Optimal control : an introduction优选的控制
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作者： Arturo Locatelli著
出 版 社：
出版时间： 2001-6-1字数：版次：页数： 294印刷时间： 2001/06/01开本： 16开印次：纸张： 胶版纸I S B N ： 9783764364083包装： 精装内容简介
From the very beginning in the late 1950s of the basic ideas of optimal control, attitudes toward the topic in the scientific and engineering community have ranged from an excessive enthusiasm for its reputed capability of solving almost any kind of problem to an (equally) unjustified rejection of it as a set of abstract mathematical concepts with no real utility. The truth, apparently, lies somewhere between these two extremes. Intense research activity in the field of optimization, in particular with reference to robust control issues, has caused it to be regarded as a source of numerous useful, powerful, and flexible tools for the control system designer. The new stream of research is deeply rooted in the well established framework of linear quadratic gaussian control theory, knowledge of which is an essential requirement for a fruitful understanding of optimization. In addition, there appears to be a widely shared opinion that some results of variational techniques are particularly suited for an approach to nonlinear solutions for complex control problems. For these reasons, even though the first significant achievements in the field were published some forty years ago, a new presentation of the basic elements of classical optimal control theory from a tutorial point of view seems meaningful and contemporary. The book reflects the author's experience of teaching control theory courses at a variety of levels over a span of thirty years. The level of exposition, the choice of topics, the relative weight given to them, the degree of mathematical sophistication, and the nature of the numerous illustrative examples, owe to the author's commitment to effective teaching. The book is suited for undergraduate/graduate students who have already been exposed to basic linear system and control theory and possess the calculus background usually found in any undergraduate curriculum in engineering.
目录
Preface
1Introduction
I Global methods
2 The HamUton-Jacobi theory
2.1Introduction
2.2Global sufficient conditions
2.3Problems
3 The LQ problem
3.1Introduction
3.2Finite control horizon
3.3Infinite control horizon
3.4The optimal regulator
3.4.1Stability properties
3.4.2Robustness properties
3.4.3The cheap control
3.4.4The inverse problem
3.5Problems
4 The LQG problem
4.1Introduction
4.2The Kalman filter
4.2.1The normal case
4.2.2The singular case
4.3The LQG control problem
4.3.1Finite control horizon
4.3.2Infinite control horizon
4.4Problems
5 The Riccati equations
5.1Introduction
5.2The differential equation
5.3The algebraic equation
5.4Problems
IIVariational methods
6The Maximum Principle
6.1Introduction
6.2Simple constraints
6.2.1Integral performance index
6.2.2Performance index function of the final event
6.3Complex constraints
6.3.1Nonregular final varieties
6.3.2Integral constraints
6.3.3Global instantaneous equality constraints
6.3.4Isolated equality constraints
6.3.5Global instantaneous inequaIity constraints
6.4Singular arcs
6.5Time optimal control
6.6Problems
7Second variation methods
7.1Introduction
7.2Local sufficient conditions
7.3Neighbouring optimal control
7.4Problems
A Basic background
A.1Canonical decomposition
A.2Transition matrix
A.3Poles and zeros
A.4Quadratic forms
A.5Expected value and covariance
B Eigenvalues assignment
B.1Introduction
B.2Assignment with accessible state
B.3Assignment with inaccessible state
B.4Assignment with asymptotic errors zeroing
C Notation
Bibliography
List of Algorithms, Assumptions~ Corollaries,
Index
