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E-raamat: Mathematical Methods in Robust Control of Linear Stochastic Systems

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  • Formaat: PDF+DRM
  • Ilmumisaeg: 04-Oct-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461486633
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Mathematical Methods in Robust Control of Linear Stochastic SystemsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 04-Oct-2013
  • Kirjastus: Springer-Verlag New York Inc.
  • Keel: eng
  • ISBN-13: 9781461486633
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This second edition of Mathematical Methods in the Robust Control of Linear Stochastic Systems includes a large number of recent results in the control of linear stochastic systems. More specifically, the new results presented are:

- A unified and abstract framework for Riccati type equations arising in the stochastic control

- Stability and control problems for systems perturbed by homogeneous Markov processes with infinite number of states

- Mixed H2 / H8 control problem and numerical procedures

- Linear differential equations with positive evolution on ordered Banach spaces with applications for stochastic systems including both multiplicative white noise and Markovian jumps represented by a Markov chain with countable infinite set of states

- Kalman filtering for stochastic systems subject both to state dependent noise and Markovian jumps

- H8 reduced order filters for stochastic systems

The book will appeal to graduate students, researchers in advanced control engineering, finance, mathematical systems theory, applied probability and stochastic processes, and numerical analysis.

From Reviews of the First Edition:

This book is concerned with robust control of stochastic systems. One of the main features is its coverage of jump Markovian systems. … Overall, this book presents results taking into consideration both white noise and Markov chain perturbations. It is clearly written and should be useful for people working in applied mathematics and in control and systems theory. The references cited provide further reading sources.

(George Yin, Mathematical Reviews, Issue 2007 m)

This book considers linear time varying stochastic systems, subjected to white noise disturbances and system parameter Markovian jumping, in the context of optimal control … robust stabilization, and disturbance attenuation. … The material presented in the book is organized in seven chapters. … The book is very well written and organized. … is a valuable reference for all researchers and graduate students in applied mathematics and control engineering interested in linear stochastic time varying control systems with Markovian parameter jumping and white noise disturbances.

(Zoran Gajic, SIAM Review, Vol. 49 (3), 2007)

1 Preliminaries to Probability Theory and Stochastic Differential Equations
1(38)
1.1 Elements of Measure Theory
1(5)
1.2 Convergence Theorems for Integrals
6(2)
1.3 Elements of Probability Theory
8(1)
1.4 Independence
9(1)
1.5 Conditional Expectation
9(2)
1.6 Stochastic Processes
11(1)
1.7 Stochastic Processes with Independent Increments
12(1)
1.8 Wiener Processes and Markov process Processes
13(3)
1.9 Stochastic Integral
16(6)
1.10 An Ito's Type Formula
22(7)
1.11 Stochastic Differential Equations
29(4)
1.12 Stochastic Linear Differential Equations
33(3)
1.13 Standard Homogeneous Markov Processes with a Countable Infinite Number of States
36(3)
2 Linear Differential Equations with Positive Evolution on Ordered Banach Spaces
39(82)
2.1 Convex Cones. Minkovski Norms
40(12)
2.2 Linear Differential Equations with Positive Evolution on Ordered Banach Spaces
52(8)
2.3 Exponential Stability of Linear Differential Equations with Positive Evolution on Ordered Banach Spaces
60(17)
2.4 The Case of Differential Equations with Positive Evolution on Ordered Hilbert Spaces
77(4)
2.5 Robustness of Exponential Stability
81(4)
2.6 Lyapunov-Type Linear Differential Equations on the Space SDn
85(16)
2.7 Exponential Stability for Lyapunov-Type Differential Equations on Sdn
101(10)
2.8 Exponential Stability for Lyapunov-Type Differential Equations on S∞n
111(10)
Notes and References
120(1)
3 Exponential Stability in Mean Square
121(42)
3.1 Representation Theorems
122(10)
3.2 Mean Square Exponential Stability
132(10)
3.3 Lyapunov-Type Criteria for Mean Square Exponential Stability in the Case D= {1,2,...,d}
142(7)
3.4 Lyapunov-Type Criteria for Mean Square Exponential Stability in the case V = Z+
149(2)
3.5 Illustrative Examples
151(7)
3.6 Affine Systems
158(5)
Notes and References
162(1)
4 Structural Properties of Linear Stochastic Systems
163(26)
4.1 Stabilizability and Detectability of Stochastic Linear Systems
163(8)
4.2 Stochastic Observability
171(9)
4.3 Stochastic Controllability
180(9)
Notes and References
187(2)
5 A Class of Nonlinear Differential Equations on an Ordered Linear Space of Symmetric Matrices with Applications to Riccati Differential Equations of Stochastic Control
189(76)
5.1 Generalized Riccati Differential Equations: Preliminaries
190(6)
5.2 A Comparison Theorem and Several Consequences
196(4)
5.3 The Maximal Solution of GRDE
200(12)
5.4 The Stabilizing Solution of the GRDE
212(8)
5.5 The Minimal Solution of the GRDE
220(10)
5.6 Systems of Generalized Riccati Equations on the Space Sdn
230(16)
5.7 The Filtering Riccati Equation
246(2)
5.8 Iterative Procedures
248(14)
5.9 Systems of Generalized Riccati Differential Equations on the Space S∞n
262(3)
Notes and References
264(1)
6 Linear Quadratic Optimization Problems for Linear Stochastic Systems
265(22)
6.1 Preliminaries
265(2)
6.2 The Linear Quadratic Optimization Problem for Stochastic Systems: The General Case
267(8)
6.3 The Linear Quadratic Optimal Regulator for a Stochastic System
275(5)
6.4 A Tracking Problem
280(7)
Notes and References
285(2)
7 Stochastic H2 Optimal Control
287(40)
7.1 Stochastic H2 Norms
287(10)
7.2 Stochastic H2 Optimal Control: The Case of Perfect State Measurements
297(7)
7.3 Stochastic H2 Optimal Control: The Output Feedback Control
304(14)
7.4 A Kalman Filtering Problem for Stochastic Systems with State-Dependent Noise and Markovian Jumps
318(9)
Notes and References
326(1)
8 Stochastic Version of Bounded Real Lemma and Applications
327(54)
8.1 Input--Output Operators
327(9)
8.2 Stochastic Version of the Bounded Real Lemma
336(25)
8.3 Robust Stability with Respect to Linear Structured Uncertainties
361(20)
Notes and References
379(2)
9 Robust Stabilization of Linear Stochastic Systems
381(56)
9.1 Formulation of the DAP
381(2)
9.2 Robust Stabilization of Linear Stochastic Systems. The Case of Full State Access
383(15)
9.3 Solution of the DAP in the Case of Output Measurement
398(21)
9.4 DAP for Linear Stochastic Systems with Markovian Jumping
419(7)
9.5 An H∞-Type Filtering Problem for Signals Corrupted with Multiplicative White Noise
426(6)
9.6 A Mixed H2/H∞ Filtering Problem for Stochastic Systems with State-Dependent Noise
432(5)
Notes and References
435(2)
Bibliography 437
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