Optimal control of constrained piecewise affine systems

Frank J. Christophersen

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.

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  • I Background.- Mathematical Necessities.- Systems and Control Theory.- Receding Horizon Control.- Piecewise Affine Systems.- II Constrained Optimal Control of Piecewise Affine Systems.- Constrained Finite Time Optimal Control.- Constrained Infinite Time Optimal Control.- III 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 over a Large Number of Polyhedra.

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書名 Optimal control of constrained piecewise affine systems
著作者等 Christophersen Frank
Christophersen Frank J.
シリーズ名 Lecture notes in control and information sciences
出版元 Springer
刊行年月 [2007]
ページ数 xxvii, 189 p.
大きさ 24 cm
ISBN 9783540727002
NCID BA82882448
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言語 英語
出版国 ドイツ