Probability Theory, Quantum Physics, Theoretical Physics, Computer Mathematics, Mathematical Programming & Operations Research, Mathematical Equations - Differential
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Overview
This book gives a self-contained and systematic exposition of the major optimal control theory for continuous-time stochastic diffusion processes, including the Pontryagin type maximum principle (MP) featuring second-order adjoint equations, the Bellman dynamic programming (DP) method via viscosity solution theory, and the Kalman linear-quadratic (LQ) models with indefinite cost functionals. A major feature of the controlled systems under consideration is that the controls enter into both the drifts and the diffusions, making it fundamentally different from the deterministic systems. The main theme of the book is on establishing relations between MP and DP, or essentially those between Hamiltonian systems and Hamilton-Jacobi-Bellman (HJB) equations. This book can be used as a textbook for graduate students majoring in stochastic controls and applications. Some knowledge in measure theory and real analysis will be helpful. It can also serve as a reference for researchers in applied probability, control theory, operations research, physics, economics, and finance.Synopsis
The maximum principle and dynamic programming are the two most commonly used approaches in solving optimal control problems. These approaches have been developed independently. The theme of this book is to unify these two approaches, and to demonstrate that the viscosity solution theory provides the framework to unify them.
Book Details
Published
July 1, 1999
Publisher
Springer-Verlag New York, LLC
Pages
461
Format
Hardcover
ISBN
9780387987231