Optimal Control of Constrained Piecewise Affine Systems

One of the most important and challenging problems in control is the derivation of systematic tools for the computation of controllers for constrained nonlinear systems that can guarantee closed-loop stability, feasibility, and optimality with respect to some
performance index. This book focuses on the efficient and systematic computation of closed-form optimal controllers for the powerful class of fast-sampled constrained piecewise affine systems. These systems may exhibit rather complex behavior and are equivalent to many other hybrid system formalisms (combining continuous-valued dynamics with logic rules) reported in the literature. Furthermore, piecewise affine
systems are a useful modeling tool that can capture general nonlinearities (e.g. by local approximation), constraints, saturations, switches, and other hybrid modeling phenomena. The first part of the book presents an introduction to the mathematical and control theoretical background material needed for the full understanding of the book. The second part provides an in depth look at the computational and control theoretic properties of the
controllers and part three presents different analysis and post-processing techniques.

From the reviews: The monograph considers the class of constrained piecewise affine systems, and then optimal control and stability. a revised and extended version of the authors PhD thesis written at the Automatic Control Laboratory of ETH Zurich in Switzerland. intended for engineers and researchers in control . (Tommi Sottinen, Zentralblatt MATH, Vol. 1171, 2009)

Inhalt
Background.- Mathematical Necessities.- Systems and Control Theory.- Receding Horizon Control.- Piecewise Affine Systems.- Optimal Control of Constrained Piecewise Affine Systems.- Constrained Finite Time Optimal Control.- Constrained Infinite Time Optimal Control.- Analysis and Post-Processing Techniques for Piecewise Affine Systems.- Linear Vector Norms as Lyapunov Functions.- Stability Analysis.- Stability Tubes.- Efficient Evaluation of Piecewise Control Laws Defined Over a Large Number of Polyhedra.