Advanced Topics in Control and Estimation of by Eli Gershon

By Eli Gershon

Complicated issues up to speed and Estimation of State-Multiplicative Noisy structures starts with an creation and large literature survey. The textual content proceeds to hide the sphere of H∞ time-delay linear structures the place the problems of balance and L2−gain are provided and solved for nominal and unsure stochastic platforms, through the input-output process. It provides strategies to the issues of state-feedback, filtering, and measurement-feedback keep watch over for those structures, for either the continual- and the discrete-time settings. within the continuous-time area, the issues of reduced-order and preview monitoring regulate also are offered and solved. the second one a part of the monograph matters non-linear stochastic nation- multiplicative platforms and covers the problems of balance, regulate and estimation of the structures within the H∞ experience, for either continuous-time and discrete-time situations. The e-book additionally describes distinctive issues reminiscent of stochastic switched platforms with live time and peak-to-peak filtering of nonlinear stochastic platforms. The reader is brought to 6 sensible engineering- orientated examples of noisy state-multiplicative keep watch over and filtering difficulties for linear and nonlinear platforms. The ebook is rounded out via a three-part appendix containing stochastic instruments beneficial for a formal appreciation of the textual content: a easy advent to stochastic keep watch over techniques, points of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback keep watch over difficulties of stochastic switched structures with dwell-time. complex themes up to speed and Estimation of State-Multiplicative Noisy structures might be of curiosity to engineers engaged on top of things platforms examine and improvement, to graduate scholars focusing on stochastic keep an eye on idea, and to utilized mathematicians drawn to keep an eye on difficulties. The reader is predicted to have a few acquaintance with stochastic keep watch over conception and state-space-based optimum keep watch over thought and techniques for linear and nonlinear systems.

Table of Contents


Advanced issues up to speed and Estimation of State-Multiplicative Noisy Systems

ISBN 9781447150695 ISBN 9781447150701



1 Introduction

1.1 Stochastic State-Multiplicative Time hold up Systems
1.2 The Input-Output process for behind schedule Systems
1.2.1 Continuous-Time Case
1.2.2 Discrete-Time Case
1.3 Non Linear regulate of Stochastic State-Multiplicative Systems
1.3.1 The Continuous-Time Case
1.3.2 Stability
1.3.3 Dissipative Stochastic Systems
1.3.4 The Discrete-Time-Time Case
1.3.5 Stability
1.3.6 Dissipative Discrete-Time Nonlinear Stochastic Systems
1.4 Stochastic approaches - brief Survey
1.5 suggest sq. Calculus
1.6 White Noise Sequences and Wiener Process
1.6.1 Wiener Process
1.6.2 White Noise Sequences
1.7 Stochastic Differential Equations
1.8 Ito Lemma
1.9 Nomenclature
1.10 Abbreviations

2 Time hold up structures - H-infinity regulate and General-Type Filtering

2.1 Introduction
2.2 challenge formula and Preliminaries
2.2.1 The Nominal Case
2.2.2 The strong Case - Norm-Bounded doubtful Systems
2.2.3 The powerful Case - Polytopic doubtful Systems
2.3 balance Criterion
2.3.1 The Nominal Case - Stability
2.3.2 strong balance - The Norm-Bounded Case
2.3.3 powerful balance - The Polytopic Case
2.4 Bounded genuine Lemma
2.4.1 BRL for not on time State-Multiplicative platforms - The Norm-Bounded Case
2.4.2 BRL - The Polytopic Case
2.5 Stochastic State-Feedback Control
2.5.1 State-Feedback keep an eye on - The Nominal Case
2.5.2 powerful State-Feedback regulate - The Norm-Bounded Case
2.5.3 strong Polytopic State-Feedback Control
2.5.4 instance - State-Feedback Control
2.6 Stochastic Filtering for not on time Systems
2.6.1 Stochastic Filtering - The Nominal Case
2.6.2 powerful Filtering - The Norm-Bounded Case
2.6.3 powerful Polytopic Stochastic Filtering
2.6.4 instance - Filtering
2.7 Stochastic Output-Feedback keep watch over for not on time Systems
2.7.1 Stochastic Output-Feedback keep an eye on - The Nominal Case
2.7.2 instance - Output-Feedback Control
2.7.3 powerful Stochastic Output-Feedback regulate - The Norm-Bounded Case
2.7.4 powerful Polytopic Stochastic Output-Feedback Control
2.8 Static Output-Feedback Control
2.9 strong Polytopic Static Output-Feedback Control
2.10 Conclusions

3 Reduced-Order H-infinity Output-Feedback Control

3.1 Introduction
3.2 challenge Formulation
3.3 The not on time Stochastic Reduced-Order H regulate 8
3.4 Conclusions

4 monitoring keep an eye on with Preview

4.1 Introduction
4.2 challenge Formulation
4.3 balance of the not on time monitoring System
4.4 The State-Feedback Tracking
4.5 Example
4.6 Conclusions
4.7 Appendix

5 H-infinity regulate and Estimation of Retarded Linear Discrete-Time Systems

5.1 Introduction
5.2 challenge Formulation
5.3 Mean-Square Exponential Stability
5.3.1 instance - Stability
5.4 The Bounded genuine Lemma
5.4.1 instance - BRL
5.5 State-Feedback Control
5.5.1 instance - strong State-Feedback
5.6 not on time Filtering
5.6.1 instance - Filtering
5.7 Conclusions

6 H-infinity-Like keep an eye on for Nonlinear Stochastic Syste8 ms

6.1 Introduction
6.2 Stochastic H-infinity SF Control
6.3 The In.nite-Time Horizon Case: A Stabilizing Controller
6.3.1 Example
6.4 Norm-Bounded Uncertainty within the desk bound Case
6.4.1 Example
6.5 Conclusions

7 Non Linear platforms - H-infinity-Type Estimation

7.1 Introduction
7.2 Stochastic H-infinity Estimation
7.2.1 Stability
7.3 Norm-Bounded Uncertainty
7.3.1 Example
7.4 Conclusions

8 Non Linear structures - dimension Output-Feedback Control

8.1 advent and challenge Formulation
8.2 Stochastic H-infinity OF Control
8.2.1 Example
8.2.2 The Case of Nonzero G2
8.3 Norm-Bounded Uncertainty
8.4 In.nite-Time Horizon Case: A Stabilizing H Controller 8
8.5 Conclusions

9 l2-Gain and strong SF regulate of Discrete-Time NL Stochastic Systems

9.1 Introduction
9.2 Su.cient stipulations for l2-Gain= .:ASpecial Case
9.3 Norm-Bounded Uncertainty
9.4 Conclusions

10 H-infinity Output-Feedback keep watch over of Discrete-Time Systems

10.1 Su.cient stipulations for l2-Gain= .:ASpecial Case
10.1.1 Example
10.2 The OF Case
10.2.1 Example
10.3 Conclusions

11 H-infinity keep an eye on of Stochastic Switched platforms with stay Time

11.1 Introduction
11.2 challenge Formulation
11.3 Stochastic Stability
11.4 Stochastic L2-Gain
11.5 H-infinity State-Feedback Control
11.6 instance - Stochastic L2-Gain Bound
11.7 Conclusions

12 strong L-infinity-Induced keep an eye on and Filtering

12.1 Introduction
12.2 challenge formula and Preliminaries
12.3 balance and P2P Norm certain of Multiplicative Noisy Systems
12.4 P2P State-Feedback Control
12.5 P2P Filtering
12.6 Conclusions

13 Applications

13.1 Reduced-Order Control
13.2 Terrain Following Control
13.3 State-Feedback regulate of Switched Systems
13.4 Non Linear structures: dimension Output-Feedback Control
13.5 Discrete-Time Non Linear structures: l2-Gain
13.6 L-infinity regulate and Estimation

A Appendix: Stochastic regulate methods - easy Concepts

B The LMI Optimization Method

C Stochastic Switching with live Time - Matlab Scripts



Show description

Read Online or Download Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems PDF

Best system theory books

Reactive systems: modelling, specification and verification

Formal tools is the time period used to explain the specification and verification of software program and software program structures utilizing mathematical good judgment. a number of methodologies were built and included into software program instruments. a major subclass is sent structures. there are numerous books that examine specific methodologies for such structures, e.

Self-Organizing Networks

With the present explosion in community site visitors, and mounting strain on operators’ company case, Self-Organizing Networks (SON) play an important position. they're conceived to lessen human intervention in engineering methods and whilst enhance process functionality to maximise Return-on-Investment (ROI) and safe shopper loyalty.

Quantitative Conservation Biology

Conservation biology is based not just at the basic suggestions, yet at the particular tools, of inhabitants ecology to either comprehend and are expecting the viability of infrequent and endangered species and to figure out how most sensible to regulate those populations. the necessity to behavior quantitative analyses of viability and administration has spawned the sector of "population viability analysis," or PVA, which, in flip, has pushed a lot of the new improvement of helpful and lifelike inhabitants research and modeling in ecology mostly.

AC Electric Motors Control Advanced Design Techniques and Applications

The complexity of AC motor keep an eye on lies within the multivariable and nonlinear nature of AC laptop dynamics. fresh developments on top of things thought now give the chance to house long-standing difficulties in AC automobiles regulate. this article expertly attracts on those advancements to use quite a lot of model-based keep an eye on designmethods to a number of AC vehicles.

Additional resources for Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems

Example text

16) 26 2 Time Delay Systems – H∞ Control and General-Type Filtering ˜ 2 ([0, ∞); Rq ) is an exogenous where x(t) ∈ Rn is the state vector, w(t) ∈ L Ft disturbance, and A0 , A1 , B1 and G, H are time invariant matrices and where β(t), ν(t) are zero-mean real scalar Wiener processes satisfying: E{β(t)β(s)} = min(t, s), E{ν(t)ν(s)} = min(t, s), E{β(t)ν(s)} = α ¯ · min(t, s), |¯ α| ≤ 1. 16), τ (t) is an unknown time-delay which satisfies: 0 ≤ τ (t) ≤ h, τ˙ (t) ≤ d < 1. 17) In order to solve the above problem, we introduce the following operators: Δ (Δ1 g)(t) = g(t − τ (t)), Δ (Δ2 g)(t) = t t−τ (t) g(s)ds.

12). 12. 12). 50). 51) ˜ f hΥi,14 . 47). 5 1 , d = 0. e α ¯ = 0). 11 . 1 Stochastic Output-Feedback Control – The Nominal Case In this section we address the dynamic output-feedback control problem of the delayed state-multiplicative uncertain noisy system [59]. 7). 52) Gξ(t)dβ(t) + F˜ ξ(t)dζ(t), ξ(θ) = 0, over[−h 0], ˜ z˜(t) = Cξ(t), with the following matrices: Aˆ0 = ˜ = H H0 0 0 A0 B2 Cc Bc C2 Ac ˜= , G G0 0 0 , Aˆ1 = , F˜ = A1 0 Bc C¯2 0 0 0 Bc F 0 ˜= , B B1 0 0 Bc D21 , C˜ = [C1 D12 Cc ]. 54) where ˜ Aˆ0 + m) + (Aˆ0 + m)T Q ˜+ Υ11 = Q( 1 R1 .

1. 16) has been done in [55] for the nominal case (with no deterministic norm-bounded uncertainties). 24). 10). 2. 25) ⎢ ⎥<0 ⎢ ∗ ∗ ⎥ ∗ − Q h QE h QE f f 0 f 1 ⎢ ⎥ ⎣ ∗ ∗ ⎦ ∗ ∗ − 1 In 0 ∗ ∗ ∗ ∗ ∗ − 2 In where Ψˆ11 Ψˆ12 Ψˆ14 Ψˆ22 Ψˆ24 = QA0 + Qm + AT0 Q + QTm + = QA1 − Qm + αG ¯ T QH, = h f AT0 Q + h f QTm , ¯ 1T H ¯1 = −R1 + H T QH + 2 H T T = h f A1 Q − h f Qm . 2. The above result provides a delay dependent stability condition. A corresponding delay independent (but rate dependent) result is readily obtained by choosing m = 0 and f → 0.

Download PDF sample

Rated 4.96 of 5 – based on 42 votes