Categoría de Lusternik-Schnirelmann y funciones de Morse en los espacios simétricos

El primero en la lista de problemas de la teoría de invariantes homotópicos numéricos de T. Ganea es calcular la categoría de variedades familiares: variedades de Stiefel, grupos de Lie, etc. La pregunta de Ganea es de 1970 y, sin embargo, aún no se ha podido responder completamente pues los avances son lentos y difíciles. La dificultad del cálculo directo ha tratado de paliarse introduciendo diferentes técnicas y aproximaciones algebraicas. El objetivo inicial de la presente Memoria era calcular de modo sencillo la categoría de Lusternik-Schnirelmann de algunos grupos de Lie clásicos

Modeling and Control of Complex Physical Systems:The port-hamiltonian approach

Well structured reference book presenting the new paradigm of Port Hamiltionian Systems which has a large potential to be successful in tackling some of the big challenges in modern control theory and engineeringThe potential reference for many new developments taking place in modeling and controlExtend the readers knowledge and understanding of advanced modeling, analysis and control methods using the Port-Hamiltonian Systems paradigmProvides systematic methods for analysis and control, closely linked to the physics of the system. The power of these methods is demonstrated in various physical domain

Cayley-Hamilton for roboticists

The Cayley-Hamilton theorem is an important theorem of linear algebra which is well known and used in system theory. Unfortunately, this powerful result is practically never used in robotics even though it is of extreme relevance. This article is a review of the use of this result for the calculation of general matrix functions which are very common in robotics. It will be shown how any analytic matrix function like exponential, logarithm and more complicated expressions in robotics, can be easily and analytically calculated in an explicit form. Examples are given for the exponential map, inverse of the exponential map, and the derivative of the exponential map. For the first two examples there exist well known expressions in the literature, but the last one is not as easy to compute without the presented method