Optimal Control of Constrained Piecewise Affine Systems [electronic resource] / by Frank J. Christophersen.Material type: TextLanguage: English Series: Lecture Notes in Control and Information Sciences: 359Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007Description: XXVII, 196 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540727019Subject(s): Engineering | Systems theory | Engineering | Control Engineering | Systems Theory, ControlAdditional physical formats: Printed edition:: No titleOnline resources: Click here to access online
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.
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.