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Attention as a Design Criterion and Analysis Tool in Control Problems
Published on Oct 16, 20123689 Views
We may reasonably why optimal control theory has not been more useful in understanding the control mechanisms found in biology. The questions there range from understanding control of the operation o
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Chapter list
The Statistical Physics of Inference and Control Theory00:00
Attention as a implementation cost00:23
More realistic control/decision making model04:08
Examples of compression ( C ) and expansion ( E )06:06
Big Challenges08:58
Some background concerning attention as a limited resource09:29
References11:03
Getting beyond polemics: Three examples + some theory11:06
Example 1: Stabilization and synchronization of group motion11:58
Equipotential contours for a lattice potential14:09
More realistic control/decision making model (2)14:35
Stabilization requires symmetry breaking15:25
Example 2: Heat Engines and the Carnot cycle15:43
More realistic control/decision making model (3)18:16
The Carnot cycle in a reduced attention context19:03
Other similar problems20:00
Example 3: Low bandwidth control via Pattern selection21:50
How to describe “pattern selection” mathematically21:53
Putting the system together21:55
In continuous time it is a parametric excitation problem21:56
Might this help explain the famous Ito diagram?21:57
Bonus Example: open loop quantum control32:01
Enough examples! What about a theory?34:19
Implementation Cost Factors: Choice of L37:01
Trajectory and implementation costs formulated jointly37:12
Towards a general theory: Producing a cheap controller38:34
Families of Trajectories and Densities: Liouville’s Equation39:18
A Prototype Formulation using Continuous Mathematics43:04
Designing a field with modest Space-Time Gradient44:00
Something less abstract44:02
What kind of solution can we expect?44:53
The Change in Performance46:13
This allows one to take bounds into account explicitly46:17
Stochastic example47:01
Conclusions47:18
Conclusions Continued48:13
References49:03