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By Eli Gershon

Complicated issues up to speed and Estimation of State-Multiplicative Noisy structures starts with an advent and huge literature survey. The textual content proceeds to hide the sphere of H∞ time-delay linear platforms the place the problems of balance and L2−gain are offered and solved for nominal and unsure stochastic platforms, through the input-output method. It offers ideas to the issues of state-feedback, filtering, and measurement-feedback keep an eye on 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 provided and solved. the second one a part of the monograph matters non-linear stochastic nation- multiplicative structures 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 targeted themes equivalent to stochastic switched platforms with reside time and peak-to-peak filtering of nonlinear stochastic structures. The reader is brought to 6 functional engineering- orientated examples of noisy state-multiplicative regulate and filtering difficulties for linear and nonlinear structures. The e-book is rounded out through a three-part appendix containing stochastic instruments important for a formal appreciation of the textual content: a simple creation to stochastic keep an eye on methods, features of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback keep watch over difficulties of stochastic switched platforms with dwell-time. complicated subject matters on top of things and Estimation of State-Multiplicative Noisy structures should be of curiosity to engineers engaged on top of things structures examine and improvement, to graduate scholars focusing on stochastic regulate thought, and to utilized mathematicians drawn to keep watch over difficulties. The reader is anticipated to have a few acquaintance with stochastic keep an eye on idea and state-space-based optimum keep watch over conception and techniques for linear and nonlinear systems.

Table of Contents

Cover

Advanced issues on top of things and Estimation of State-Multiplicative Noisy Systems

ISBN 9781447150695 ISBN 9781447150701

Preface

Contents

1 Introduction

1.1 Stochastic State-Multiplicative Time hold up Systems
1.2 The Input-Output method for behind schedule Systems
1.2.1 Continuous-Time Case
1.2.2 Discrete-Time Case
1.3 Non Linear keep an eye on 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 tactics - 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 strong Case - Polytopic doubtful Systems
2.3 balance Criterion
2.3.1 The Nominal Case - Stability
2.3.2 powerful balance - The Norm-Bounded Case
2.3.3 strong balance - The Polytopic Case
2.4 Bounded genuine Lemma
2.4.1 BRL for behind schedule 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 keep an eye on - The Norm-Bounded Case
2.5.3 powerful 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 strong 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 watch over - 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 strong 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 behind schedule Stochastic Reduced-Order H regulate 8
3.4 Conclusions

4 monitoring keep watch over with Preview

4.1 Introduction
4.2 challenge Formulation
4.3 balance of the behind schedule monitoring System
4.4 The State-Feedback Tracking
4.5 Example
4.6 Conclusions
4.7 Appendix

5 H-infinity keep an eye on 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 watch over 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 platforms - dimension Output-Feedback Control

8.1 creation 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 powerful SF keep watch over 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 an eye on 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 watch over of Stochastic Switched structures 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 powerful L-infinity-Induced regulate 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 keep an eye on methods - easy Concepts

B The LMI Optimization Method

C Stochastic Switching with stay Time - Matlab Scripts

References

Index

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Extra info for Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems

Example text

The sample space. σ−algebra of subsets of Ω called events. the probability measure on F . probability of (·). the space of square-summable Rn − valued functions. 10 Abbreviations 19 on the probability space (Ω, F , P). (Fk )k∈N an increasing family of σ−algebras Fk ⊂ F . ˜l2 ([0, N ]; Rn ) the space of nonanticipative stochastic processes. {fk }={fk }k∈[0,N ] in Rn with respect to (Fk )k∈[0,N ) satisfying N N ||fk ||˜2l = E{ 0 ||fk ||2 } = 0 E{||fk ||2 } < ∞ 2 l2 ([0, ∞); Rn ). , fk ∈ ˜ ˜l2 ([0, ∞); Rn ) the above space for N → ∞ ˜ 2 ([0, T ); Rk ) the space of non anticipative stochastic processes.

2 Example – Output-Feedback Control We bring a stationary modified version of an example which is taken from the field of guidance control ([136], see also [53], Chapter 11). 1, A1 = 0, H = 0 and F = 0. The first two components of the state vector x(t) are the pursuer-evader relative position and velocity, respectively, and the third component is the actual pursuer’s acceleration. The control u represents the pursuer’s acceleration command and the delay appears in the measurement of the position. , pursuit.

7). 61) ξ(θ) = 0, over[−h 0], ˜ z˜(t) = Cξ(t), with the following matrices: Aˆ0 = A0 B2 Cc Bc C2 Ac ˜= G , Aˆ1 = G0 0 0 A1 0 ¯2 0 Bc C , F˜ = 0 , ˜= B B1 0 , 0 Bc D21 0 Bc F 0 , C˜ = [C1 D12 Cc ]. 12), the corresponding matrices of uncertain polytopic countertope Ω ˜ i , C˜ i , F˜ i , G ˜i, H ˜ i . 1a–c). 63) where ˜ Aˆi + m) + (Aˆi + m)T Q ˜ + R1 + Qm + mT Q.

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