Symbolic Computing in Probabilistic and Stochastic Analysis

Kamiński, Marcin

doi:10.1515/amcs-2015-0069

Cited by 3 publications

(1 citation statement)

References 28 publications

(22 reference statements)

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“…Over the last two decades, the use of symbolic models for control design has spurred on substantial research efforts, among many others; see, e.g., the works of Nilsson (2017), Weber et al (2017), Gruber et al (2017) or Nilsson and Ozay (2020) and the references therein. They are also other symbolic contexts, e.g., symbolic computing, with applications in probabilistic and stochastic analysis (Kamiński, 2015). The main motivation has been handling complex heterogeneous systems that should satisfy complex specifications (Belta et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

On distributed symbolic control of interconnected systems under persistency specifications

Apaza-Perez

Combastel

Zolghadri

2020

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This paper presents an abstraction-based technique to solve the problem of distributed controller design enforcing persistency specifications for interconnected systems. For each subsystem, controller synthesis is based on local distributed sensor information from other subsystems. An effective method is presented for quantification of such partial information in an abstraction in terms of level sets of Lyapunov-like ranking functions. The results are illustrated on a laboratory hydraulic system.

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Section: Introductionmentioning

confidence: 99%

On distributed symbolic control of interconnected systems under persistency specifications

Apaza-Perez

Combastel

Zolghadri

2020

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A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion

Tagade

Choi

2017

International Journal of Applied Mathematics and Computer Science

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This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen-Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.

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Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

Zeifman

Razumchik

Satin

et al. 2018

International Journal of Applied Mathematics and Computer Science

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In this paper we present a method for the computation of convergence bounds for four classes of multiserver queueing systems, described by inhomogeneous Markov chains. Specifically, we consider an inhomogeneous M/M/S queueing system with possible state-dependent arrival and service intensities, and additionally possible batch arrivals and batch service. A unified approach based on a logarithmic norm of linear operators for obtaining sharp upper and lower bounds on the rate of convergence and corresponding sharp perturbation bounds is described. As a side effect, we show, by virtue of numerical examples, that the approach based on a logarithmic norm can also be used to approximate limiting characteristics (the idle probability and the mean number of customers in the system) of the systems considered with a given approximation error.

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Symbolic Computing in Probabilistic and Stochastic Analysis

Cited by 3 publications

References 28 publications

On distributed symbolic control of interconnected systems under persistency specifications

On distributed symbolic control of interconnected systems under persistency specifications

A Dynamic BI–Orthogonal Field Equation Approach to Efficient Bayesian Inversion

Bounds on the rate of convergence for one class of inhomogeneous Markovian queueing models with possible batch arrivals and services

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