文档介绍：Principles of Information Science
Chapter 8
Information Execution
Control Theory
§1 Fundamentals of Control Theory
Controller
Object
N. Wiener: Control theory in engineering, whether it is
Concerned with Man, animal or machine, can only be
regarded as a part of the theory of information.
I(O,E)
F(S(I))
I(G)
s1
§ Description of Controlled Object
Object Description: The states, The Ways
s1
s2
s3
s4
P(11) … P(14)
……
P(41) … P(44)
s1 … sN
t1
.
.
tM
.
T
x1
xM
yN
y1
§ Description of Goal and Effect
s
g
The initial condition, s, of
the controlled object and
the final condition, g, are
two states of the object in
the state space of control
problem. The path connecting all the states from s to g is
one the possible solutions for the control problem.
In an N dimensional space, the states and the control effect
can be described as
s={s1, …, sN}, g={g1, …, gN}
= [ (gn – g’n) ]
2
__
n
1/2
2
§3 The Mechanism of Control
Mechanism of Control: from Information to Action
Strategy
Execution
Object
Information
Action
§ The Categories of Control
Open-Loop & Closed-Loop
Object
Execution
Controlling
Noise
Controlling
Execution
Object
Noise
Goal
Effect
§ Control Strategy Producing
Mathematical Programming: Strategy Producing
X – N dimensional column vector
f(X) – dependence relationship between goal and the
system states
g(X) – environment constraints of the system
The optimum control strategy can be produced through the
maximizing (minimizing) the goal function under the given
constraints:
Max(Min) f(X)
{g(X)}
An Example: Linear Programming
Goal function: f = 5 x1 + x2
Constraints: (1) x1 0; (2) x2 0; (3) x1 + x2 6;
(4) 3 x1 + x2 12; (5) x1 – x2 2.
Solution:
(1)
(2)
(3)
(5)
(4)
O
A
B
C
D
Point C:
x1 = 26/7
x2 = 6/7
f = 136/7
max
Other Approaches
Non-Linear Programming
Integer Programming
One dimensional Search
Higher dimensional search
Dynamic Programming, etc.
§ Th