Bayesian Control of a Discrete-Time Linear System with Uniformly Distributed Disturbances

Walczak, Dariusz

doi:10.14708/ma.v43i2.827

Cited by 1 publication

(2 citation statements)

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“…, for n = 0, 1, ..., M −1, i = 1, 2, ..., k. In addition (see [19,20]) by direct calculation we get Lemma 1. The following equations are fulfilled:…”

Section: Filteringmentioning

confidence: 79%

“…Duncan & Pasik-Duncan [6]) and the disturbance distributions (cf. Walczak [19,20]). Stochastic discrete time systems have many applications which we have described in [3] where the Bayes control of the linear system with quadratic cost function and the disturbances having the distribution belonging to the exponential family with conjugate priors is solved.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Non-autonomous Stochastic Discrete Time System with Uniform Disturbances

Dassios

Szajowski

2016

IFIP Advances in Information and Communication Technology

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The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family.

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“…, for n = 0, 1, ..., M −1, i = 1, 2, ..., k. In addition (see [19,20]) by direct calculation we get Lemma 1. The following equations are fulfilled:…”

Section: Filteringmentioning

confidence: 79%