The signals represent measurements or signals that are directly variables, measurable plant “outputs,” measurable control signals, measurable exogenous signals, Generally, the more indep
Trang 1
• Measurement Signals The signals represent measurements or signals that are directly
variables, measurable plant “outputs,” measurable control signals, measurable exogenous signals,
Generally, the more independent measurements we have the better—since, in theory, more useful
information can be extracted
Comment 30.1 (Toward a Separation Principle)
defines a regulation or control problem This is analogous to the situation addressed in classical LQR
problems In such problems, one trades off control action (size) versus speed of regulation
that the pair implicitly defines an information extraction or estimation problem This is analogous to
the situation addressed in classical KBF problems In such problems, one trades off sensor cost (or
immunity to noise) versus speed of estimate construction
Such associations suggest that just as in classical LQG problems, our surprisingly general structure
(30.1) where
(30.2)
(30.3) (30.4)
Comment 30.2 (Use of Two Norm: Wide Band Exogenous Signals)
Noting that the two norm measures the energy of the response to an impulse and noting that the transform
Comment 30.3 (Control and Estimation Problems)
Given the above problem statement, it is appropriate to recall the following elementary result:
y R n y
∈
H
min
K ||Twz( )||K H2
||F|| H2 def
= 2p - 1 trace F{ H ( )F jw jω ( )} w d
∞ –
∞
∫
trace f{ H ( )f t t ( )} t d
0
∞
∫
=
|| f ||
L2(R+)
=
0066_Frame_C30 Page 3 Thursday, January 10, 2002 4:43 PM
©2002 CRC Press LLC
Trang 2
• Measurement Signals The signals represent measurements or signals that are directly
variables, measurable plant “outputs,” measurable control signals, measurable exogenous signals,
Generally, the more independent measurements we have the better—since, in theory, more useful
information can be extracted
Comment 30.1 (Toward a Separation Principle)
defines a regulation or control problem This is analogous to the situation addressed in classical LQR
problems In such problems, one trades off control action (size) versus speed of regulation
that the pair implicitly defines an information extraction or estimation problem This is analogous to
the situation addressed in classical KBF problems In such problems, one trades off sensor cost (or
immunity to noise) versus speed of estimate construction
Such associations suggest that just as in classical LQG problems, our surprisingly general structure
(30.1) where
(30.2)
(30.3) (30.4)
Comment 30.2 (Use of Two Norm: Wide Band Exogenous Signals)
Noting that the two norm measures the energy of the response to an impulse and noting that the transform
Comment 30.3 (Control and Estimation Problems)
Given the above problem statement, it is appropriate to recall the following elementary result:
y R n y
∈
H
min
K ||Twz( )||K H2
||F|| H2 def
= 2p - 1 trace F{ H ( )F jw jω ( )} w d
∞ –
∞
∫
trace f{ H ( )f t t ( )} t d
0
∞
∫
=
|| f ||
L2(R+)
=
0066_Frame_C30 Page 3 Thursday, January 10, 2002 4:43 PM
©2002 CRC Press LLC