A Continuous Time Markov Chain Based Sequential Analytical Approach for Composite Power System Reliability Assessment

This paper proposes a continuous time Markov chain (CTMC) based sequential analytical approach for composite generation and transmission systems reliability assessment. The basic idea is to construct a CTMC model for the composite system. Based on this model, sequential analyses are performed. Various kinds of reliability indices can be obtained, including expectation, variance, frequency, duration and probability distribution. In order to reduce the dimension of the state space, traditional CTMC modeling approach is modified by merging all high order contingencies into a single state, which can be calculated by Monte Carlo simulation (MCS). Then a state mergence technique is developed to integrate all normal states to further reduce the dimension of the CTMC model. Moreover, a time discretization method is presented for the CTMC model calculation. Case studies are performed on the RBTS and a modified IEEE 300-bus test system. The results indicate that sequential reliability assessment can be performed by the proposed approach. Comparing with the traditional sequential Monte Carlo simulation method, the proposed method is more efficient, especially in small scale or very reliable power systems.

The effect of clock jitter on the performance of continuous-time delta-sigma ADC for GNSS signals

Next generation Global Navigation Satellite System (GNSS) receivers will operate in multiple navigation bands. An efficient way to achieve this with lower power and cost is to employ BandPass Sampling (BPS); nevertheless, the sampling operation injects large amounts of jitter noise, which degrades the performance of the receiver. Continuous–Time (CT) Delta–Sigma (ΔΣ) modulators are capable of suppressing this noise but the impact of clock jitter at the output of the Digital– to–Analog Converter (DAC) in the feedback path of the modulator should be taken into account. This paper presents an analytical approach for describing clock jitter in GNSS receivers when a CT–ΔΣ modulator is utilized for Analog–to–Digital Conversion (ADC). The validity of the presented approach is verified through time–domain simulations using a behavioural model of the fourth–order CT–ΔΣ modulator with 1–bit NRZ DAC feedback pulse.

Forecasting overseas visitors into the United Kingdom using continuous time and autoregressive fractional integrated moving average models with discrete data

This paper applies Gaussian estimation methods to continuous time models for modelling overseas visitors into the UK. The use of continuous time modelling is widely used in economics and finance but not in tourism forecasting. Using monthly data for 1986–2010, various continuous time models are estimated and compared to autoregressive integrated moving average (ARIMA) and autoregressive fractionally integrated moving average (ARFIMA) models. Dynamic forecasts are obtained over different periods. The empirical results show that the ARIMA model performs very well, but that the constant elasticity of variance (CEV) continuous time model has the lowest root mean squared error (RMSE) over a short period.

An FPGA based decimation filter processor design for real-time continuous-time Σ−Δ modulator performance measurement and evaluation

This paper reports on a Field Programmable Gate Array (FPGA) implementation as well as prototyping for real-time testing of a low complexity high efficiency decimation filter processor which is deployed in conjunction with a custom built low-power jitter insensitive Continuous Time (CT) Sigma-Delta (Σ-Δ) Modulator to measure and assess its performance. The CT Σ-Δ modulator/decimation filter cascade can be used in integrated all-digital microphone interfaces for a variety of applications including mobile phone handsets, wireless handsets as well as other applications requiring all-digital microphones. The work reported here concentrates on the design and implementation as well as prototyping on a Xilinx Spartan 3 FPGA development system and real-time testing of the decimation processing part deploying All-Pass based structures to process the bit stream coming from CT Σ-Δ modulator hence measuring in real-time and fully assessing the modulator's performance.

An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

Continuous Time Finance

Exercises, exams and solutions for a third year finance course.

Approximation of non-autonomous dynamic systems by continuous time recurrent neural networks

This work provides a framework for the approximation of a dynamic system of the form x˙=f(x)+g(x)u by dynamic recurrent neural network. This extends previous work in which approximate realisation of autonomous dynamic systems was proven. Given certain conditions, the first p output neural units of a dynamic n-dimensional neural model approximate at a desired proximity a p-dimensional dynamic system with n>p. The neural architecture studied is then successfully implemented in a nonlinear multivariable system identification case study.

Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

On variational data assimilation in continuous time

Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalization of what is known as weakly constrained four-dimensional variational assimilation (4D-Var) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two-point boundary value problem. For imperfect models, the trade-off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. This trade-off turns out to be trivial if the model is perfect. However, even in this situation, allowing for minute deviations from the perfect model is shown to have positive effects, namely to regularize the problem. The presented formalism is dynamical in character. No statistical assumptions on dynamical or observational noise are imposed.

Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

On equilibrium prices in continuous time

We combine general equilibrium theory and théorie générale of stochastic processes to derive structural results about equilibrium state prices.

Continuous-time and discrete-time sliding mode control accomplished using a computer

A computer-based sliding mode control (SMC) is analysed. The control law is accomplished using a computer and A/D and D/A converters. Two SMC designs are presented. The first one is a continuous-time conventional SMC design, with a variable structure law, which does not take into consideration the sampling period. The second one is a discrete-time SMC design, with a smooth sliding law, which does not have a structure variable and takes into consideration the sampling period. Both techniques are applied to control an inverted pendulum system. The performance of both the continuous-time and discrete-time controllers are compared. Simulations and experimental results are shown and the effectiveness of the proposed techniques is analysed.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonsmooth continuous-time optimization problems: Necessary conditions

We consider Lipschitz continuous-time nonlinear optimization problems and provide first-order necessary optimality conditions of both Fritz John and Karush-Kuhn-Tucker types. (C) 2001 Elsevier B.V. Ltd. All rights reserved.