Optimal and Robust Control : Advanced Topics with MATLAB® book cover
1st Edition

Optimal and Robust Control
Advanced Topics with MATLAB®

ISBN 9781466501911
Published February 2, 2012 by CRC Press
251 Pages 62 B/W Illustrations

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Book Description

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.

Table of Contents

Modelling of uncertain systems and the robust control problem
Uncertainty and robust control
The essential chronology of major findings into robust control

Fundamentals of stability
Lyapunov criteria
Positive definite matrices
Lyapunov theory for linear time-invariant systems
Lyapunov equations
Stability with uncertainty

Kalman canonical decomposition
Controllability canonical partitioning
Observability canonical partitioning
General partitioning
Remarks on Kalman decomposition

Singular value decomposition
Singular values of a matrix
Spectral norm and condition number of a matrix

Open-loop balanced realization
Controllability and observability gramians
Principal component analysis
Principal component analysis applied to linear systems
State transformations of gramians
Singular values of linear time-invariant systems
Computing the open-loop balanced realization
Balanced realization for discrete-time linear systems

Reduced order models
Reduced order models based on the open-loop balanced realization
Reduced order model exercises

Symmetrical systems
Reduced order models for SISO systems
Properties of symmetrical systems
The cross-gramian matrix
Relations between W2c , W2o and Wco
Open-loop parameterization
Relation between the Cauchy index and the Hankel matrix
Singular values for a FIR filter
Singular values of all-pass systems

Linear quadratic optimal control
LQR optimal control
Hamiltonian matrices
Resolving the Riccati equation by Hamiltonian matrix
The Control Algebraic Riccati Equation
Optimal control for SISO systems
Linear quadratic regulator with cross-weighted cost
Finite-horizon linear quadratic regulator
Optimal control for discrete-time linear systems

Closed-loop balanced realization
Filtering Algebraic Riccati Equation
Computing the closed-loop balanced realization
Procedure for closed-loop balanced realization
Reduced order models based on closed-loop balanced realization
Closed-loop balanced realization for symmetrical systems

Passive and bounded-real systems
Passive systems
Circuit implementation of positive-real systems
Bounded-real systems
Relationship between passive and bounded-real systems

H∞ linear control
Solution of the H∞ linear control problem
The H∞ linear control and the uncertainty problem

Linear Matrix Inequalities for optimal and robust control
Definition and properties of LMI
LMI problems
Formulation of control problems in LMI terms
Solving a LMI problem
LMI problem for simultaneous stabilizability
Solving algebraic Riccati equations through LMI
Computation of gramians through LMI
Computation of the Hankel norm through LMI
H∞ control
Multiobjective control

The class of stabilizing controllers
Parameterization of stabilizing controllers for stable processes
Parameterization of stabilizing controllers for unstable processes
Parameterization of stable controllers
Simultaneous stabilizability of two systems
Coprime factorizations for MIMO systems and unitary factorization
Parameterization in presence of uncertainty

Recommended essential references

Appendix A. Norms

Appendix B. Algebraic Riccati Equations


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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.


"This textbook deals with advanced topics from optimal and robust control and presents these topics in particular for non specialists. ... The book is well-written and provides a self-contained overview about advanced topics in optimal and robust control. It is in particular written for electrical, electronic, computer science, space and automatic engineers interested in automatic control."
—Birgit Jacob (Wuppertal), Zentralblatt MATH, 1248 — 1

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