New Trends In Differential Equations Control Theory And Optimization

The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics. Contents:Dirichlet Problems with Mean Curvature Operator in Minkowski Space (Cristian Bereanu, Petru Jebelean and Călin Şerban)Free Boundary Fluid-Elasticity Interactions: Adjoint Sensitivity Analysis (Lorena Bociu and Kristina Martin)Non-Smooth Regularization of a Forward-Backward Parabolic Equation (Elena Bonetti, Pierluigi Colli and Giuseppe Tomassetti)Approaching Monotone Inclusion Problems via Second Order Dynamical Systems with Linear and Anisotropic Damping (Radu Ioan Boţ and Ernö Robert Csetnek)On the Solutions of a Quadratic Integral Inclusion (Aurelian Cernea)On the Bounded and Stabilizing Solution of a Generalized Riccati Differential Equation with Periodic Coefficients Arising in Connection with a Zero Sum Linear Quadratic Stochastic Differential Game (Vasile Dragan and Toader Morozan)A Maximum Principle for a Class of First Order Differential Operators (Maria Fărcăşeanu, Mihai Mihăilescu and Denisa Stancu-Dumitru)Differentiability and Integrability Properties for Solutions to Nonlocal Equations (Mikil Foss and Petronela Radu)Ferroelectric Thin Structures (Antonio Gaudiello and Kamel Hamdache)Sliding Modes for a Phase-Field System (Gianni Gilardi)Uniformly Hyperbolic Viable Sets in Affine IFS (Vasile Glavan and Valeriu Guţu)Some Support Considerations in the Asymptotic Optimality of Two-Scale Controlled PDMP (Dan Goreac and Oana Silvia Serea)Inverse Problems for Control Theory (Mohammed Al Horani and Angelo Favini)On the Ill-Posedness of Active Scalar Equations with Odd Singular Kernels (Igor Kukavica, Vlad Vicol and Fei Wang)Equilibrium in an Individual — Societal SIR Vaccination Model in Presence of Discounting and Finite Vaccination Capacity (Laetitia Laguzet, Gabriel Turinici and Ghozlane Yahiaoui)On Some Minimization Problems in RN (Mihai Mariş)Recent Results on Multiple Periodic Solutions of Forced Relativistic Pendulum-Type Continuous and Discrete Systems (Jean Mawhin)On the Anisotropic Caginalp Phase-Field System with Singular Nonlinear Terms (Alain Miranville)Space, Time, Similarity (Umberto Mosco)Singularly Perturbed Problems for Abstract Differential Equations of Second Order in Hilbert Spaces (Andrei Perjan and Galina Rusu)Global Controllability and Mixing for the Burgers Equation with Localised Finite-Dimensional External Force (Armen Shirikyan)Boundary Observation in Shape Optimization (Dan Tiba)Recent Progress on Steady Gravity Water Waves (Eugen Vărvărucă) Readership: Researchers in partial differential equations, calculus of variations and optimal control, difference and functional equations.

This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.

"The volume contains a collection of original papers and surveys in various areas of Differential Equations, Control Theory and Optimization written by well-known specialists and is thus useful for PhD students and researchers in applied mathematics."--

This book collects the latest results and new trends in the application of mathematics to some problems in control theory, numerical simulation and differential equations. The work comprises the main results presented at a thematic minisymposium, part of the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019), held in Valencia, Spain, from 15 to 18 July 2019. The topics covered in the 6 peer-review contributions involve applications of numerical methods to real problems in oceanography and naval engineering, as well as relevant results on switching control techniques, which can have multiple applications in industrial complexes, electromechanical machines, biological systems, etc. Problems in control theory, as in most engineering problems, are modeled by differential equations, for which standard solving procedures may be insufficient. The book also includes recent geometric and analytical methods for the search of exact solutions for differential equations, which serve as essential tools for analyzing problems in many scientific disciplines.

This work describes all basic equaitons and inequalities that form the necessary and sufficient optimality conditions of variational calculus and the theory of optimal control. Subjects addressed include developments in the investigation of optimality conditions, new classes of solutions, analytical and computation methods, and applications.

World Scientific Series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. This volume contains 30 research articles on the theory of optimization and its applications by the leading scientists in the field. It is hoped that the material in the present volume will open new vistas in research. Contributors: B D O Anderson, M Bertaja, O J Boxma, O Burdakov, A Cantoni, D J Clements, B D Craven, J B Cruz, Jr., P Diamond, S V Drakunov, Y G Evtushenko, N M Filatov, I Galligani, J C Geromel, F Giannessi, M J Grimble, G O Guardabassi, D-W Gu, C H Houpis, D G Hull, C Itiki, X Jian, M A Johnson, R E Kalaba, J C Kalkkuhl, M R Katebi, T J Kim, P Kloeden, T Kobylarz, A J Laub, C S Lee, G Leitmann, B-G Liu, J Liu, Z-Q Luo, K A Lurie, P Maponi, J B Matson, A Mess, G Pacelli, M Pachter, I Postlethwaite, T Rapcsak, M C Recchioni, Y Sakawa, S V Savastyuk, K Schittkowski, Y Shi, M A Sikora, D D Siljak, K L Teo, C Tovey, P Tseng, F E Udwadia, H Unbehauen, A Vladimirov, B Vo, J F Whidborne, R Xu, P L Yu, V G Zhadan, F Zirilli. Contents:Dual Cones in Spaces of Convex Sets and Fuzzy Sets (P Diamond et al.)Dual Barrier-Projection Methods in Linear Programming (Y G Evtushenko & V G Zhadan)Solving Parameter Identification Problems on a Parallel-Vector Computer (I Galligani & M Bertaja)Appell's Equations of Motion and the Generalized Inverse Form (C Itiki et al.)Dynamic Nonlinear Optimisation Using the Gate Function Approach (M R Katebi et al.)Control Strategies for an Endemic Disease in the Presence of Uncertainty (C S Lee & G Leitmann)On Global Convergence of an Algorithm for Optimal Control of Discrete-Time Systems (Y Sakawa)Parameter Estimation in Differential Equations (K Schittkowski)A Sliding Mode Based Leader-Follower Strategy for Multi-Level Hierarchies (M A Sikora et al.)Synthesis of Adaptive Controllers Using Bicriterial Optimization and Lyapunov Functions (H Unbehauen & N M Filatov)and other papers Readership: Researchers in applied mathematics and mathematical physics. keywords:Optimization Theory

This is the first book to systematically present control theory for stochastic distributed parameter systems, a comparatively new branch of mathematical control theory. The new phenomena and difficulties arising in the study of controllability and optimal control problems for this type of system are explained in detail. Interestingly enough, one has to develop new mathematical tools to solve some problems in this field, such as the global Carleman estimate for stochastic partial differential equations and the stochastic transposition method for backward stochastic evolution equations. In a certain sense, the stochastic distributed parameter control system is the most general control system in the context of classical physics. Accordingly, studying this field may also yield valuable insights into quantum control systems. A basic grasp of functional analysis, partial differential equations, and control theory for deterministic systems is the only prerequisite for reading this book.

Optimization and optimal control are the main tools in decision making. Because of their numerous applications in various disciplines, research in these areas is accelerating at a rapid pace. “Optimization and Optimal Control: Theory and Applications” brings together the latest developments in these areas of research as well as presents applications of these results to a wide range of real-world problems. This volume can serve as a useful resource for researchers, practitioners, and advanced graduate students of mathematics and engineering working in research areas where results in optimization and optimal control can be applied.