Introduction to Stochastic Control Theory (Mathematics in Science and Engineering, Volume 70)

This text for upper-level undergraduates and graduate students explores stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria, it covers discrete time as well as continuous time systems. 1970 edition. In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;
methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and
methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.

As a result, the book represents a blend of new methods in general computational analysis,
and specific, but also generic, techniques for study of systems theory ant its particular
branches, such as optimal filtering and information compression.

- Best operator approximation,
- Non-Lagrange interpolation,
- Generic Karhunen-Loeve transform
- Generalised low-rank matrix approximation
- Optimal data compression
- Optimal nonlinear filtering This text for upper-level undergraduates and graduate students explores stochastic control theory in terms of analysis, parametric optimization, and optimal stochastic control. Limited to linear systems with quadratic criteria, it covers discrete time as well as continuous time systems.The first three chapters provide motivation and background material on stochastic processes, followed by an analysis of dynamical systems with inputs of stochastic processes. A simple version of the problem of optimal control of stochastic systems is discussed, along with an example of an industrial application of this theory. Subsequent discussions cover filtering and prediction theory as well as the general stochastic control problem for linear systems with quadratic criteria.Each chapter begins with the discrete time version of a problem and progresses to a more challenging continuous time version of the same problem. Prerequisites include courses in analysis and probability theory in addition to a course in dynamical systems that covers frequency response and the state-space approach for continuous time and discrete time systems. Content: Edited by Page iii Copyright page Page iv Dedication Page v Preface Pages ix-x Acknowledgments Page xi Chapter 1 Stochastic Control Pages 1-12 Chapter 2 Stochastic Processes Pages 13-43 Chapter 3 Stochastic State Models Pages 44-90 Chapter 4 Analysis of Dynamical Systems Whose Inputs are Stochastic Processes Pages 91-114 Chapter 5 Parametric Optimization Pages 115-158 Chapter 6 Minimal Variance Control Strategies Pages 159-209 Chapter 7 Prediction and Filtering Theory Pages 210-255 Chapter 8 Linear Stochastic Control Theory Pages 256-294 Index Pages 295-299 Studies theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. This title considers many computing techniques, such as methods of operator approximation with any given accuracy; methods of covariance matrix estimation; and, methods for low-rank matrix approximations.