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Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions [Kõva köide]

, (Department of Electrical Engineering, Institute of Technical Education & Research, SOA University, Bhubaneswar, India)
  • Formaat: Hardback, 248 pages, kõrgus x laius: 234x156 mm, kaal: 480 g, 28 Tables, black and white; 66 Illustrations, black and white
  • Ilmumisaeg: 24-Oct-2012
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466517298
  • ISBN-13: 9781466517295
Teised raamatud teemal:
Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal FunctionsSuurem pilt
  • Formaat: Hardback, 248 pages, kõrgus x laius: 234x156 mm, kaal: 480 g, 28 Tables, black and white; 66 Illustrations, black and white
  • Ilmumisaeg: 24-Oct-2012
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1466517298
  • ISBN-13: 9781466517295
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781466517295.html
Märksõnad:
"This book presents the developments in problems of state estimation and optimal control of continuous-time dynamical systems using orthogonal functions since 1975. It deals with both full and reduced-order state estimation and problems of linear time-invariant systems. It also addresses optimal control problems of varieties of continuous-time systems such as linear and nonlinear systems, time-invariant and time-varying systems, as well as delay-free and time-delay systems. Content focuses on developmentof recursive algorithms for studying state estimation and optimal control problems"--



Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional.

This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria.

Illustrated throughout with detailed examples, the book covers topics including:

  • Block-pulse functions and shifted Legendre polynomials
  • State estimation of linear time-invariant systems
  • Linear optimal control systems incorporating observers
  • Optimal control of systems described by integro-differential equations
  • Linear-quadratic-Gaussian control
  • Optimal control of singular systems
  • Optimal control of time-delay systems with and without reverse time terms
  • Optimal control of second-order nonlinear systems
  • Hierarchical control of linear time-invariant and time-varying systems

Arvustused

" provides a good introduction of using orthogonal function approaches for state estimation and optimal control problems. the first book Ive seem that puts it all together in one text. The authors provide several detailed examples that clearly explain how the shown theory can be applied. This makes it much easier to understand the basic algorithms." John L. Crassidis, University at Buffalo, State University of New York

"The approach and selection of topics are very appropriate, because the book has considered all the important components of optimal control problems using orthogonal functions. Overall, the book is quite good and comprehensive." Anish Deb, University of Caluctta, India

"A majority of the presentation relies on existing results; the authors main contribution is contained in Chapters 710. This book may be useful to postgraduate and doctoral students interested in system and control theory as well as inspiring to control engineers." Zentralblatt Math,Vol. 1272

List of Abbreviations
xi
List of Figures
xiii
Preface xix
Acknowledgements xxi
About the Authors xxiii
1 Introduction
1(10)
1.1 Optimal Control Problem
1(2)
1.2 Historical Perspective
3(5)
1.3 Organisation of the Book
8(3)
2 Orthogonal Functions and Their Properties
11(24)
2.1 Introduction
11(3)
2.2 Block-Pulse Functions (BPFs)
14(5)
2.2.1 Integration of B(t)
15(1)
2.2.2 Product of two BPFs
16(1)
2.2.3 Representation of C(t)f(t) in terms of BPFs
16(1)
2.2.4 Representation of a time-delay vector in BPFs
17(1)
2.2.5 Representation of reverse time function vector in BPFs
18(1)
2.3 Legendre Polynomials (LPs)
19(1)
2.4 Shifted Legendre Polynomials (SLPs)
20(10)
2.4.1 Integration of L(t)
22(1)
2.4.2 Product of two SLPs
23(1)
2.4.3 Representation of C(t)f(t) in terms of SLPs
24(1)
2.4.4 Representation of a time-delay vector function in SLPs
25(2)
2.4.5 Derivation of a time-advanced matrix of SLPs
27(1)
2.4.6 Algorithm for evaluating the integral in Eq. (2.75)
28(2)
2.4.7 Representation of a reverse time function vector in SLPs
30(1)
2.5 Nonlinear Operational Matrix
30(2)
2.6 Rationale for Choosing BPFs and SLPs
32(3)
3 State Estimation
35(30)
3.1 Introduction
35(3)
3.2 Inherent Filtering Property of OFs
38(1)
3.3 State Estimation
39(8)
3.3.1 Kronecker product method
43(1)
3.3.2 Recursive algorithm via BPFs
43(1)
3.3.3 Recursive algorithm via SLPs
44(1)
3.3.4 Modification of the recursive algorithm of Sinha and Qi-Jie
45(2)
3.4 Illustrative Examples
47(11)
3.5 Conclusion
58(7)
4 Linear Optimal Control Systems Incorporating Observers
65(14)
4.1 Introduction
65(3)
4.2 Analysis of Linear Optimal Control Systems Incorporating Observers
68(4)
4.2.1 Kronecker product method
69(1)
4.2.2 Recursive algorithm via BPFs
70(1)
4.2.3 Recursive algorithm via SLPs
71(1)
4.3 Illustrative Example
72(5)
4.4 Conclusion
77(2)
5 Optimal Control of Systems Described by Integro-Differential Equations
79(10)
5.1 Introduction
79(1)
5.2 Optimal Control of LTI Systems Described by Integro-Differential Equations
80(4)
5.3 Illustrative Example
84(2)
5.4 Conclusion
86(3)
6 Linear-Quadratic-Gaussian Control
89(20)
6.1 Introduction
89(1)
6.2 LQG Control Problem
90(3)
6.3 Unified Approach
93(4)
6.3.1 Illustrative example
96(1)
6.4 Recursive Algorithms
97(8)
6.4.1 Recursive algorithm via BPFs
101(1)
6.4.2 Recursive algorithm via SLPs
102(2)
6.4.3 Illustrative example
104(1)
6.5 Conclusion
105(4)
7 Optimal Control of Singular Systems
109(16)
7.1 Introduction
109(2)
7.2 Recursive Algorithms
111(4)
7.2.1 Recursive algorithm via BPFs
113(1)
7.2.2 Recursive algorithm via SLPs
114(1)
7.3 Unified Approach
115(2)
7.4 Illustrative Examples
117(4)
7.5 Conclusion
121(4)
8 Optimal Control of Time-Delay Systems
125(34)
8.1 Introduction
126(3)
8.2 Optimal Control of Multi-Delay Systems
129(17)
8.2.1 Using BPFs
133(2)
8.2.2 Using SLPs
135(2)
8.2.3 Time-invariant systems
137(1)
8.2.4 Delay free systems
138(1)
8.2.5 Illustrative examples
138(8)
8.3 Optimal Control of Delay Systems with Reverse Time Terms
146(9)
8.3.1 Using BPFs
151(2)
8.3.2 Using SLPs
153(1)
8.3.3 Illustrative example
154(1)
8.4 Conclusion
155(4)
9 Optimal Control of Nonlinear Systems
159(10)
9.1 Introduction
159(1)
9.2 Computation of the Optimal Control Law
160(2)
9.3 Illustrative Examples
162(4)
9.4 Conclusion
166(3)
10 Hierarchical Control of Linear Systems
169(30)
10.1 Introduction
169(1)
10.2 Hierarchical Control of LTI Systems with Quadratic Cost Functions
170(4)
10.2.1 Partial feedback control
172(1)
10.2.2 Interaction prediction approach
173(1)
10.3 Solution of Hierarchical Control Problem via BPFs
174(6)
10.3.1 State transition matrix
175(2)
10.3.2 Riccati matrix and open-loop compensation vector
177(1)
10.3.3 State vector
178(2)
10.3.4 Adjoint vector and local control
180(1)
10.3.5 Coordination
180(1)
10.3.6 Error
180(1)
10.4 Extension to Linear Time-Varying Systems
180(3)
10.5 Computational Algorithm
183(1)
10.6 Illustrative Examples
184(6)
10.7 Conclusion
190(9)
11 Epilogue
199(4)
Bibliography 203(14)
Index 217
B.M. Mohan, S.K. Kar