Constrained Optimal Control of Linear and Hybrid Systems

Many practical control problems are dominated by characteristics such as state, input and operational constraints, alternations between different operating regimes, and the interaction of continuous-time and discrete event systems. At present no methodology is available to design controllers in a systematic manner for such systems. This book introduces a new design theory for controllers for such constrained and switching dynamical systems and leads to algorithms that systematically solve control synthesis problems. The first part is a self-contained introduction to multiparametric programming, which is the main technique used to study and compute state feedback optimal control laws. The book's main objective is to derive properties of the state feedback solution, as well as to obtain algorithms to compute it efficiently. The focus is on constrained linear systems and constrained linear hybrid systems. The applicability of the theory is demonstrated through two experimental case studies: a mechanical laboratory process and a traction control system developed jointly with the Ford Motor Company in Michigan.

• Constrained Systems
• Hybrid Systems
• Linear Systems
• Multiparametric Programming
• Optimal Control
• algorithm
• algorithms
• programming
• complexity

From the reviews:

"The book focuses on two classes of discrete-time dynamical systems, namely constrained linear systems and linear hybrid systems. … All the main results presented in the book are contributed originally by the author and his collaborators. The style of the book is clear and concise with many illustrative examples. … the book provides a valuable resource for researchers from both academia and industry. The book is also of interest to the operations research community … ." (Hai Lin, IEEE Transactions on Automatic Control, Vol. 50 (7), 2005)

"The book introduces a control design for constrained and switching dynamic systems. … The book is a revised version of the author’s PhD thesis. It presents a self-contained and clearly written text. The book is an up-to-date reference which will be useful to professionals, researchers, practitioners, and graduate students in control, electrical, and mechanical engineering interested in control design problems for constrained and switching dynamic systems." (Lubomír Bakule, Zentralblatt MATH, Vol. 1030, 2005)

"This book … presents a computational approach for optimal and model predictive control of linear and piecewise affine discrete-time systems with (linear) constraints on inputs and states. … This book gives an excellent and extensive introduction and overview of the use of linear, quadratic, and mixed-integer multi-parametric programming for optimal and model predictive control of constrained systems. Furthermore, all the concepts and algorithms are illustrated with many examples and figures. As such, this book is recommended literature for both students and researchers … ." (Bart De Schutter, Mathematical Reviews, Issue 2005 i)

• Automatic Control Labratory, Swiss Federal Institute of Technology, Zürich, Switzerland

  Francesco Borrelli

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