Published March 14, 2005
by Springer .
Written in English
|Contributions||Didier Henrion (Editor), Andrea Garulli (Editor)|
|The Physical Object|
|Number of Pages||316|
Positive Polynomials in Control originates from an invited session presented at the IEEE CDC and gives a comprehensive overview of existing results in this quickly emerging area. Rating: (not yet rated) 0 with reviews - Be the first. Positive Polynomials in Control originates from an invited session presented at the IEEE CDC and gives a comprehensive overview of existing results in this quickly emerging area. This carefully edited book collects important contributions from several fields of control, optimization, and mathematics, in order to show different views and approaches of polynomial by: Applied on appropriate cones, standard duality in convex optimization nicely expresses the duality between moments and positive polynomials. In the second part, the methodology is particularized and described in detail for various applications, including global optimization, probability, optimal control, mathematical finance, multivariate. In mathematics, a positive polynomial on a particular set is a polynomial whose values are positive on that set.. Let p be a polynomial in n variables with real coefficients and let S be a subset of the n-dimensional Euclidean space ℝ say that: p is positive on S if p(x) > 0 for every x ∈ S.; p is non-negative on S if p(x) ≥ 0 for every x ∈ S.; p is zero on S if p(x) = 0 for every.
Positive Trigonometric Polynomials and Signal Processing Applications (Signals and Communication Technology) [Bogdan Dumitrescu] on *FREE* shipping on qualifying offers. This book gathers the main recent results on positive trigonometric polynomials within a unitary framework. The book has two parts: theory and applications. The theory of sum-of-squares trigonometric polynomials . The book is organized in three parts, reflecting the current trends in the area: 1. applications of positive polynomials and LMI optimization to solve various control problems, 2. a mathematical overview of different algebraic techniques used to cope with polynomial positivity, 3. numerical aspects of positivity of polynomials, and recently. Positive 1D and 2D Systems Book Summary: Moving on from earlier stochastic and robust control paradigms, this book introduces the reader to the fundamentals of probabilistic methods in the analysis and design of uncertain systems. It significantly reduces the computational cost of high-quality control and the complexity of the algorithms involved. Moments, Positive Polynomials and Their Applications Jean-Bernard Lasserre Many important problems in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of .
An Introduction to Polynomial and Semi-Algebraic Optimization; Cited by. Crossref Citations. This book has been cited by the following publications. This list is generated based on data D. and Garulli, A. (editors), Positive Polynomials in Control, pp. – Lecture Notes in Control and Information Science, vol. Berlin Cited by: Positive polynomials obviously form a convex set and were recently studied in the area of convex optimization [1, 5]. It was shown in [2, 5] that positive polynomial matrices can be parametrized. Positive polynomial matrices play a fundamental role in systems and control theory. We give here a simplified proof of the fact that the convex set of positive polynomial matrices can be. As with the original book, the theory of sum-of-squares trigonometric polynomials is presented unitarily based on the concept of Gram matrix (extended to Gram pair or Gram set). The programming environment has also evolved, and the books examples are changed accordingly.