✦ LIBER ✦

On the steady state behaviour of stochastic systems

✍ Scribed by P. E. Caines; S. P. Meynt; E. Moscas

Publisher: John Wiley and Sons
Year: 1988
Tongue: English
Weight: 562 KB
Volume: 2
Category: Article
ISSN: 0890-6327
DOI: 10.1002/acs.4480020205

No coin nor oath required. For personal study only.

✦ Synopsis

The question of the existence of steady state solutions to the closed loop system equations for stochastic systems, and in particular ARMAX systems under non-linear feedback control, is addressed. Using the ergodic theory of time-invariant Markov processes, it is shown that corresponding to a large class of control laws there exist shift-invariant probabilities for the joint disturbance input-output processes. This permits an asymptotic analysis of (i) averages of functions of the state process, (ii) the probability distributions governing the state process and (iii) loss functions on the system in the steady state.

KEY WORDS Stochastic systems Steady state ARMAX systems Markov processes

Input-output processes

📜 SIMILAR VOLUMES

Near-optimum steady state regulators for

Near-optimum steady state regulators for stochastic linear weakly coupled systems

✍ Xue-Min Shen; Zoran Gajic 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 406 KB

This paper presents an approach to the decomposition and approximation of the linear quadratic Gaussian estimation and control problems for weakly coupled systems. The global Kalman filter is decomposed into separate reduced-order local filters via the use of a decoupling transformation. A near-opti

A PROPOSAL OF TESTING METHOD ON THE EXAC

A PROPOSAL OF TESTING METHOD ON THE EXACT STEADY STATE PROBABILITY DENSITY FUNCTION OF NON-LINEAR STOCHASTIC SYSTEM

✍ R. WANG; K. YASUDA; Z. ZHANG 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 137 KB

This paper is concerned with the exact analysis method of the response process of second order non-linear stochastic systems excited by Gaussian white noise. A main feature is that a testing method is presented in this paper for the exact steady state probability density of two dimensions to demonst

EXPERIMENTAL AND NUMERICAL ANALYSIS OF T

EXPERIMENTAL AND NUMERICAL ANALYSIS OF THE STEADY STATE BEHAVIOUR OF A BEAM SYSTEM WITH IMPACT

✍ E.L.B. van de Vorst; M.F. Heertjes; D.H. van Campen; A. de Kraker; R.H.B. Fey 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 283 KB

In this paper the steady state behaviour of a beam system with a periodically moving support and an elastic stop is analysed both numerically and experimentally. In the numerical analysis a continuous model for the elastic stop is used based on the contact force law of Hertz. The beam is modelled us

On the steady-state modelling of a two-s

On the steady-state modelling of a two-stage evaporator system

✍ M. N. A. Hawlader; S. K. Chou; K. J. Chua; J. C. Ho; A. S. Mujumdar 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 244 KB 👁 1 views

On the Definitions of Stochastic, Determ

On the Definitions of Stochastic, Deterministic and Near-Stochastic Systems

✍ Iosif Rizkin 📂 Article 📅 1992 🏛 John Wiley and Sons 🌐 English ⚖ 301 KB

Steady States of the Vlasov–Poisson–Fokk

Steady States of the Vlasov–Poisson–Fokker–Planck System

✍ Robert Glassey; Jack Schaeffer; Yuxi Zheng 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 188 KB

The form of steady state solutions to the Vlasov᎐Poisson᎐Fokker᎐Planck system is known from the works of Dressler and others. In these papers an external < < potential is present which tends to infinity as x ª ϱ. It is shown here that this assumption is needed to obtain nontrivial steady states. Thi