Piermarco Cannarsa - Böcker

Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations. The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions.

Semiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations.The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions.

This book presents important recent applied mathematics research on environmental problems and impacts due to climate change. The book also provides useful material and mathematical problem-solving tools for doctoral programs dealing with the complexities of climate change.

This book presents important recent applied mathematics research on environmental problems and impacts due to climate change. The book also provides useful material and mathematical problem-solving tools for doctoral programs dealing with the complexities of climate change.

The book consists of the proceedings of the workshop "New Trends and Challenges in Optimization Theory Applied to Space Engineering", held in l'Aquila (Italy), and organized by the Gran Sasso Science Institute (GSSI), on December 13-15, 2023. The main purpose of the book is to provide an overview of the most important current topics concerning optimal control in space. Optimal control theory is an exciting research area, where both new theoretical approaches and application problems come into play. The “New Trends and Challenges in Optimization Theory Applied to Space Engineering” conference brought together influential academic researchers and experts from industry and government to build bridges between their respective groups. The topics of the conference panels are selected to include the most advanced areas of interest for space applications. In line with the mission of the Gran Sasso Tech Foundation, interdisciplinary dialogue is promoted between the sciences, and different experts are encouraged to work together to identify new problems and generate new solutions. Covering a wide range of space-related topics and challenges, this conference aims to lay the foundation for a long-term collaboration between different groups of experts. A broad overview of control theory applications in space is presented, highlighting the most recent aspects, both from a theoretical and practical point of view, in particular on the following topics: - manifold dynamics, trajectory design and related control aspects;- AI techniques in guidance control problems and space missions;- optimization techniques for constellations with applications to space operations;- multi-stage control problems for launch and landing problems;- optimal control problems in the presence of uncertain parameters;- improved sufficient and necessary conditions in optimal control problems for space problems. New methods, specific mathematical models, ad hoc algorithms and heuristics, innovative mission scenarios, and advances in classical control theory are presented.

Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences. However, since its emergence, there has been a need to rethink and extend fields such as calculus of variations, differential geometry and nonsmooth analysis, which are closely tied to research on applications. Today control theory is a rich source of basic abstract problems arising from applications, and provides an important frame of reference for investigating purely mathematical issues. In many fields of mathematics, the huge and growing scope of activity has been accompanied by fragmentation into a multitude of narrow specialties. However, outstanding advances are often the result of the quest for unifying themes and a synthesis of different approaches. Control theory and its applications are no exception. Here, the interaction between analysis and geometry has played a crucial role in the evolution of the field. This book collects some recent results, highlighting geometrical and analytical aspects and the possible connections between them. Applications provide the background, in the classical spirit of mutual interplay between abstract theory and problem-solving practice.

This book introduces readers to theories that play a crucial role in modern mathematics, such as integration and functional analysis, employing a unifying approach that views these two subjects as being deeply intertwined. This feature is particularly evident in the broad range of problems examined, the solutions of which are often supported by generous hints. If the material is split into two courses, it can be supplemented by additional topics from the third part of the book, such as functions of bounded variation, absolutely continuous functions, and signed measures.This textbook addresses the needs of graduate students in mathematics, who will find the basic material they will need in their future careers, as well as those of researchers, who will appreciate the self-contained exposition which requires no other preliminaries than basic calculus and linear algebra.

Since the 1950s control theory has established itself as a major mathematical discipline, particularly suitable for application in a number of research fields, including advanced engineering design, economics and the medical sciences.

This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 (“Mathematics of Planet Earth 2013”). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth’s environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation techniques for climate modeling is amply illustrated in this volume, which also identifies important future challenges.

This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science.

Il libro introduce la teoria della misura e l'analisi funzionale con una coda di argomenti scelti. Contiene un'ampia gamma di esempi ed esercizi, per i quali si forniscono spesso suggerimenti generosi. É rivolto principalmente a studenti della laurea in Matematica e Ingegneria.