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- 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 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. Exercises. Kalman canonical decomposition. Introduction. Controllability canonical partitioning. Observability canonical partitioning. General partitioning. Remarks on Kalman decomposition. Exercises. Singular value decomposition. Singular values of a matrix. Spectral norm and condition number of a matrix. Exercises. 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. Exercises. Reduced order models. Reduced order models based on the open-loop balanced realization. Reduced order model exercises. 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. Exercises. 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. Exercises. 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. Exercises. Passive and bounded-real systems. Passive systems. Circuit implementation of positive-real systems. Bounded-real systems. Relationship between passive and bounded-real systems. Exercises. H- linear control. Introduction. Solution of the H- linear control problem. The H- linear control and the uncertainty problem. Exercises. 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 LMIH-control. Multiobjective control. Exercises. 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. Exercises. Recommended essential references. Appendix A. Norms. Appendix B. Algebraic Riccati Equations. Index.

Academic researchers and R&D; electrical, electronic, computer science, space and automation engineers working in automatic control and advanced topics; mechanical and other engineers; control engineers; engineers working on automation and robust control applications such as power system control, electric drives for transport applications, environmental control, building automation and energy saving, chemical industrial process, aerospace and control of large flexible structures, automotive, drug control, vibration control in large structures, biosystems control, robotics, and factory automation.