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Title:
Optimal and robust control : advanced topics with MATLAB́
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Publication Information:
Boca Raton, FL : CRC Press, c2012
Physical Description:
xviii, 233 p. : ill. ; 25 cm.
ISBN:
9781466501911
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30000010297796 TJ217.2 F67 2012 Open Access Book Book
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Summary

Summary

While there are many books on advanced control for specialists, there are few that present these topics for nonspecialists. Assuming only a basic knowledge of automatic control and signals and systems, Optimal and Robust Control: Advanced Topics with MATLAB® offers a straightforward, self-contained handbook of advanced topics and tools in automatic control.

Techniques for Controlling System Performance in the Presence of Uncertainty

The book deals with advanced automatic control techniques, paying particular attention to robustness--the ability to guarantee stability in the presence of uncertainty. It explains advanced techniques for handling uncertainty and optimizing the control loop. It also details analytical strategies for obtaining reduced order models. The authors then propose using the Linear Matrix Inequalities (LMI) technique as a unifying tool to solve many types of advanced control problems.

Topics covered include:

LQR and H-infinity approaches Kalman and singular value decomposition Open-loop balancing and reduced order models Closed-loop balancing Passive systems and bounded-real systems Criteria for stability control

This easy-to-read text presents the essential theoretical background and provides numerous examples and MATLAB exercises to help the reader efficiently acquire new skills. Written for electrical, electronic, computer science, space, and automation engineers interested in automatic control, this book can also be used for self-study or for a one-semester course in robust control.


Author Notes

Luigi Fortuna is a Full Professor of System Theory at the University of Catania, Italy. He was the coordinator of the courses in electronic engineering and Head of the Dipartimento di Ingegneria Elettrica Elettronica e dei Sistemi (DIEES). Since 2005, he has been the Dean of the Engineering Faculty. He currently teaches complex adaptive systems and robust control. He has published more than 450 technical papers and is the coauthor of ten scientific books. His scientific interests include robust control, nonlinear science and complexity, chaos, cellular neural networks, soft-computing strategies for control and robotics, micronanosensor and smart devices for control, and nanocellular neural networks modeling. Dr. Fortuna is an IEEE Fellow.

Mattia Frasca received his PhD in Electronics and Automation Engineering in 2003, at the University of Catania, Italy. Currently, he is a research associate at the University of Catania, where he also teaches systems theory. His scientific interests include robust control, nonlinear systems and chaos, cellular neural networks, complex systems, and bio-inspired robotics. He is involved in many research projects and collaborations with industries and academic centers. He is also a referee for many international journals and conferences. Dr. Frasca was on the organizing committee of the 10th Experimental Chaos Conference and was co-chair of the 4th International Conference on Physics and Control. He is the coauthor of three research monographs, has published more than 150 papers in refereed international journals and international conference proceedings, and is the coauthor of two international patents. He is also a Senior Member of IEEE.

For more information on Dr. Frasca's work, see his web page at the University of Catania.


Table of Contents

List of Figuresp. xi
Prefacep. xv
Symbol Listp. xvii
1 Modelling of uncertain systems and the robust control problemp. 1
1.1 Uncertainty and robust controlp. 1
1.2 The essential chronology of major findings into robust controlp. 6
2 Fundamentals of stabilityp. 9
2.1 Lyapunov criteriap. 9
2.2 Positive definite matricesp. 11
2.3 Lyapunov theory for linear time-invariant systemsp. 14
2.4 Lyapunov equationsp. 18
2.5 Stability with uncertaintyp. 21
2.6 Exercisesp. 24
3 Kalman canonical decompositionp. 27
3.1 Introductionp. 27
3.2 Controllability canonical partitioningp. 29
3.3 Observability canonical partitioningp. 31
3.4 General partitioningp. 32
3.5 Remarks on Kalman decompositionp. 39
3.6 Exercisesp. 40
4 Singular value decompositionp. 43
4.1 Singular values of a matrixp. 43
4.2 Spectral norm and condition number of a matrixp. 45
4.3 Exercisesp. 50
5 Open-loop balanced realizationp. 51
5.1 Controllability and observability gramiansp. 51
5.2 Principal component analysisp. 54
5.3 Principal component analysis applied to linear systemsp. 55
5.4 State transformations of gramiansp. 58
5.5 Singular values of linear time-invariant systemsp. 60
5.6 Computing the open-loop balanced realizationp. 61
5.7 Balanced realization for discrete-time linear systemsp. 65
5.8 Exercisesp. 67
6 Reduced order modelsp. 69
6.1 Reduced order models based on the open-loop balanced realizationp. 70
6.1.1 Direct truncation methodp. 71
6.1.2 Singular perturbation methodp. 72
6.2 Reduced order model exercisesp. 74
6.3 Exercisesp. 77
7 Symmetrical systemsp. 79
7.1 Reduced order models for SISO systemsp. 79
7.2 Properties of symmetrical systemsp. 81
7.3 The cross-gramian matrixp. 83
7.4 Relations between W c 2 and W o op. 83
7.5 Open-loop parameterizationp. 89
7.6 Relation between the Cauchy index and the Hankel matrixp. 91
7.7 Singular values for a FIR filterp. 92
7.8 Singular values of all-pass systemsp. 95
7.9 Exercisesp. 96
8 Linear quadratic optimal controlp. 99
8.1 LQR optimal controlp. 99
8.2 Hamiltonian matricesp. 105
8.3 Resolving the Riccati equation by Hamiltonian matrixp. 109
8.4 The Control Algebraic Riccati Equationp. 110
8.5 Optimal control for SISO systemsp. Ill
8.6 Linear quadratic regulator with cross-weighted costp. 117
8.7 Finite-horizon linear quadratic regulatorp. 117
8.8 Optimal control for discrete-time linear systemsp. 118
8.9 Exercisesp. 119
9 Closed-loop balanced realizationp. 121
9.1 Filtering Algebraic Riccati Equationp. 122
9.2 Computing the closed-loop balanced realizationp. 124
9.3 Procedure for closed-loop balanced realizationp. 125
9.4 Reduced order models based on closed-loop balanced realizationp. 127
9.5 Closed-loop balanced realization for symmetrical systemsp. 131
9.6 Exercisesp. 132
10 Passive and bounded-real systemsp. 135
10.1 Passive systemsp. 135
10.1.1 Passivity in the frequency domainp. 136
10.1.2 Passivity in the time domainp. 141
10.1.3 Factorizing positive-real functionsp. 143
10.1.4 Passificationp. 143
10.1.5 Passive reduced order modelsp. 148
10.1.6 Energy considerations connected to the Positive-Real Lemmap. 148
10.1.7 Closed-loop stability and positive-real systemsp. 149
10.1.8 Optimal gain for loss-less systemsp. 150
10.2 Circuit implementation of positive-real systemsp. 152
10.3 Bounded-real systemsp. 153
10.3.1 Properties of bounded-real systemsp. 156
10.3.2 Bounded-real reduced order modelsp. 157
10.4 Relationship between passive and bounded-real systemsp. 157
10.5 Exercisesp. 158
11 H∞ linear controlp. 161
11.1 Introductionp. 161
11.2 Solution of the H∞ linear control problemp. 163
11.3 The H∞ linear control and the uncertainty problemp. 168
11.4 Exercisesp. 171
12 Linear Matrix Inequalities for optimal and robust controlp. 173
12.1 Definition and properties of LMIp. 173
12.2 LMI problemsp. 175
12.2.1 Feasibility problemp. 175
12.2.2 Linear objective minimization problemp. 176
12.2.3 Generalized eigenvalue minimization problemp. 176
12.3 Formulation of control problems in LMI termsp. 176
12.3.1 Stabilityp. 177
12.3.2 Simultaneous stabilizabilityp. 177
12.3.3 Positive real lemmap. 178
12.3 A Bounded real lemmap. 178
12.3.5 Calculating the H∞ norm through LMIp. 178
12.4 Solving a LMI problemp. 179
12.5 LMI problem for simultaneous stabilizabilityp. 181
12.6 Solving algebraic Riccati equations through LMIp. 184
12.7 Computation of gramians through LMIp. 187
12.8 Computation of the Hankel norm through LMIp. 188
12.9 H∞ controlp. 190
12.10 Multiobjective controlp. 192
12.11 Exercisesp. 198
13 The class of stabilizing controllersp. 201
13.1 Parameterization of stabilizing controllers for stable processesp. 201
13.2 Parameterization of stabilizing controllers for unstable processesp. 203
13.3 Parameterization of stable controllersp. 206
13.4 Simultaneous stabilizability of two systemsp. 209
13.5 Coprime facto rizations for MIMO systems and unitary factorizationp. 210
13.6 Parameterization in presence of uncertaintyp. 211
13.7 Exercisesp. 214
Recommended essential referencesp. 217
Appendix A Normsp. 223
Appendix B Algebraic Riccati Equationsp. 227
Indexp. 231