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By Eli Gershon

Complicated themes up to the mark and Estimation of State-Multiplicative Noisy platforms starts off with an creation 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 structures, through the input-output technique. 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 provided and solved. the second one a part of the monograph issues non-linear stochastic country- multiplicative platforms and covers the problems of balance, keep watch over and estimation of the platforms within the H∞ experience, for either continuous-time and discrete-time situations. The e-book additionally describes detailed subject matters equivalent to stochastic switched structures with stay time and peak-to-peak filtering of nonlinear stochastic platforms. 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 way 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 approaches, facets of linear matrix inequality optimization, and MATLAB codes for fixing the L2-gain and state-feedback keep an eye on difficulties of stochastic switched structures with dwell-time. complicated themes up to speed and Estimation of State-Multiplicative Noisy platforms could be of curiosity to engineers engaged on top of things structures examine and improvement, to graduate scholars focusing on stochastic regulate idea, and to utilized mathematicians attracted to keep watch over difficulties. The reader is anticipated to have a few acquaintance with stochastic keep an eye on concept and state-space-based optimum keep an eye on concept and techniques for linear and nonlinear systems.

Table of Contents


Advanced themes up to speed and Estimation of State-Multiplicative Noisy Systems

ISBN 9781447150695 ISBN 9781447150701



1 Introduction

1.1 Stochastic State-Multiplicative Time hold up Systems
1.2 The Input-Output process 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 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 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 strong balance - The Norm-Bounded Case
2.3.3 powerful balance - The Polytopic Case
2.4 Bounded genuine Lemma
2.4.1 BRL for not on time 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 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 regulate for not on time Systems
2.7.1 Stochastic Output-Feedback keep an eye on - 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 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 not on time 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 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 structures - 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 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 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 reside 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 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 keep an eye on and Estimation

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

B The LMI Optimization Method

C Stochastic Switching with stay Time - Matlab Scripts



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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.

4 1 T R1 + Gi QGi . 1a,c) with B2 = 0 and D12 = 0 and the following index of performance ∞ Δ JB = E{ 0 ∞ ||z(t)||2 dt − γ 2 ||w(t)||2 dt}. 24) is satisfied, we seek a condition that guarantees the following: ∞ E [LV + z T (t)z(t) − γ 2 wT (t)w(t)]dt < 0, 0 where in the expression for E{LV } the operators Δ1 and Δ2 are used. 4. 1a,c) with B2 = 0 and D12 = 0. 1 = QA0 + Qm + AT0 Q + QTm + = QA1 − Qm + α ¯ GT QH, = h f AT0 Q + h f QTm , = −R1 + H T QH, = h f AT1 Q − h f QTm . 10). 5. 1a,c) with B2 = 0 and D12 = 0.

20) 1 and ||Δ2 ||∞ ≤ h are diagonal operators having identiwhere ||Δ1 ||∞ ≤ √1−d cal scalar operators on the main diagonal. 20) are usually derived using the small gain theorem. 3 Stability Criterion 27 xT (t)Δ¯T1 Δ¯1 x(t) ≤ (1 − d)−1 x(t) 2 and y¯T (t)Δ¯T2 Δ¯2 y¯(t) ≤ h2 y¯(t) 2 . 19), with B1 = 0, and the following positive definite function: V (x) = xT Qx, where Q > 0 is a constant matrix. g. [133]) and taking expectation we obtain: ¯2 y¯(t)] } E{(LV )(t)} = E{ Qx(t), [(A0 + m)x(t) + (A1 − m)Δ¯1 x(t) − mΔ T +E{T r{Q[Gx(t) Hw1 (t)]P¯ [Gx(t) Hw1 (t)] }}, 1α ¯ is the covariance matrix of the augmented Wiener process α ¯ 1 vector col{β(t) ν(t)}, that is E{col{β(t) ν(t)}{β(t) ν(t)}} = P¯ t.

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