By Eli Gershon

ISBN-10: 1447150694

ISBN-13: 9781447150695

Complex issues up to speed and Estimation of State-Multiplicative Noisy platforms starts off with an creation and wide 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 structures, through the input-output technique. It provides suggestions to the issues of state-feedback, filtering, and measurement-feedback keep watch over for those platforms, 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 awarded and solved. the second one a part of the monograph issues non-linear stochastic kingdom- multiplicative structures and covers the problems of balance, keep watch over and estimation of the platforms within the H∞ feel, for either continuous-time and discrete-time circumstances. The ebook additionally describes particular themes comparable to stochastic switched structures with stay time and peak-to-peak filtering of nonlinear stochastic platforms. The reader is brought to 6 sensible engineering- orientated examples of noisy state-multiplicative regulate and filtering difficulties for linear and nonlinear structures. The e-book is rounded out by way of a three-part appendix containing stochastic instruments important for a formal appreciation of the textual content: a easy creation to stochastic keep an eye on strategies, points of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback keep an eye on difficulties of stochastic switched platforms with dwell-time. complicated issues on top of things and Estimation of State-Multiplicative Noisy platforms may be of curiosity to engineers engaged up to speed structures study and improvement, to graduate scholars focusing on stochastic regulate concept, and to utilized mathematicians drawn to keep an eye on difficulties. The reader is anticipated to have a few acquaintance with stochastic regulate conception and state-space-based optimum keep an eye on idea and strategies for linear and nonlinear systems.

Table of Contents

Cover

Advanced themes up to speed 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 technique for not on time Systems

1.2.1 Continuous-Time Case

1.2.2 Discrete-Time Case

1.3 Non Linear keep watch over 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 platforms - H-infinity keep watch over and General-Type Filtering

2.1 Introduction

2.2 challenge formula and Preliminaries

2.2.1 The Nominal Case

2.2.2 The powerful 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 structures - The Norm-Bounded Case

2.4.2 BRL - The Polytopic Case

2.5 Stochastic State-Feedback Control

2.5.1 State-Feedback keep watch over - The Nominal Case

2.5.2 powerful State-Feedback keep watch over - 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 an eye on for behind schedule Systems

2.7.1 Stochastic Output-Feedback regulate - The Nominal Case

2.7.2 instance - Output-Feedback Control

2.7.3 powerful Stochastic Output-Feedback keep watch over - 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 not on time Stochastic Reduced-Order H keep an eye on 8

3.4 Conclusions

4 monitoring regulate 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 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 behind schedule 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 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 keep an eye on 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 regulate 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 powerful L-infinity-Induced keep watch over and Filtering

12.1 Introduction

12.2 challenge formula and Preliminaries

12.3 balance and P2P Norm sure 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 keep watch over 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 - uncomplicated Concepts

B The LMI Optimization Method

C Stochastic Switching with reside Time - Matlab Scripts

References

Index

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

**Example text**

56). 56) involves a search for two scalar variables: α and f . One may start by line searching for α, taking a ﬁxed value for f , that leads to a stabilizing controller of minimum γ. Once such a controller is obtained, standard optimization techniques can be used, say Matlab function ”fminsearch”, which seek the combination of the two scalar parameters that bring γ to a local minimum. 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).

In other words: N ¯= Ω N ¯ i fi Ω i=1 , fi = 1 i=1 , fi ≥ 0. 3). Our objective is to ﬁnd a state-feedback polytope Ω control law u(t) = Kx(t) that achieves JE < 0, for the worst-case of the pro˜ 2 ([0, ∞); Rq ) and for a prescribed scalar γ > 0. 6). 6) is negative for all nonzero w(t), n(t) where ˜ 2 ([0, ∞); Rq ), n(t) ∈ L ˜ 2 ([0, T ]; Rp ). 3). 7) that achieves JE < 0, for the worst-case distur˜ 2 ([0, ∞); Rq ) and measurement noise n(t) ∈ L ˜ 2 ([0, T ]; Rp ), bance w(t) ∈ L Ft Ft and for a prescribed scalar γ > 0.

45). 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 ].

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