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From: HardySpicer on 11 Jul 2010 18:07
If you have a simple relationship

y(t)=ax(t)

where a is a constant then

y'(t) = ax'(t)

where ' is derivative wrt time.

If however a is time varying then we get

y(t)=a(t)x(t)

y'(t)=a(t)x'(t) + x(t)a'(t)

ie an extra term. In adaptive filters we derive the case for constant
weights and then assume that the case for time-varying weights is the
same but the weights vary with time. Is this really true though? You
can imagine a simple case like the above where a weight is time
varying.


Hardy
From: Tim Wescott on 11 Jul 2010 20:05
On 07/11/2010 03:07 PM, HardySpicer wrote:
> If you have a simple relationship
>
> y(t)=ax(t)
>
> where a is a constant then
>
> y'(t) = ax'(t)
>
> where ' is derivative wrt time.
>
> If however a is time varying then we get
>
> y(t)=a(t)x(t)
>
> y'(t)=a(t)x'(t) + x(t)a'(t)
>
> ie an extra term. In adaptive filters we derive the case for constant
> weights and then assume that the case for time-varying weights is the
> same but the weights vary with time. Is this really true though? You
> can imagine a simple case like the above where a weight is time
> varying.

Thorough discussions of adaptive control take care to make the assertion
that the weights vary slowly, i.e.

|a'(t)x(t)| << |a(t)x'(t)|.

Make that assumption (and make sure it's correct!) and you're good to go.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
From: HardySpicer on 11 Jul 2010 23:40
On Jul 12, 12:05 pm, Tim Wescott <t...(a)seemywebsite.com> wrote:
> On 07/11/2010 03:07 PM, HardySpicer wrote:
>
>
>
> > If you have a simple relationship
>
> > y(t)=ax(t)
>
> > where a is a constant then
>
> > y'(t) = ax'(t)
>
> > where ' is derivative wrt time.
>
> > If however a is time varying then we get
>
> > y(t)=a(t)x(t)
>
> > y'(t)=a(t)x'(t) + x(t)a'(t)
>
> > ie an extra term. In adaptive filters we derive the case for constant
> > weights and then assume that the case for time-varying weights is the
> > same but the weights vary with time. Is this really true though? You
> > can imagine a simple case like the above where a weight is time
> > varying.
>
> Thorough discussions of adaptive control take care to make the assertion
> that the weights vary slowly, i.e.
>
> |a'(t)x(t)| << |a(t)x'(t)|.
>
> Make that assumption (and make sure it's correct!) and you're good to go.
>
> --
>
> Tim Wescott
> Wescott Design Serviceshttp://www.wescottdesign.com
>
> Do you need to implement control loops in software?
> "Applied Control Theory for Embedded Systems" was written for you.
> See details athttp://www.wescottdesign.com/actfes/actfes.html

Yes but in adaptive filters they don't move slowly at all (and may not
even in some robotic applications). For example acoustic dynamics
moves like the clappers when you speak due to reverberations.


Hardy
From: Muzaffer Kal on 12 Jul 2010 00:24
On Sun, 11 Jul 2010 20:40:30 -0700 (PDT), HardySpicer
<gyansorova(a)gmail.com> wrote:

>> Thorough discussions of adaptive control take care to make the assertion
>> that the weights vary slowly, i.e.
>>
>> |a'(t)x(t)| << |a(t)x'(t)|.
>>
>> Make that assumption (and make sure it's correct!) and you're good to go.
>>
>
>Yes but in adaptive filters they don't move slowly at all (and may not
>even in some robotic applications). For example acoustic dynamics
>moves like the clappers when you speak due to reverberations.
>
>
>Hardy

Most systems when unperturbed change slowly so modelling them with a
fast enough adaptive filter is possible. In robotics and acoustics,
the new feature is applying control signals into the system which also
changes its behavior. This new input, output can also be added to the
state matrix. Then, in addition to location/speed sensors there is a
new feature which is how much electric potential was applied to the
motor which would help you figure out an incremental estimate on where
the robot should be. Now you only have to adapt the "motor voltage vs
speed" variable which would change slowly once converged. If you don't
have this variable your adaptation speed would need to be much faster
to. The same thing would apply to acoustics it seems. If you model how
reverberations happen when you speak, you can estimate based on the
speech input. Then the speech input to reverberations system would
change slowly (due to material aging, temperature etc.)
--
Muzaffer Kal

DSPIA INC.
ASIC/FPGA Design Services

http://www.dspia.com
From: Tim Wescott on 12 Jul 2010 02:12
On 07/11/2010 09:24 PM, Muzaffer Kal wrote:
> On Sun, 11 Jul 2010 20:40:30 -0700 (PDT), HardySpicer
> <gyansorova(a)gmail.com> wrote:
>
>>> Thorough discussions of adaptive control take care to make the assertion
>>> that the weights vary slowly, i.e.
>>>
>>> |a'(t)x(t)|<< |a(t)x'(t)|.
>>>
>>> Make that assumption (and make sure it's correct!) and you're good to go.
>>>
>>
>> Yes but in adaptive filters they don't move slowly at all (and may not
>> even in some robotic applications). For example acoustic dynamics
>> moves like the clappers when you speak due to reverberations.
>>
>>
>> Hardy
>
> Most systems when unperturbed change slowly so modelling them with a
> fast enough adaptive filter is possible. In robotics and acoustics,
> the new feature is applying control signals into the system which also
> changes its behavior. This new input, output can also be added to the
> state matrix. Then, in addition to location/speed sensors there is a
> new feature which is how much electric potential was applied to the
> motor which would help you figure out an incremental estimate on where
> the robot should be. Now you only have to adapt the "motor voltage vs
> speed" variable which would change slowly once converged. If you don't
> have this variable your adaptation speed would need to be much faster
> to. The same thing would apply to acoustics it seems. If you model how
> reverberations happen when you speak, you can estimate based on the
> speech input. Then the speech input to reverberations system would
> change slowly (due to material aging, temperature etc.)

If I may clarify, it sounds like what you're saying is that you should
try to find an accurate model of the system that doesn't change rapidly
in the parameters, then use (and adapt) that.

Yes?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" was written for you.
See details at http://www.wescottdesign.com/actfes/actfes.html
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