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This monograph presents theoretical methods involving the Hamilton–Jacobi–Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control  synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Dynamics and Control of Trajectory Tubes: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.

Tubes. --- Tubing --- Tubular goods --- Shells (Engineering) --- Mathematical optimization. --- Discrete groups. --- K-theory. --- Calculus of Variations and Optimal Control; Optimization. --- Control and Systems Theory. --- Convex and Discrete Geometry. --- K-Theory. --- Algebraic topology --- Homology theory --- Groups, Discrete --- Infinite groups --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Discrete mathematics --- Calculus of variations. --- Control engineering. --- Convex geometry . --- Discrete geometry. --- Geometry --- Combinatorial geometry --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Automation --- Programmable controllers --- Isoperimetrical problems --- Variations, Calculus of

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This monograph presents theoretical methods involving the Hamilton–Jacobi–Bellman formalism in conjunction with set-valued techniques of nonlinear analysis to solve significant problems in dynamics and control. The emphasis is on issues of reachability, feedback control  synthesis under complex state constraints, hard or double bounds on controls, and performance in finite time. Guaranteed state estimation, output feedback control, and hybrid dynamics are also discussed. Although the focus is on systems with linear structure, the authors indicate how to apply each approach to nonlinear and nonconvex systems. The main theoretical results lead to computational schemes based on extensions of ellipsoidal calculus that provide complete solutions to the problems. These computational schemes in turn yield software tools that can be applied effectively to high-dimensional systems. Dynamics and Control of Trajectory Tubes: Theory and Computation will interest graduate and senior undergraduate students, as well as researchers and practitioners interested in control theory, its applications, and its computational realizations.

Geometry --- Numerical methods of optimisation --- Operational research. Game theory --- Discrete mathematics --- Mathematics --- Physics --- Geology. Earth sciences --- Engineering sciences. Technology --- Artificial intelligence. Robotics. Simulation. Graphics --- discrete wiskunde --- controleleer --- wiskunde --- KI (kunstmatige intelligentie) --- fysica --- kansrekening --- geometrie --- optimalisatie

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Dynamic Programming for Impulse Feedback and Fast Controls offers a description of feedback control in the class of impulsive inputs. This book deals with the problem of closed-loop impulse control based on generalization of dynamic programming techniques in the form of variational inequalities of the Hamilton–Jacobi–Bellman type. It provides exercises and examples in relation to software, such as techniques for regularization of ill-posed problems. It also gives an introduction to applications such as hybrid dynamics, control in arbitrary small time, and discontinuous trajectories. This book walks the readers through: the design and description of feedback solutions for impulse controls; the explanation of impulses of higher order that are derivatives of delta functions; the description of their physically realizable approximations - the fast controls and their approximations; the treatment of uncertainty in impulse control and the applications of impulse feedback. Of interest to both academics and graduate students in the field of control theory and applications, the book also protects users from common errors, such as inappropriate solution attempts, by indicating Hamiltonian techniques for hybrid systems with resets.

Electrical engineering --- systeemtheorie --- automatische regeltechniek

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Differentiable dynamical systems