Optimal control : an introduction优选的控制

出版时间:  出版社:  作者:Arturo  ISBN:9783764364083  页码:
Optimal control : an introduction优选的控制
 1 Introduction
I Global methods
 2 The HamUton-Jacobi theory
  2.1 Introduction
  2.2 Global sufficient conditions
  2.3 Problems
 3 The LQ problem
  3.1 Introduction
  3.2 Finite control horizon
  3.3 Infinite control horizon
  3.4 The optimal regulator
   3.4.1 Stability properties
   3.4.2 Robustness properties
   3.4.3 The cheap control
   3.4.4 The inverse problem
  3.5 Problems
 4 The LQG problem
  4.1 Introduction
  4.2 The Kalman filter
   4.2.1 The normal case
   4.2.2 The singular case
  4.3 The LQG control problem
   4.3.1 Finite control horizon
   4.3.2 Infinite control horizon
  4.4 Problems
 5 The Riccati equations
  5.1 Introduction
  5.2 The differential equation
  5.3 The algebraic equation
  5.4 Problems
II Variational methods
 6 The Maximum Principle
  6.1 Introduction
  6.2 Simple constraints
   6.2.1 Integral performance index
   6.2.2 Performance index function of the final event
  6.3 Complex constraints
   6.3.1 Nonregular final varieties
   6.3.2 Integral constraints
   6.3.3 Global instantaneous equality constraints
   6.3.4 Isolated equality constraints
   6.3.5 Global instantaneous inequaIity constraints
  6.4 Singular arcs
  6.5 Time optimal control
  6.6 Problems
 7 Second variation methods
  7.1 Introduction
  7.2 Local sufficient conditions
  7.3 Neighbouring optimal control
  7.4 Problems
A Basic background
 A.1 Canonical decomposition
 A.2 Transition matrix
 A.3 Poles and zeros
 A.4 Quadratic forms
 A.5 Expected value and covariance
B Eigenvalues assignment
 B.1 Introduction
 B.2 Assignment with accessible state
 B.3 Assignment with inaccessible state
 B.4 Assignment with asymptotic errors zeroing
C Notation
 List of Algorithms, Assumptions~ Corollaries,
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.