Optimal and Robust Control Advanced Topics with MATLAB®

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.

Modelling of uncertain systems and the robust control problemUncertainty and robust controlThe essential chronology of major findings into robust controlFundamentals of stabilityLyapunov criteriaPositive definite matricesLyapunov theory for linear time-invariant systemsLyapunov equationsStability with uncertaintyExercisesKalman canonical decompositionIntroductionControllability canonical partitioningObservability canonical partitioningGeneral partitioningRemarks on Kalman decompositionExercisesSingular value decompositionSingular values of a matrixSpectral norm and condition number of a matrixExercisesOpen-loop balanced realizationControllability and observability gramiansPrincipal component analysisPrincipal component analysis applied to linear systemsState transformations of gramiansSingular values of linear time-invariant systemsComputing the open-loop balanced realizationBalanced realization for discrete-time linear systemsExercisesReduced order modelsReduced order models based on the open-loop balanced realizationReduced order model exercisesExercisesSymmetrical systemsReduced order models for SISO systemsProperties of symmetrical systemsThe cross-gramian matrixRelations between W2c , W2o and WcoOpen-loop parameterizationRelation between the Cauchy index and the Hankel matrixSingular values for a FIR filterSingular values of all-pass systemsExercisesLinear quadratic optimal controlLQR optimal controlHamiltonian matricesResolving the Riccati equation by Hamiltonian matrixThe Control Algebraic Riccati EquationOptimal control for SISO systemsLinear quadratic regulator with cross-weighted costFinite-horizon linear quadratic regulatorOptimal control for discrete-time linear systemsExercisesClosed-loop balanced realizationFiltering Algebraic Riccati EquationComputing the closed-loop balanced realizationProcedure for closed-loop balanced realizationReduced order models based on closed-loop balanced realizationClosed-loop balanced realization for symmetrical systemsExercisesPassive and bounded-real systemsPassive systemsCircuit implementation of positive-real systemsBounded-real systemsRelationship between passive and bounded-real systemsExercisesH8 linear controlIntroductionSolution of the H8 linear control problemThe H8 linear control and the uncertainty problemExercisesLinear Matrix Inequalities for optimal and robust controlDefinition and properties of LMILMI problemsFormulation of control problems in LMI termsSolving a LMI problemLMI problem for simultaneous stabilizabilitySolving algebraic Riccati equations through LMIComputation of gramians through LMIComputation of the Hankel norm through LMIH8 controlMultiobjective controlExercisesThe class of stabilizing controllersParameterization of stabilizing controllers for stable processesParameterization of stabilizing controllers for unstable processesParameterization of stable controllersSimultaneous stabilizability of two systemsCoprime factorizations for MIMO systems and unitary factorizationParameterization in presence of uncertaintyExercisesRecommended essential referencesAppendix A. NormsAppendix B. Algebraic Riccati EquationsIndex

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.