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Mathematical optimization is the selection of the best element in a set with respect to a given criterion. Optimization has become one of the most-used tools in modern control theory for computing the control law, adjusting the controller parameters (tuning), model fitting, and finding suitable conditions in order to fulfill a given closed-loop property, among others. In the simplest case, optimization consists of maximizing or minimizing a function by systematically choosing input values from a valid input set and computing the function value. Nevertheless, real-world control systems need to comply with several conditions and constraints that have to be taken into account in the problem formulation—these represent challenges in the application of the optimization algorithms. The aim of this Special Issue is to offer the state-of-the-art of the most advanced optimization techniques (online and offline) and their applications in control engineering.]

optimization --- optimal control --- optimal conditions

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Model predictive control (MPC) is an advanced control design used in many industries worldwide. An MPC selects control actions which are optimal with respect to a given performance metric as well as any physically-motivated constraints. MPC has therefore gained significant research attention over the past several decades. Advances in MPC continue to unlock its potential to solve a wide variety of practical issues. This book presents some of the state-of-the-art in MPC design from theoretical and applications perspectives. It covers a broad spectrum of MPC application areas, reviewing applications as diverse as air conditioning, pharmaceutical manufacturing, mineral column flotation, actuator faults, and hydraulic fracturing, while also highlighting recent theoretical advancements in control technology that integrate it with data-driven models, zone tracking, or process safety and cybersecurity. Both centralized and distributed MPC formulations are presented. The purpose of this book is to assemble a collection of current research in MPC that handles practically-motivated theoretical issues as well as recent MPC applications, with the aim of highlighting the significant potential benefits of new MPC theory and design.

receding horizon control --- optimal control --- predictive control

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optimal control --- mathematical modeling --- differential equations --- dynamical systems --- pdes

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This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.

Calculus of variations. --- Algorithms. --- Mathematics. --- Visualization. --- Calculus of Variations and Optimal Control; Optimization.

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This volume presents original contributions from renowned researchers in sports economics, management, and optimization.The book discusses up-to-date developments in several topics, including resource allocation strategies in sports industry, impact of the financial crisis on professional sports around the world, fairness in sports competitions, and optimization-based gambling strategies. "Optimal Strategies in Sports Economics and Management" will be of interest not only to students, researchers and practitioners involved with the sports industry, but also to the general public interested in sports such as soccer, hockey, American football, basketball, golf, and jai alai.

Mathematics. --- Financial Economics. --- Control. --- Calculus of Variations and Optimal Control; Optimization. --- Mathematics. --- Mathematical optimization. --- Finance. --- Mathématiques --- Optimisation mathématique --- Finances