Gajić Z., Shen X. Parallel Algorithms for Optimal Control of Large Scale Linear Systems

Springer, 1993. — 462 p.This book is designed to be a comprehensive treatment of parallel algorithms for optimal control of large scale linear and bilinear systems. These algorithms were originally evolved in the context of the recursive reduced-order methods for singularly perturbed and weakly coupled linear systems. There are numerous examples of large scale singularly perturbed and weakly coupled dynamic systems that provide great challenges to engineers, mathematicians and computer scientists. Some of the examples of singularly perturbed and weakly coupled systems include electric power systems, aerospace systems, large electric and conununication networks, robotics, and process control systems in the chemical and petroleum industries.
The parallel algorithms presented in this book are applicable to a wider classes of practical systems than the traditional methods for large• scale singularly perturbed and weakly coupled systems based on the power-series expansion methods. The synchronous parallel reducedorder algorithms presented in this book offer several advantages: the higher order of accuracy can be easily achieved at low cost, the parallel processing of information can be used, results are obtained under much milder assumptions (no analyticity requirements imposed on the problem coefficients), the software and hardware implementation of the control algorithms is highly simplified due to complete parallelism in the design procedures.
This book is intended for a wide readership, including control engineers, applied mathematicians, computer scientists, and advanced graduate students who seek a comprehensive view of the current developments in the theory of large scale linear and bilinear singularly perturbed and weakly coupled control systems. The book emphasizes mathematical developments as well as their application to solving practical problems without requiring a strong mathematical background.Linear-Quadratic Control Problems
Decoupling Transformations
Output Feedback Control
Linear Stochastic Systems
Open-Loop Optimal Control Problems
Exact Decompositions of Algebraic Riccati Equations
Differential and Difference Riccati Equations
Quasi Singularly Perturbed and Weakly Coupled Linear Systems
Singularly Perturbed Weakly Coupled Linear Control Systems
Stochastic Output Feedback of Linear Discrete Systems
Applications to Differential Games
Recursive Approach to High Gain and Cheap Control
Linear Approach to Bilinear Control Systems