Modern Control Theory Fundamentals

Author: Cheng Peng
Publisher:
Publish Date: 2004-06-01
Features: Currently, automatic control technology has been widely applied to industrial and agricultural production, transportation, and national defense construction. The control theory that guides the analysis and design of automatic control systems has also developed significantly. The classical control theory developed in the 1940s and 1950s is still successfully applied to the analysis and design of single-variable time-invariant systems. Modern control theory, which emerged in the late 1950s and early 1960s, has broader applicability and can be used for multi-variable, time-invariant, or time-varying systems. The problems discussed are more complex and in-depth. The concepts, methods, and frameworks of modern control theory have permeated many disciplines. The interdisciplinary development of disciplines requires senior engineering technicians to have a better understanding and mastery of knowledge from related disciplines and fields. Therefore, it is necessary for master's students from non-control-related fields to take foundational courses in modern control theory based on the requirements of their research work and knowledge structure. This textbook is written for readers who wish to understand modern control theory but are constrained by limited study time and cannot engage in systematic learning. The first part is on linear system theory, including controllability and observability, state feedback design, state observer design, and system stability analysis. The second part is on optimal control theory, introducing constrained and equality-constrained optimization problems, the minimization principle for continuous and discrete systems, and linear quadratic Gaussian optimal control. The third part is on optimal estimation and filtering, covering least squares estimation and linear min variance estimation; introducing the discrete Kalman optimal prediction equation and optimal filtering equation based on orthogonal projection; and discussing filter divergence and methods to overcome divergence.