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The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. Well-known dynamic programming arguments show there is a direct relationship between the solution of a control problem and the solution of a corresponding Hamilton–Jacobi–Bellman (HJB) partial differential equation (PDE). The max-plus-based methods examined in this monograph belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated HJB PDEs; they are not equivalent to either of the more commonly used finite element or characteristic approaches. The potential advantages of the max-plus-based approaches lie in the fact that solution operators for nonlinear HJB problems are linear over the max-plus algebra, and this linearity is exploited in the construction of algorithms. The book will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods. Researchers and practitioners tangentially interested in this area will also find a readable, concise discussion of the subject through a careful selection of specific chapters and sections. Basic knowledge of control theory for systems with dynamics governed by differential equations is required.

Nonlinear control theory. --- Matrices. --- Algebra, Matrix --- Cracovians (Mathematics) --- Matrix algebra --- Matrixes (Algebra) --- Algebra, Abstract --- Algebra, Universal --- Control theory --- Nonlinear theories --- Global analysis (Mathematics). --- Mathematics. --- Algebra. --- System theory. --- Differential equations, partial. --- Analysis. --- Applications of Mathematics. --- Systems Theory, Control. --- Control, Robotics, Mechatronics. --- Partial Differential Equations. --- Partial differential equations --- Mathematics --- Mathematical analysis --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Systems, Theory of --- Systems science --- Philosophy --- Systems theory. --- Mathematical analysis. --- Analysis (Mathematics). --- Applied mathematics. --- Engineering mathematics. --- Control engineering. --- Robotics. --- Mechatronics. --- Partial differential equations. --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Engineering instruments --- Programmable controllers --- Engineering --- Engineering analysis --- 517.1 Mathematical analysis

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The central focus of this book is the control of continuous-time/continuous-space nonlinear systems. Using new techniques that employ the max-plus algebra, the author addresses several classes of nonlinear control problems, including nonlinear optimal control problems and nonlinear robust/H-infinity control and estimation problems. Several numerical techniques are employed, including a max-plus eigenvector approach and an approach that avoids the curse-of-dimensionality. Well-known dynamic programming arguments show there is a direct relationship between the solution of a control problem and the solution of a corresponding Hamilton-Jacobi-Bellman (HJB) partial differential equation (PDE). The max-plus-based methods examined in this monograph belong to an entirely new class of numerical methods for the solution of nonlinear control problems and their associated HJB PDEs; they are not equivalent to either of the more commonly used finite element or characteristic approaches. The potential advantages of the max-plus-based approaches lie in the fact that solution operators for nonlinear HJB problems are linear over the max-plus algebra, and this linearity is exploited in the construction of algorithms. The book will be of interest to applied mathematicians, engineers, and graduate students interested in the control of nonlinear systems through the implementation of recently developed numerical methods. Researchers and practitioners tangentially interested in this area will also find a readable, concise discussion of the subject through a careful selection of specific chapters and sections. Basic knowledge of control theory for systems with dynamics governed by differential equations is required.

Partial differential equations --- Applied physical engineering --- Engineering sciences. Technology --- Computer. Automation --- procesautomatisering --- differentiaalvergelijkingen --- analyse (wiskunde) --- informatica --- systeemtheorie --- wiskunde --- systeembeheer --- ingenieurswetenschappen --- regeltechniek

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The volume presents recent mathematical methods in the area of optimal control with a particular emphasis on the computational aspects and applications. Optimal control theory concerns the determination of control strategies for complex dynamical systems in order to optimize measures of their performance. The field was created in the 1960's, in response to the pressures of the "space race" between the US and the former USSR, but it now has a far wider scope and embraces a variety of areas ranging from process control to traffic flow optimization, renewable resources exploitation and financial market management. These emerging applications require increasingly efficient numerical methods to be developed for their solution – a difficult task due the huge number of variables. Providing an up-to-date overview of several recent methods in this area, including fast dynamic programming algorithms, model predictive control and max-plus techniques, this book is intended for researchers, graduate students and applied scientists working in the area of control problems, differential games and their applications.

Numerical analysis --- Mathematics --- Applied physical engineering --- Engineering sciences. Technology --- Computer science --- Recreation. Games. Sports. Corp. expression --- computers --- economie --- informatica --- spellen --- systeemtheorie --- wiskunde --- informaticaonderzoek --- systeembeheer --- ingenieurswetenschappen --- computerkunde --- numerieke analyse