New PDF release: Advanced Topics in Control and Estimation of

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By Eli Gershon

ISBN-10: 1447150694

ISBN-13: 9781447150695

Complicated subject matters up to the mark and Estimation of State-Multiplicative Noisy platforms starts with an advent 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 offered and solved for nominal and unsure stochastic platforms, through the input-output method. It offers options 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 keep watch over also are offered and solved. the second one a part of the monograph matters non-linear stochastic kingdom- multiplicative platforms and covers the problems of balance, regulate and estimation of the structures within the H∞ feel, for either continuous-time and discrete-time instances. The e-book additionally describes distinct themes equivalent to stochastic switched structures with live time and peak-to-peak filtering of nonlinear stochastic platforms. 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 booklet is rounded out through a three-part appendix containing stochastic instruments valuable for a formal appreciation of the textual content: a simple advent to stochastic keep an eye on tactics, facets of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback regulate difficulties of stochastic switched platforms with dwell-time. complex subject matters up to the mark and Estimation of State-Multiplicative Noisy platforms can be of curiosity to engineers engaged up to the mark structures study and improvement, to graduate scholars focusing on stochastic keep watch over conception, and to utilized mathematicians drawn to keep an eye on difficulties. The reader is predicted to have a few acquaintance with stochastic regulate concept and state-space-based optimum keep an eye on idea and techniques for linear and nonlinear systems.

Table of Contents

Cover

Advanced issues up to the mark 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 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 techniques - 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 an eye on 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 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 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 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 behind schedule 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 keep watch over - 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 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 regulate 8
3.4 Conclusions

4 monitoring keep watch over 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 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 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 - 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 powerful 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 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 platforms with live 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 an eye on 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 an eye on 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 keep an eye on and Estimation

A Appendix: Stochastic keep an eye on techniques - easy Concepts

B The LMI Optimization Method

C Stochastic Switching with live Time - Matlab Scripts

References

Index

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

Sample text

8) that achieves Jstatic < 0, for the worst-case ˜ 2 ([0, ∞); Rq ) and for a prescribed scalar γ > 0. 3 Stability Criterion We first consider the issue of stability of the stochastic delayed nominal autonomous system and then the stability of the norm-bounded and polytopic uncertain systems. Once the criteria for stability is found, we formulate and obtain the nominal and robust H∞ BRL for the latter system. We use the resulting BRL to solve the state-feedback, filtering, dynamic output-feedback, and static output-feedback control problems that were defined above.

009⎦ , Cc = 1 1 0 . 22 Case No. 22 and various values of d. 7 Stochastic Output-Feedback Control for Delayed Systems 49 achieved for the non-delayed case is, obviously, the lowest one. In cases 2– 5, it is seen that the attenuations levels increase as the bound on the delay derivative (d) increases. Similar behavior appears for different delay lengths (not shown). Also, the maximum value of the derivative bound is reduced as the delay length is increased. 10). 14. 10). 56) which includes the adˆ T 1H ˆ T 2H ˆ 0 in Υ¯11 and the additional term of H ˆ 1 in the ditional term of H 0 1 (2, 2) block, where ˆ0 = E0 , E 0 ˆ1 = E1 , E 0 ¯0 H ¯ 2 Cc , ˆ0 = H H ¯1 0 .

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. 9). 8) that achieves Jstatic < 0, for the worst-case ˜ 2 ([0, ∞); Rq ) and for a prescribed scalar γ > 0. 3 Stability Criterion We first consider the issue of stability of the stochastic delayed nominal autonomous system and then the stability of the norm-bounded and polytopic uncertain systems.

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