New PDF release: Advanced Topics in Control and Estimation of

By Eli Gershon

ISBN-10: 1447150694

ISBN-13: 9781447150695

Complicated issues up to the mark 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 platforms the place the problems of balance and L2−gain are offered and solved for nominal and unsure stochastic structures, through the input-output process. It offers strategies to the issues of state-feedback, filtering, and measurement-feedback keep an eye on 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 keep watch over also are offered and solved. the second one a part of the monograph issues non-linear stochastic nation- multiplicative structures and covers the problems of balance, keep an eye on and estimation of the structures within the H∞ experience, for either continuous-time and discrete-time instances. The ebook additionally describes distinctive issues akin 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 keep an eye on and filtering difficulties for linear and nonlinear platforms. The e-book is rounded out through a three-part appendix containing stochastic instruments helpful for a formal appreciation of the textual content: a uncomplicated creation to stochastic regulate strategies, elements of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback regulate difficulties of stochastic switched structures with dwell-time. complicated subject matters up to the mark 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 regulate thought, and to utilized mathematicians drawn to regulate difficulties. The reader is anticipated to have a few acquaintance with stochastic keep an eye on idea and state-space-based optimum keep an eye on concept and strategies for linear and nonlinear systems.

Table of Contents

Cover

Advanced themes 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 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 methods - 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 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 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 actual 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 watch over - The Nominal Case
2.5.2 strong 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 behind schedule Systems
2.6.1 Stochastic Filtering - The Nominal Case
2.6.2 powerful Filtering - The Norm-Bounded Case
2.6.3 strong 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 regulate - The Nominal Case
2.7.2 instance - Output-Feedback Control
2.7.3 powerful Stochastic Output-Feedback keep an eye on - The Norm-Bounded Case
2.7.4 powerful Polytopic Stochastic Output-Feedback Control
2.8 Static Output-Feedback Control
2.9 powerful 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 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 keep watch over 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 actual 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 structures - 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 - size 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 strong 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 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 regulate 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 strong 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 keep watch over of Switched Systems
13.4 Non Linear platforms: size Output-Feedback Control
13.5 Discrete-Time Non Linear structures: l2-Gain
13.6 L-infinity keep an eye on and Estimation

A Appendix: Stochastic keep watch over approaches - easy Concepts

B The LMI Optimization Method

C Stochastic Switching with stay Time - Matlab Scripts

References

Index

Show description

By Eli Gershon

ISBN-10: 1447150694

ISBN-13: 9781447150695

Complicated issues up to the mark 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 platforms the place the problems of balance and L2−gain are offered and solved for nominal and unsure stochastic structures, through the input-output process. It offers strategies to the issues of state-feedback, filtering, and measurement-feedback keep an eye on 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 keep watch over also are offered and solved. the second one a part of the monograph issues non-linear stochastic nation- multiplicative structures and covers the problems of balance, keep an eye on and estimation of the structures within the H∞ experience, for either continuous-time and discrete-time instances. The ebook additionally describes distinctive issues akin 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 keep an eye on and filtering difficulties for linear and nonlinear platforms. The e-book is rounded out through a three-part appendix containing stochastic instruments helpful for a formal appreciation of the textual content: a uncomplicated creation to stochastic regulate strategies, elements of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback regulate difficulties of stochastic switched structures with dwell-time. complicated subject matters up to the mark 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 regulate thought, and to utilized mathematicians drawn to regulate difficulties. The reader is anticipated to have a few acquaintance with stochastic keep an eye on idea and state-space-based optimum keep an eye on concept and strategies for linear and nonlinear systems.

Table of Contents

Cover

Advanced themes 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 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 methods - 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 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 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 actual 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 watch over - The Nominal Case
2.5.2 strong 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 behind schedule Systems
2.6.1 Stochastic Filtering - The Nominal Case
2.6.2 powerful Filtering - The Norm-Bounded Case
2.6.3 strong 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 regulate - The Nominal Case
2.7.2 instance - Output-Feedback Control
2.7.3 powerful Stochastic Output-Feedback keep an eye on - The Norm-Bounded Case
2.7.4 powerful Polytopic Stochastic Output-Feedback Control
2.8 Static Output-Feedback Control
2.9 powerful 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 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 keep watch over 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 actual 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 structures - 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 - size 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 strong 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 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 regulate 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 strong 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 keep watch over of Switched Systems
13.4 Non Linear platforms: size Output-Feedback Control
13.5 Discrete-Time Non Linear structures: l2-Gain
13.6 L-infinity keep an eye on and Estimation

A Appendix: Stochastic keep watch over approaches - easy Concepts

B The LMI Optimization Method

C Stochastic Switching with stay Time - Matlab Scripts

References

Index

Show description

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

Example text

The delay independent BRL is readily obtained from the latter LMI by deleting the 3rd and 5th column and row blocks in Γ and by choosing Qm = 0 in Ψ˜11 and Ψ¯12 . 12). 6. 12). 5 T = Ψˆ11,i + C i 1 C i 1 , = QAi1 − Qm , T = −R1 + H i QH i , T = h f (Ai0 Q + QTm ), T = h f (Ai1 Q − QTm ). 32) that stabilizes the system and achieves a prescribed level of attenuation. 32), where A0 is replaced by A0 + B2 K, C1 is replaced by C1 + D12 K and where we assume, for simplicity, that α ¯ = 0. 5 Stochastic State-Feedback Control ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣ Υ11 QA1 − Qm Qm 33 QB1 Υ15 Ψ˜25 Υ16 GT Q 0 0 0 ∗ −R1 + H T QH 0 T 0 ∗ ∗ − f Q 0 −h f Qm 0 0 ∗ ∗ ∗ −γ 2 Iq h f B1T Q 0 0 0 ∗ ∗ ∗ ∗ − fQ ∗ ∗ ∗ ∗ ∗ −Ir 0 ∗ ∗ ∗ ∗ ∗ ∗ −Q ⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ < 0, ⎥ ⎥ ⎥ ⎥ ⎦ where Υ11 = QB2 K + K T B2T Q + QA0 + Qm + A0 T Q + QTm + 1 1−d R1 , Υ15 = h f ([A0 + B2 K]T Q + QTm ), Υ16 = (C1 + D12 K)T , Ψ˜25 = h f (A1 T Q − QTm ).

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.

In order to remain in the linear domain, we pre-choose the matrix Cc at the cost of some overdesign. 13. 1a-c). 56). 58) with a pre-chosen structure of Cc . 4. Note that if one pursuits the method of [104] and apply it to the solution of the delayed output-feedback control problem, it will be necessary to incorporate the delay also in the structure of the controller. 54), admittedly involving an overdesign. The above structure of Q used in [58] for the solution of the discrete-time stochastic output-feedback control problem and has been shown to yield good results.

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Advanced Topics in Control and Estimation of State-Multiplicative Noisy Systems by Eli Gershon


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