Download Advanced Topics in Control and Estimation of by Eli Gershon PDF

By Eli Gershon

Complicated subject matters up to the mark and Estimation of State-Multiplicative Noisy structures starts with an advent and wide literature survey. The textual content proceeds to hide the sector of H∞ time-delay linear structures the place the problems of balance and L2−gain are awarded and solved for nominal and unsure stochastic platforms, through the input-output process. It offers strategies 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 keep an eye on 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 an eye on and estimation of the platforms within the H∞ feel, for either continuous-time and discrete-time instances. The ebook additionally describes distinctive issues comparable to stochastic switched structures with stay time and peak-to-peak filtering of nonlinear stochastic structures. The reader is brought to 6 useful engineering- orientated examples of noisy state-multiplicative keep watch over and filtering difficulties for linear and nonlinear platforms. The publication is rounded out by means of a three-part appendix containing stochastic instruments useful for a formal appreciation of the textual content: a simple advent to stochastic keep watch over tactics, facets 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 issues up to speed and Estimation of State-Multiplicative Noisy structures can be of curiosity to engineers engaged on top of things structures study and improvement, to graduate scholars focusing on stochastic keep an eye on concept, and to utilized mathematicians drawn to keep an eye on difficulties. The reader is predicted to have a few acquaintance with stochastic regulate idea and state-space-based optimum keep watch over idea and techniques for linear and nonlinear systems.

Table of Contents

Cover

Advanced themes 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 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 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 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 strong 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 regulate - The Nominal Case
2.5.2 strong State-Feedback keep an eye on - 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 strong Filtering - The Norm-Bounded Case
2.6.3 strong Polytopic Stochastic Filtering
2.6.4 instance - Filtering
2.7 Stochastic Output-Feedback keep an eye on 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 strong 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 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 behind schedule 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 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 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 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 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 regulate of Switched Systems
13.4 Non Linear structures: size Output-Feedback Control
13.5 Discrete-Time Non Linear structures: l2-Gain
13.6 L-infinity keep watch over and Estimation

A Appendix: Stochastic keep watch over tactics - simple Concepts

B The LMI Optimization Method

C Stochastic Switching with stay Time - Matlab Scripts

References

Index

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

Example text

23) holds if the following inequality holds: 2 T ζ T (t) ¯ GT QH Ψ¯11 Q(A1 − m) + α ζ(t)+h2 y¯T (t)R2 y¯(t) < 0, ∗ −R1 + H T QH where Ψ¯11 = Q(A0 + m) + (A0 + m)T Q + 1 R1 + GT QG + QmR2−1 mT Q. 24) 1 R1 + GT QG. 1. 24). 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 .

1a–c) where B2 = 0, D12 = 0, C¯2 = 0 and consider the following general-type estimator: dˆ x(t) = Ac x ˆ(t)dt + Bc y(t), zˆ = Cc x ˆ(t). 5) and we consider the following cost function: ∞ Δ JF = E{ ∞ ||¯ z (t)||2 dt − γ 2 [ 0 ∞ ||w(t)||2 dt + 0 ||n(t)||2 dt]}. 6) is negative for all nonzero w(t), n(t) ˜ 2 ([0, ∞); Rq ), n(t) ∈ L ˜ 2 ([0, T ]; Rp ). 1a–c). 3), for the worst-case disturbance ˜ 2 ([0, ∞); Rq ) and measurement noise n(t) ∈ L ˜ 2 ([0, T ]; Rp ), and for w(t) ∈ L Ft Ft the prescribed scalar γ > 0.

Fk ||2R the product fkT Rfk . f the Euclidean norm of f. Ev {·} the expectation operator with respect to v. , N }. , N }. the trace of a matrix. the Kronecker delta function. the Dirac delta function. the set of natural numbers. 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 .

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