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# Graduate Texts in Mathematics

01 Jan 1977-

About: The article was published on 1977-01-01 and is currently open access. It has received 8187 citations till now.

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TL;DR: An algorithm--the TPS-RPM algorithm--with the thin-plate spline (TPS) as the parameterization of the non-rigid spatial mapping and the softassign for the correspondence is developed.

1,633 citations

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01 Jan 1998

TL;DR: A comprehensive exposition of the theory of central simple algebras with involution, in relation with linear algebraic groups is given in this article, which provides the algebra-theoretic foundations for much of the recent work on linear algebraIC groups over arbitrary fields.

Abstract: This monograph yields a comprehensive exposition of the theory of central simple algebras with involution, in relation with linear algebraic groups It aims to provide the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields Involutions are viewed as twisted forms of similarity classes of hermitian or bilinear forms, leading to new developments on the model of the algebraic theory of quadratic forms Besides classical groups, phenomena related to triality are also discussed, as well as groups of type F_4 or G_2 arising from exceptional Jordan or composition algebras Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type D_4 For research mathematicians and graduate students working in central simple algebras, algebraic groups, nonabelian Galois cohomology or Jordan algebras

1,216 citations

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27 Jul 2017

TL;DR: Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

Abstract: Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.

1,142 citations

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TL;DR: The three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to: coalgebra, homomorphicism of coalgebrAs, and bisimulation, respectively, which are taken as the basic ingredients of a theory called universal coalgebra.

1,127 citations