Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Bücher
Zeitschriften
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
ATZ-Fachkongress

Chassis.tech plus 2024


4 Kongresse in einer Veranstaltung

Treffen Sie in München die Fachleute von Chassis, Lenkung, Bremsen sowie Reifen/Räder.
Erweiterte Suche
Anmelden
nach oben

2000 | Buch

Preliminaries Kapitel lesen Erstes Kapitel lesen

Bounded Dynamic Stochastic Systems

Modelling and Control

verfasst von: Hong Wang, BSc, MEng, PhD

Verlag: Springer London

Buchreihe : Advances in Industrial Control

Enthalten in: Professional Book Archive

Einloggen, um Zugang zu erhalten
insite
SUCHEN

Über dieses Buch

Over the past decades, although stochastic system control has been studied intensively within the field of control engineering, all the modelling and control strategies developed so far have concentrated on the performance of one or two output properties of the system. such as minimum variance control and mean value control. The general assumption used in the formulation of modelling and control strategies is that the distribution of the random signals involved is Gaussian. In this book, a set of new approaches for the control of the output probability density function of stochastic dynamic systems (those subjected to any bounded random inputs), has been developed. In this context, the purpose of control system design becomes the selection of a control signal that makes the shape of the system outputs p.d.f. as close as possible to a given distribution. The book contains material on the subjects of: - Control of single-input single-output and multiple-input multiple-output stochastic systems; - Stable adaptive control of stochastic distributions; - Model reference adaptive control; - Control of nonlinear dynamic stochastic systems; - Condition monitoring of bounded stochastic distributions; - Control algorithm design; - Singular stochastic systems.
A new representation of dynamic stochastic systems is produced by using B-spline functions to descripe the output p.d.f. Advances in Industrial Control aims to report and encourage the transfer of technology in control engineering. The rapid development of control technology has an impact on all areas of the control discipline. The series offers an opportunity for researchers to present an extended exposition of new work in all aspects of industrial control.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Preliminaries
Abstract
It is well known that control for stochastic systems has been an important subject of research over the past decades. This is because a majority of industrial processes exhibit stochastic behaviour. As a result, many approaches have been developed and widely used successfully in real applications. Successful and most representative examples are minimum variance control ([2, 3]), selftuning control ([4, 14, 47]), stochastic linear quadratic control ([1, 17]) and jumping parameter systems ([12]).
Hong Wang
Chapter 2. Control of SISO Stochastic Systems: A Fundamental Control law
Abstract
In this chapter the controller design for SISO stochastic systems will be considered, where the purpose of controller design is to select a control input so that the output probability density function of the system output can follow a given stochastic distribution as close as possible. For this purpose, the model representation will be discussed first. Since B-splines artificial neural networks are used to represent the coupled links between control input variables and the considered probability density functions, in the next section fundamental aspects on B-splines neural networks will be given.
Hong Wang
Chapter 3. Control of Mimo Stochastic Systems: Robustness and Stability
Abstract
In Chapter 2, modelling and control algorithms for SISO stochastic systems have been presented, where the fundamental form of the control strategy is derived. However, in practice many systems are subjected to multiple inputs and external disturbances. An added modelling error will also present when B-spline functions are used to approximate the output probability density function of the stochastic system. As such, a control algorithm for MIMO stochastic systems should be formulated. This forms the main part of this chapter, where robust control algorithms will be described together with closed loop stability analysis.
Hong Wang
Chapter 4. Realization of Perfect Tracking
Abstract
In Chapters 1 and 2, several control algorithms have been described ([41, 42, 43]) on the control of the output probability density functions of the stochastic systems. Using the B-spline approximations, the dynamic part of the stochastic system has been logically decoupled from the output density function itself. This leads to a group offeedback control algorithms (2.5.10), (2.5.12), (2.5.20), (2.5.22), (3.3.15) and (3.4.18), where it has been shown that the control inputs are always related to the weighted integration of the measured probability density functions of the system. However, in these approaches, the design criteria has been set to minimize a finite indexed quadratic performance function which characterises the tracking performance of the output probability density function with respect to a given density function. Although the control algorithm obtained can minimise the performance function, it cannot always guarantee the perfect tracking of the output probability density function with respect to the given distribution.
Hong Wang
Chapter 5. Stable Adaptive Control of Stochastic Distributions
Abstract
The stochastic systems considered in Chapters 2–4 are all known systems. In this chapter, an adaptive solution is presented for unknown stochastic systems, where again the purpose of control is to make the output probability density function of the system as close as possible to a given distribution function. Also, the control algorithm should guarantee the closed loop stability whilst improving the tracking performance of the system.
Hong Wang
Chapter 6. Model Reference Adaptive Control
Abstract
Control algorithms discussed in Chapters 2–5 are generally based on the discrete-time model and in most cases the input and output models are used to formulate the algorithm. In this chapter, an alternative approach will be described using the state space model. We will only consider unknown continuous-time linear systems, where the model reference adaptive control algorithm ([20, 21, 19, 25]) will be applied to design stable adaptive control input which
  • stablizes the closed loop system, and
  • realises the perfect tracking of the output probability density function with respect to the given distribution.
Hong Wang
Chapter 7. Control of Nonlinear Stochastic Systems
Abstract
The work presented so far has been focussed on linear dynamic systems where several modelling and control algorithms have been developed and are shown to work well for some linear systems ([41, 44]). However, due to the wide existence of nonlinear systems in practice, it is also important to investigate the control algorithms for the control of the output probability density functions for general nonlinear stochastic systems. This forms the main purpose of this chapter, where an extended solution to the control of nonlinear systems will be described. We will present two solutions, one for a specific class of nonlinear system and the other for a general system as given in Equation (2.8.1). The former will involve the use of a one-step-ahead nonlinear predictor whilst the later will need the use of Multi-Layer Perceptron (MLP) neural networks ([49]). The stability of the closed loop control for the specific class of nonlinear system will also be formulated.
Hong Wang
Chapter 8. Application to Fault Detection
Abstract
Research into condition monitoring, or fault detection and diagnosis, for dynamic systems has long been recognised as one of the important aspects in seeking effective solutions to an improved reliability of practical control systems. As a result, many methods have been developed in the past two decades. In general, these approaches can be classified into the following three groups:
i)
Observer based fault detection and diagnosis for systems whose models are almost known;
 
ii)
Identification based fault detection and diagnosis for systems whose models are unknown;
 
iii)
Unexpected change detection for stochastic signals.
 
Hong Wang
Chapter 9. Advanced Topics
Abstract
In Chapters 2–8, modelling, control and fault detection algorithms have been developed, where in terms of the control algorithm design, the focus has been made on the control of the total shape of the output probability density functions of stochastic systems. In these approaches, the stochastic system considered has its outputs taken as the measured probability density functions of the system output and its inputs as a set of deterministic variables. As shown in Fig 9.1, these variables affect the shape of the probability density functions of the system output. The purpose here is to design a control strategy u(k), k = 0,1,2, … so that the output probability density function of the considered stochastic system follows the given distribution as close as possible.
Hong Wang
Backmatter
Metadaten
Titel
Bounded Dynamic Stochastic Systems
verfasst von
Hong Wang, BSc, MEng, PhD
Copyright-Jahr
2000
Verlag
Springer London
Electronic ISBN
978-1-4471-0481-0
Print ISBN
978-1-4471-1151-1
DOI
https://doi.org/10.1007/978-1-4471-0481-0