a PID controller can be designed with the proposed approach which gives better H∞ performance than a 7th order unstable controller obtained by the standard H∞ solution.

In this paper, we study a regression model in which explanatory variables are sampling points of a continuous-time process. We propose an estimator of regression by means of a Functional Principal Component Analysis analogous to the one introduced by Bosq [(1991) NATO, ASI Series, pp. 509–529] in the case of Hilbertian AR processes. Both convergence in probability and almost sure

This paper investigates the system stability of a sampled-data fuzzy-model-based control system, formed by a nonlinear plant and a sampled-data fuzzy controller connected in a closed loop. The sampled-data fuzzy controller has an advantage that it can be implemented using a microcontroller or a digital computer to lower the implementation cost and time. However, discontinuity introduced by the sampling activity complicates the system dynamics and makes the stability analysis difficult compared with the pure continuous-time fuzzy control systems. Moreover, the favourable property of the continuous-time fuzzy control systems which is able to relax the stability analysis result vanishes in the sampled-data fuzzy control systems. A Lyapunov-based approach is employed to derive the LMI-based stability conditions to guarantee the system stability. To facilitate the stability analysis, a switching fuzzy model consisting of some local fuzzy models is employed to represent the nonlinear plant to be controlled. The comparatively less strong nonlinearity of each local fuzzy model eases the satisfaction of the stability conditions. Furthermore, membership functions of both fuzzy model and sampled-data fuzzy controller are considered to alleviate the conservativeness of the stability analysis result. A simulation example is given to illustrate the merits of the proposed approach.

An observation regarding the nature of the spectrum of a windowed swept-frequency sinusoid is exploited to time-scale (stretch or compress) time-variant sinusoids within the window or frame of an otherwise basic phase vocoder process. Nonstationary sinusoids are more closely represented as a series of windowed linearly swept sinusoids than as a series of windowed constant frequency sinusoids. Both the frequency sweep rate and the amplitude ramp rate can be identified and modified according to the time-scale ratio. The mathematics outlining this concept will be developed in the continuous time domain whereas a MATLAB program demonstrating the concept is in discrete time. An example is shown, using a swept and ramped sinusoid, that there are visible differences between using this correction and not using it. These differences predictably get more pronounced as the time rate of change of frequency or amplitude increases

Model-based design methodologies are commonly used in industry for the development of complex cyber-physical systems (CPSs). There are many different languages, tools, and formalisms for model-based design, each with its strengths and weaknesses. Instead of accepting some weaknesses of a particular tool, an alternative Communicated by Prof. J. Sztipanovits, M. Broy, and H. Daembkes. This work is partially based on previous work published by the authors [7,8,15], but the contributions presented in this article stand on their own. is to embrace heterogeneity, and to develop tool integration platforms and protocols to leverage the strengths from different environments. A fairly recent attempt in this direction is the functional mock-up interface (FMI) standard that includes support for co-simulation. Although this standard has reached acceptance in industry, it provides only limited support for simulating systems that mix continuous and discrete behavior, which are typical of CPS. This paper identifies the representation of time as a key problem, because the FMI representation does not support well the discrete events that typically occur at the cyber-physical boundary. We analyze alternatives for representing time in hybrid co-simulation and conclude that a superdense model of time using integers only solves many of these problems. We show how an execution engine can pick an adequate time resolution, and how disparities between time representations internal to co-simulated components and the resulting effects of time quantization can be managed. We propose a concrete extension to the FMI standard for supporting hybrid co-simulation that includes integer time, automatic choice of time resolution, and the use of absent signals. We explain how these extensions can be implemented modularly within the frameworks of existing simulation environments.

Petri nets (PN) are useful for the modelling, analysis and control of hybrid dynamical systems (HDS) because PN combine in a comprehensive way discrete events and continuous behaviours. On one hand, PN are suitable for modelling the discrete part of HDS and for providing a discrete abstraction of continuous behaviours. On the other hand, continuous PN are suitable for modelling the continuous part of HDS and for working out a continuous approximation of the discrete part in order to avoid the complexity associated with the exponential growth of discrete states. This paper focuses on the advantages of PN as a modelling tool for HDS. Investigations of such models for diagnosis and control issues are detailed.

It has been proven that the batch renewal process is the least biased choice of trac process given the infinite sets of measures of the trac correlation, (i.e. indices of dispersion, covariances or correlation functions) in the discrete time domain. The same conclusion is expected to hold in the continuous time domain. That motivates the study and comparison of similar

This paper presents the distributed formation control of a multi-agent system using graph theory with emphasis on consensus and cooperation issues. The focal point is to achieve and maintain a formation from any initial condition, with and without a leader that the entire formation must follow. Our analysis framework is based on tools from algebraic graph theory, matrix theory and control theory. We present a brief derivation of multi-agent consensus in continuous-time and the corresponding iterative form stated in discrete-time, because while the real scenario is continuous, the implementation that we simulate is discrete. Based on the discrete-time algorithm, we propose a solution to obtain and uphold consensus when there is a leader to command the entire network. Simulation results are presented, indicating the capabilities and limitations of the algorithms.

The aim of this paper is to present an R library, called tdc.msm, developed to analyze multi-state survival data. In this library, the time-dependent regression model and multi-state models are included as two possible approaches for such data. For the multi-state modelling five different models are considered, allowing the user to choose between Markov and semi-Markov property, as well as

In classical time domain Box-Jenkins identification discrete-time plant and noise models are estimated using sampled input/output signals. The frequency content of the input/output samples covers uniformly the whole unit circle in a natural way, even in case of prefiltering. Recently, the classical time domain Box-Jenkins framework has been extended to frequency domain data captured in open loop. The proposed frequency domain maximum likelihood (ML) solution can handle (i) discrete-time models using data that only covers a part of the unit circle, and (ii) continuous-time models. Part I of this series of two papers (i) generalizes the frequency domain ML solution to the closed loop case, and (ii) proves the properties of the ML estimator under non-standard conditions. Contrary to the classical time domain case it is shown that the controller should be either known or estimated. The proposed ML estimators are applicable to frequency domain data as well as time domain data. ᭧

This paper presents different novel CMOS realizations for the differential difference operational floating amplifier (DDOFA). The DDOFA was first introduced in Ref. 1 and was used to realize different analog circuits like integrators, filters and variable gain amplifiers. New CMOS realizations for the DDOFA are introduced in this literature. Furthermore the DDOFA is modified to realize a fully differential current conveyor (FDCC). Novel CMOS realizations of the FDCC are presented. The FDCC is used to realize second-order band pass-low-pass filter. Performance comparisons between the different realizations of the DDOFA and FDCC are given in this literature. PSPICE simulations of the overall proposed circuits are given using 0.25 µm CMOS Technology from TMSC MOSIS model and dual supply voltages of ±1.5 V.

This article presents an overview of the recent development on mathematical treatment of behavioural finance, primarily in the setting of continuous-time portfolio choice under the cumulative prospect theory. Financial motivations and mathematical challenges of the problem are highlighted. It is demonstrated that the solutions to the problem have in turn led to new financial and mathematical problems and machineries.

In this paper, passive continuous-time (CT) 61 modulators are briefly reviewed and compared with conventional active CT 61 modulators. A fifth-order CT 61 modulator with a hybrid active-passive loop filter is realized with only three active integrators. The hybrid CT 61 modulator is robust to the excess loop delay, clock jitter, and RC product variations. The prototype chip is designed in a 0.25-m CMOS technology targeting for GPS or WCDMA applications. The experimental results show that the prototype 61 modulator achieves a 68-dB dynamic range and a 75 dB IM3 over a 2-MHz bandwidth with a 150-MHz clock, consuming 1.8 mA from a 1.5-V supply.

Analysis of heart rate variation (HRV) has become a popular non-invasive tool for assessing the activities of the autonomic nervous system (ANS). HRV analysis is based on the concept that fast fluctuations may specifically reflect changes of sympathetic and vagal activity. It shows that the structure generating the signal is not simply linear, but also involves nonlinear contributions. These signals are essentially nonstationary; may contain indicators of current disease, or even warnings about impending diseases. The indicators may be present at all times or may occur at random in the time scale. However, to study and pinpoint abnormalities in voluminous data collected over several hours is strenuous and time consuming. This paper presents the continuous time wavelet analysis of heart rate variability signal for disease identification. Fractal dimension (FD) of heart rate signals are calculated and compared with the wavelet analysis patterns. The FD obtained indicates more than 90% confidence interval for all the classes studied.

The adoption of a common formalism for describing planning domains fosters far greater reuse of research and allows more direct comparison of systems and approaches, and therefore supports faster progress in the field. A common formalism is a compromise between expressive power (in which development is strongly driven by potential applications) and the progress of basic research (which encourages development from well-understood foundations). The role of a common formalism as a communication medium ...

Purpose -The purpose of this paper is to analyze the effect of the white, colored and mixture noise perturbations as Gaussian process on the parameters of the RL electrical circuit including potential source and resistance. Design/methodology/approach -By adding different noise terms in the voltage and resistance parameters of an RL electrical circuit, the deterministic model is replaced by a stochastic differential equation (SDE). Findings -Owing to the application of multiple Ito's formula the analytical solutions of resulted SDEs have been obtained. Furthermore, based on a numerical method involving Euler-Maruyama scheme, the solution of the problem at the point of interest as a continuous time stochastic process has been obtained. Also shown is that the confidence interval for mean of solutions with colored and mixture noises is better than white noise. Practical implications -Numerical tests via Matlab programming are performed in order to show the efficiency and accuracy of the present work. Numerical experiments show that an excellent estimation on the solution can be obtained within a couple of minutes time at Pentium IV-2.4 GHz PC. Originality/value -It is believed that the stochastic model of an RL circuit with colored and mixture noises in potential source has not been studied before. Furthermore, according to latest information from the research works, two stochastic parameters in voltage and resistance of RL circuit including colored and mixture noise processes have been investigated for the first time in this paper.

Proportional-integral-derivative (PID) controllers are widely used in process control, and consequently they are described in most of the textbooks on automatic control. However, rather than presenting the overall design process, the examples given in such textbooks are intended to illuminate specific focused aspects of selection, tuning and implementation of the controller. This paper describes in detail the design of a PID controller for temperature control of a polymerase chain reaction (PCR) microreactor showing how different aspects, which necessarily are taught separately, interact in a real-world design. After setting the design targets by taking the hardware limitations into consideration, a continuous time controller, having two degrees of freedom, is designed by placing its dominant pair of poles using the root locus technique. Then, the integrator wind-up is addressed, the controller is translated into a discrete time version and, after implementation, the experimental performances are measured.

Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and restricted to a finite domain. We investigate by analytic calculations and simulations how time-averaged observables (e.g., the time averaged mean squared displacement and displacement correlation) are

The resource-constrained production planning problem in semicontinuous multiproduct food industries is addressed. In particular, the case of yogurt production, a representative food process, in a real-life dairy facility is studied in detail. The problem in question is mainly focused on the packing stage, whereas timing and capacity constraints are imposed with respect to the batch stage to ensure the generation of feasible production plans. A novel mixed discrete/continuous-time mixed-integer linear programming model, based on the definition of families of products, is proposed. Timing and sequencing decisions are taken for product families rather than for products; thus, reducing significantly the model size. Additionally, material balances are realized for every particular product, permitting the detailed optimization of inventory and operating costs. Packing units operate in parallel and share resources. Qualitative as well as quantitative objectives are considered. Several industrial case studies, including also some unexpected events scenarios, have been solved to optimality.

The central autonomic network (CAN) has been described in animal models but has been difficult to elucidate in humans. Potential confounds include physiological noise artifacts affecting brainstem neuroimaging data, and difficulty in deriving non-invasive continuous assessments of autonomic modulation. We have developed and implemented a new method which relates cardiac-gated fMRI timeseries with continuous-time heart rate variability (HRV) to estimate central autonomic processing. As many autonomic structures of interest are in brain regions strongly affected by cardiogenic pulsatility, we chose to cardiac-gate our fMRI acquisition to increase sensitivity. Cardiac-gating introduces T1-variability, which was corrected by transforming fMRI data to a fixed TR using a previously published method [Guimaraes, A.R., Melcher, J.R., et al., 1998. Imaging subcortical auditory activity in humans. Hum. Brain Mapp. 6(1), 33–41]. The electrocardiogram was analyzed with a novel point process adaptive-filter algorithm for computation of the high-frequency (HF) index, reflecting the time-varying dynamics of efferent cardiovagal modulation. Central command of cardiovagal outflow was inferred by using the resample HF timeseries as a regressor to the fMRI data. A grip task was used to perturb the autonomic nervous system. Our combined HRV-fMRI approach demonstrated HF correlation with fMRI activity in the hypothalamus, cerebellum, parabrachial nucleus/locus ceruleus, periaqueductal gray, amygdala, hippocampus, thalamus, and dorsomedial/dorsolateral prefrontal, posterior insular, and middle temporal cortices. While some regions consistent with central cardiovagal control in animal models gave corroborative evidence for our methodology, other mostly higher cortical or limbic-related brain regions may be unique to humans. Our approach should be optimized and applied to study the human brain correlates of autonomic modulation for various stimuli in both physiological and pathological states.

The Czech Republic represents one of the European transit countries for distribution of natural gas in east-west directions. The aim of our contribution is to provide the mathematical model of actual natural gas compression station which is situated in the Czech Republic and its surrounding gas pipeline network with assuming of performance changes of the amount of transported natural gas. The assumed performance changes are based on consumer wishes which are changing during time and are provided and supervised by a human dispatcher. We describe a multi-state Markov model in continuous time of our problem. The model parameters are based on historical data, on the list of rules of possible human dispatcher performance changes behaviour and also on expert information from the gas network industry. An effect of change of the hardware configuration of the system by a human dispatcher and its corresponding change of the system availability will be presented and discussed as well.

This article presents an overview of the state-of-the art in modeling and simulation, and studies to which extent current simulation technologies can effectively support the design process. For simulation-based design, modeling languages and simulation environments must take into account the special characteristics of the design process. For instance, languages should allow models to be easily updated and extended to accommodate the various analyses performed throughout the design process. Furthermore, the simulation software should be well integrated with the design tools so that designers and analysts with expertise in different domains can effectively collaborate on the design of complex artifacts. This review focuses in particular on modeling for design of multi-disciplinary engineering systems that combine continuous time and discrete time phenomena.

This paper deals with the foundations of the stochastic mathematical finance, and it has three main purposes: 1. We present a self-contained construction of the vector stochastic integral HX with respect to a d-dimensional semimartingale X = (X1 t ,...,Xd t ). This notion is more general than the componentwise stochastic integral Pd i=1 H iXi. 2. We show that

In this paper, an electrocardiographic (ECG) signal processing IC, which is used for portable biomedical application, was designed using continuous-time technique. The circuit consists of an instrumentation amplifier (INA) with driven-right-leg circuit (DRL), a 5th order Gm -C low pass filter (Gm-C LPF) operating in sub-threshold mode, and amplifiers. DRL circuit is used to detect small amplitude signal in the presence of large common-mode voltage from the human body. The CMRR of the INA is 78 dB and the Gm-C LPF has a cutoff frequency of 18 Hz. As a result of using the DRL, a small signal can be detected in the presence of large common-mode differential. The circuit consumes 1.23 mW when operating from with a supply voltage of plusmn1.5-V and occupies a core area of 0.94 mm2. The circuit was designed in a 0.35mum CMOS process and simulation results have successfully demonstrated the functionalities

This paper focuses on commonalities and differences between the two mixed-signal hardware description languages VHDL-AMS and Verilog-AMS in the case of modeling heterogeneous or multi-discipline systems. The paper has two objectives. The first one consists of modeling the structure and the behavior of an airbag system using both the VHDL-AMS and the Verilog-AMS languages. Such a system encompasses several time abstractions (i.e. discrete-time and continuous-time), several disciplines, or energy domains (i.e., electrical, thermal, optical, mechanical, and chemical), and several continuous-time description formalisms (i.e., conservative-law and signal-flow descriptions). The second objective is to discuss the results of the proposed modeling process in terms of the descriptive capabilities of the VHDL-AMS and Verilog-AMS languages and of the generated simulation results. The tools used are Advance-MS from Mentor Graphics for VHDL-AMS and AMS Simulator from Cadence Design Systems for Verilog-AMS. The paper shows that both languages offer effective means to describe and simulate multi-discipline systems, although using different descriptive approaches. It also highlights current tool limitations since full language definitions are not yet supported.

This is an important book that will influence future research on R&D and innovation. It brings together a number of pioneering papers by Adam Jaffe and Manuel Trajtenberg (and various co-authors) on the use of patent citations to study the innovation process, plus several new pieces of work. The book is organised in four parts. The papers in Part 1 lay the 'conceptual' groundwork for research on patent citations. The first is the classic paper by Trajtenberg demonstrating that citations are linked to demand-based measures of social surplus for one important medical innovation, CT scanners. Making this link between patent citations and social (and private) value provides powerful justification for using citations in economic studies. It is surprising and unfortunate that there have not been similar studies on other innovations, despite the huge growth of empirical work on vertically differentiated product markets.

In this paper we investigate a continuous time autoregressive moving- average model (CARMA) for the instantaneous spot interest rate. This model can be interpreted as a generalized Vasicek (1977) model where higher order lags and moving average terms are allowed in the spot rate dynamics. Our model fit in the general ane class of term structure models, and we provide

In this work, a bidimensional continuous-time differential equations system is analyzed which is derived of Leslie-type predator-prey schemes by considering a nonmonotonic functional response and Allee effect on population prey. For the system obtained we describe the bifurcation diagram of limit cycles that appears in the first quadrant, the only quadrant of interest for the sake of realism. We show that, under certain conditions over the parameters, the system allows the existence of three limit cycles: The first two cycles are infinitesimal ones generated by Hopf bifurcation; the third one arises from a homoclinic bifurcation. Furthermore, we give conditions over the parameters such that the model allows long-term extinction or survival of both populations. In particular, the presence of a weak Allee effect does not imply extinction of populations necessarily for our model.

We prove that the attractor of the 1D quintic complex Ginzburg-Landau equation with a broken phase symmetry has strictly positive space-time entropy for an open set of parameter values. The result is obtained by studying chaotic oscillations in grids of weakly interacting solitons in a class of Ginzburg-Landau type equations. We provide an analytic proof for the existence of twosoliton configurations with chaotic temporal behavior, and construct solutions which are closed to a grid of such chaotic soliton pairs, with every pair in the grid well spatially separated from the neighboring ones for all time. The temporal evolution of the well-separated multi-soliton structures is described by a weakly coupled lattice dynamical system (LDS) for the coordinates and phases of the solitons. We develop a version of normal hyperbolicity theory for the weakly coupled LDS's with continuous time and establish for them the existence of space-time chaotic patterns similar to the Sinai-Bunimovich chaos in discrete-time LDS's. While the LDS part of the theory may be of independent interest, the main difficulty addressed in the paper concerns with lifting the space-time chaotic solutions of the LDS back to the initial PDE. The equations we consider here are space-time autonomous, i.e. we impose no spatial or temporal modulation which could prevent the individual solitons in the grid from drifting towards each other and destroying the well-separated grid structure in a finite time. We however manage to show that the set of space-time chaotic solutions for which the random soliton drift is arrested is large enough, so the corresponding space-time entropy is strictly positive.

Two types of brain model are currently the center of a fundamental controversy in cognitive science. Traditional artificial intelligence models are based on the discrete, programmable symbol systems normally associated with Turing/von Neumann computation, and for which language and logic are the essential tools. This type of model is now being challenged by the rebirth of concurrent, distributed networks that are based on analog models of physical systems, and that also claim some similarity to neural architecture. In the former, discrete symbols are local, sequential, and rewritten under total program control. In the latter, symbols are only the end result of coherent network dynamics that need little explicit program control. The behavior of these networks is determined by the constraints within the network and the initial conditions. In this respect, network behavior is functionally similar to a complex measurement process, since measurement in physics discriminates and classifies implicate dynamical patterns by mapping them to explicit symbols. But what determines when a measurement is completed is an unresolved problem in physics, especially in quantum theory. It involves complementary modes of description, one based on the rate-dependent, continuous, time-symmetric dynamics of inexorable physical laws, and the other based on the rateindependent, discrete, irreversible constraints of programmable symbol systems. In physics, these modes are both distinguished and related only by measurement, but when a measurement occurs appears to be a matter of arbitrary choice. The brain uses many complementary modes of description, and must constantly choose among them, but the ultimate nature of this choice remains a problem.

This paper introduces a novel design of an artificial neural network tailored for wafer-scale integration. The presented VLSI implementation includes continuous-time analog neurons with up to 16k inputs. A novel interconnection and routing scheme allows the mapping of a multitude of network models derived from biology on the VLSI neural network while maintaining a high resource usage. A single 20 cm wafer contains about 60 million synapses. The implemented neurons are highly accelerated compared to biological real time. The power consumption of the dense interconnection network providing the necessary communication bandwidth is a critical aspect of the system integration. A novel asynchronous lowvoltage signaling scheme is presented that makes the wafer-scale approach feasible by limiting the total power consumption while simultaneously providing a flexible, programmable network topology.

Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d'une subvention d'infrastructure du ministère de la Recherche, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de recherche.

This paper describes a high-performance strain sensing microsystem. A MEMS capacitive strain sensor converts an input strain to a capacitance change with a sensitivity of 26.5 aF per 0.1 µε. Low-noise integrated sensing electronics employing a continuous time synchronous detection architecture convert the capacitive signal to an output voltage for further signal processing. The prototype microsystem achieves a minimum detectable strain of 0.09 µε over a 10 kHz bandwidth with a dynamic range of 81 dB. The sensing electronics consume 1.5 mA from a 3V supply.