Foundations of Deterministic and Stochastic Control

Davis, Jon H.

doi:10.1007/978-1-4612-0071-0

Cited by 40 publications

(16 citation statements)

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“…Fundamental to the treatment of the input stochastic perturbations, i.e., the u of equation (A14) as some form of noise process is the concept of the Wiener process W, also known as Brownian motion (Doob 1990;Davis 2002;Jacobs 2010;Øksendal 2014). Wiener processes and processes derived from it are of importance in a number of areas of physics, engineering and finance (Jacobs 2010).…”

Section: Appendix C: the Mathematics Of The Driving Stochastic Impulsesmentioning

confidence: 99%

Extracting information from AGN variability

Kasliwal

Vogeley

Richards

2017

Monthly Notices of the Royal Astronomical Society

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AGN exhibit rapid, high amplitude stochastic flux variations across the entire electromagnetic spectrum on timescales ranging from hours to years. The cause of this variability is poorly understood. We present a Green's Function-based method for using variability to (1) measure the time-scales on which flux perturbations evolve and (2) characterize the driving flux perturbations. We model the observed light curve of an AGN as a linear differential equation driven by stochastic impulses. We analyze the light curve of the Kepler AGN Zw 229-15 and find that the observed variability behavior can be modeled as a damped harmonic oscillator perturbed by a colored noise process. The model powerspectrum turns over on time-scale 385 d. On shorter timescales, the log-powerspectrum slope varies between 2 and 4, explaining the behavior noted by previous studies. We recover and identify both the 5.6 d and 67 d timescales reported by previous work using the Green's Function of the C-ARMA equation rather than by directly fitting the powerspectrum of the light curve. These are the timescales on which flux perturbations grow, and on which flux perturbations decay back to the steady-state flux level respectively. We make the software package kālī used to study light curves using our method available to the community.

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Section: Appendix C: the Mathematics Of The Driving Stochastic Impulsesmentioning

confidence: 99%

Extracting information from AGN variability

Kasliwal

Vogeley

Richards

2017

Monthly Notices of the Royal Astronomical Society

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“…The term ''control law" is standard and central in the mathematical theory of control (e.g., Davis 2002). It describes the dependence of control action (expressed, e.g., in joint torques or muscle activity) on the parameters of the motor plant, which in our experimental paradigm includes the dynamics of the arm and its relationship with the reach target.…”

Section: Introductionmentioning

confidence: 99%

Control of aperture closure during reach-to-grasp movements in parkinson’s disease

et al. 2005

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This study examined whether the pattern of coordination between arm-reaching toward an object (hand transport) and the initiation of aperture closure for grasping is different between PD patients and healthy individuals, and whether that pattern is affected by the necessity to quickly adjust the reach-to-grasp movement in response to an unexpected shift of target location. Subjects reached for and grasped a vertical dowel, the location of which was indicated by illuminating one of the three dowels placed on a horizontal plane. In control conditions, target location was fixed during the trial. In perturbation conditions, target location was shifted instantaneously by switching the illumination to a different dowel during the reach. The hand distance from the target at which the subject initiated aperture closure (aperture closure distance) was similar for both the control and perturbation conditions within each group of subjects. However, that distance was significantly closer to the target in the PD group than in the control group. The timing of aperture closure initiation varied considerably across the trials in both groups of subjects. In contrast, aperture closure distance was relatively invariant, suggesting that aperture closure initiation was determined by spatial parameters of arm kinematics rather than temporal parameters. The linear regression analysis of aperture closure distance showed that the distance was highly predictable based on the following three parameters: the amplitude of maximum grip aperture, hand velocity, and hand acceleration. This result implies that a control law, the arguments of which include the above parameters, governs the initiation of aperture closure. Further analysis revealed that the control law was very similar between the subject groups under each condition as well as between the control and perturbation conditions for each group. Consequently, the shorter aperture closure distance observed in PD patients apparently is a result of the hypometria of their grip aperture and bradykinesia of hand transport movement, rather than a consequence of a deficit in transport-grasp coordination. It is also concluded that the perturbation of target location does not disrupt the transport-grasp coordination in either healthy individuals or PD patients.

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“…In Equation , the fault described by ϕ i ( x , u ). f i can be detected with a filter of the form

\dot{\hat{x} ((), t)} = A_{σ} \overset{x}{true} ((), t) + B_{σ} normalu ((), t) + L_{σ} ((), y ((), t) - \overset{y}{true} ((), t)), \overset{y}{true} ((), t) = normalC \overset{x}{true} ((), t),

where

\overset{x}{true} ((), t)

is an estimate of the state vector x(t) from Equation , y(t) is the measured output, and

\overset{y}{true} ((), t)

is the estimated output. In each active mode of the system determined by σ , L σ is chosen in such a way that the vector f i associated with the particular fault will manifest in the filter residual.…”

Section: Converter Fault Diagnosismentioning

confidence: 99%

Fault diagnosis in switched‐linear systems by emulation of behavioral models on FPGA: A case study of current‐mode buck converter

Bhattacharya

Kumar

Biswas

2017

Int J Numerical Modelling

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This paper presents an Field‐Programmable Gate Array (FPGA)‐based fault emulation and detection framework for switched‐linear systems commonly encountered in power electronics. The proposed framework exploits high‐level behavioral modeling that maps analog functionality into fixed‐point architectures supported by FPGAs. This work is mainly concerned with modeling and validation of effectiveness of a fault diagnoser of a power converter much before its fabrication. The proposed concept of fault diagnosis at presilicon stage overcomes several reliability issues in power electronic systems and enables design and development of test resources, verification of test bed, and interconnecting circuitry at an early stage of the design. To illustrate applicability of this environment, well‐accepted fault events including hard and soft faults are emulated with the help of a nonideal model of a buck converter and a piecewise linear detection filter, which follow an observer‐based residual generation for fault detection. The paper also shows that the proposed method is equally applicable for detection of faults under unstable operation of the converter. The effectiveness of the proposed framework is evaluated through FPGA‐based simulation (or “emulation”) of a peak‐current‐mode–controlled buck‐type switching converter implemented on Xilinx Kintex‐7 FPGA in MATLAB/Simulink environment with Xilinx System Generator support. To the best of our knowledge, fault diagnosis in power converter by emulation of its nonideal model on FPGA is attempted for the first time in the literature. Experimental results show that power converter faults can be easily detected by monitoring detection filter residuals while some of the faults can be precisely identified.

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Foundations of Deterministic and Stochastic Control

Cited by 40 publications

References 0 publications

Extracting information from AGN variability

Extracting information from AGN variability

Control of aperture closure during reach-to-grasp movements in parkinson’s disease

Fault diagnosis in switched‐linear systems by emulation of behavioral models on FPGA: A case study of current‐mode buck converter

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