1 General Characteristic of Control
Systems...............................................1
1.1 Subject and
Scope of Control
Theory................................................1
1.2 Basic Terms
.......................................................................................2
1.2.1
Control Plant
...............................................................................4
1.2.2
Controller
....................................................................................6
1.3
Classification of Control
Systems......................................................7
1.3.1
Classification with Respect to Connection Between Plant and
Controller
.............................................................................................7
1.3.2
Classification with Respect to Control
Goal...............................9
1.3.3 Other Cases
...............................................................................11
1.4
Stages of Control System Design
....................................................13
1.5 Relations
Between Control Science and Related Areas in Science
and Technology
.....................................................................................14
1.6
Character, Scope and Composition of the
Book..............................15
2 Formal Models of Control Systems
........................................................17
2.1 Description
of a Signal
....................................................................17
2.2
Static Plant
.......................................................................................18
2.3
Continuous Dynamical Plant
...........................................................19
2.3.1 State
Vector
Description...........................................................20
2.3.2
“Input-output” Description by Means of Differential Equation24
2.3.3
Operational Form of “Input-output” Description......................25
2.4
Discrete Dynamical Plant
................................................................29
2.5
Control Algorithm
...........................................................................31
2.6
Introduction to Control System
Analysis.........................................33
2.6.1 Continuous
System...................................................................35
2.6.2
Discrete
System........................................................................37
3 Control for the Given State (the Given
Output)......................................41
3.1 Control of a Static
Plant...................................................................41
3.2
Control of a Dynamical Plant.
Controllability.................................44
3.3 Control of a
Measurable Plant in the Closed-loop System.............47
3.4
Observability....................................................................................50
VIII
Contents
3.5 Control with an Observer in the Closed-loop System
.....................55
3.6 Structural
Approach.........................................................................59
3.7
Additional Remarks
.........................................................................62
4 Optimal Control with Complete Information on
the Plant .....................65
4.1 Control of a Static
Plant...................................................................65
4.2
Problems of Optimal Control for Dynamical
Plants........................69
4.2.1 Discrete Plant
............................................................................69
4.2.2
Continuous
Plant.......................................................................72
4.3
Principle of Optimality and Dynamic Programming
.......................74
4.4 Bellman Equation
............................................................................79
4.5
Maximum Principle
.........................................................................85
4.6
Linear-quadratic
Problem................................................................93
5 Parametric
Optimization.........................................................................97
5.1
General Idea of Parametric Optimization
........................................97
5.2 Continuous Linear Control
System..................................................99
5.3 Discrete
Linear Control
System.....................................................105
5.4 System
with the Measurement of Disturbances.............................107
5.5
Typical Forms of Control Algorithms in Closed-loop Systems ....110
5.5.1
Linear
Controller.....................................................................111
5.5.2
Two-position Controller
.........................................................112
5.5.3
Neuron-like
Controller............................................................112
5.5.4
Fuzzy Controller
.....................................................................113
6 Application of Relational Description of
Uncertainty.........................117
6.1 Uncertainty and Relational
Knowledge Representation ................117
6.2 Analysis
Problem...........................................................................122
6.3
Decision Making
Problem.............................................................127
6.4
Dynamical Relational Plant
...........................................................130
6.5
Determinization
.............................................................................136
7 Application of Probabilistic Descriptions of
Uncertainty.....................143
7.1 Basic Problems for Static Plant and
Parametric Uncertainty........143
7.2 Basic Problems for Static Plant and
Non-parametric Uncertainty152
7.3 Control of Static Plant Using Results of
Observations..................157
7.3.1 Indirect Approach
...................................................................158
7.3.2
Direct
Approach......................................................................164
7.4
Application of Games
Theory........................................................165
7.5 Basic
Problem for Dynamical
Plant...............................................170
7.6 Stationary
Stochastic Process
........................................................174
IX
7.7
Analysis and Parametric Optimization of Linear Closed-loop
Control System
with Stationary Stochastic Disturbances....................178
7.8
Non-parametric Optimization of Linear Closed-loop Control System
with
Stationary Stochastic
Disturbances..............................................183
7.9
Relational Plant with Random Parameter
......................................188
8 Uncertain Variables and Their
Applications.........................................193
8.1 Uncertain
Variables
.......................................................................193
8.2
Application of Uncertain Variables to Analysis and Decision
Making
(Control) for Static Plant
........................................................201
8.2.1
Parametric Uncertainty
...........................................................201
8.2.2
Non-parametric Uncertainty
...................................................205
8.3 Relational Plant
with Uncertain Parameter....................................211
8.4 Control
for Dynamical Plants. Uncertain Controller
.....................216
9 Fuzzy Variables, Analogies and Soft Variables
...................................221
9.1 Fuzzy Sets and Fuzzy
Numbers.....................................................221
9.2
Application of Fuzzy Description to Decision Making (Control) for
Static
Plant
...........................................................................................228
9.2.1
Plant without Disturbances
.....................................................228
9.2.2 Plant with
External Disturbances............................................233
9.3
Comparison of Uncertain Variables with Random and Fuzzy
Variables
..............................................................................................238
9.4
Comparisons and Analogies for Non-parametric Problems ..........242
9.5
Introduction to Soft
Variables........................................................246
9.6
Descriptive and Prescriptive Approaches. Quality of Decisions ...249
9.7
Control for Dynamical Plants. Fuzzy Controller
...........................255
10 Control in Closed-loop System. Stability
...........................................259
10.1 General Problem
Description.......................................................259
10.2
Stability Conditions for Linear Stationary
System......................264
10.2.1 Continuous
System...............................................................264
10.2.2
Discrete
System....................................................................266
10.3
Stability of Non-linear and Non-stationary Discrete Systems .....270
10.4
Stability of Non-linear and Non-stationary Continuous Systems 277
10.5
Special Case. Describing Function
Method.................................278
10.6 Stability of Uncertain
Systems. Robustness ................................282
10.7 An Approach
Based on Random and Uncertain Variables..........291
10.8 Convergence of
Static Optimization Process...............................295
11 Adaptive and Learning Control Systems
............................................299
11.1 General Concepts of
Adaptation..................................................299
X
Contents
11.2 Adaptation via Identification for Static Plant
..............................303
11.3 Adaptation via Identification for
Dynamical Plant ......................309
11.4 Adaptation via Adjustment of
Controller Parameters..................311
11.5 Learning Control System
Based on Knowledge of the Plant.......313
11.5.1 Knowledge Validation and
Updating....................................314
11.5.2 Learning Algorithm
for Decision Making in
Closed-loop
System..............................................................................................317
11.6
Learning Control System Based on Knowledge of Decisions....319
11.6.1
Knowledge Validation and
Updating....................................319
11.6.2 Learning Algorithm
for Control in Closed-loop System......321
12 Intelligent and Complex Control Systems
..........................................327
12.1 Introduction to
Artificial Intelligence ..........................................327
12.2
Logical Knowledge
Representation.............................................328
12.3
Analysis and Decision Making Problems
....................................332
12.4 Logic-algebraic
Method...............................................................334
12.5
Neural Networks
..........................................................................341
12.6
Applications of Neural Networks in Control
Systems.................346
12.6.1 Neural Network as a Controller
............................................346
12.6.2 Neural Network in
Adaptive System....................................348
12.7 Decomposition
and Two-level Control........................................349
12.8
Control of Complex Plant with Cascade Structure
......................355
12.9 Control of Plant with Two-level Knowledge
Representation......358
13 Control of Operation
Systems.............................................................363
13.1
General
Characteristic..................................................................363
13.2
Control of Task
Distribution........................................................365
13.3
Control of Resource
Distribution.................................................371
13.4
Control of Assignment and Scheduling
.......................................375
13.5 Control of Allocation in
Systems with Transport ........................382
13.6 Control of an
Assembly Process..................................................386
13.7
Application of Relational Description and Uncertain Variables .391
13.8
Application of Neural Network
...................................................398
Conclusions..............................................................................................401
Appendix..................................................................................................405
References................................................................................................411
Index
........................................................................................................419
