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CONTROL of NONLINEAR SYSTEMS under COMMUNICATION CONSTRAINTS

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CONTROL of NONLINEAR SYSTEMS under COMMUNICATION CONSTRAINTS ... on not containing 0 (annulus) Gives 25% decrease in for 2-D example. DYNAMIC QUANTIZATION ... – PowerPoint PPT presentation

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Title: CONTROL of NONLINEAR SYSTEMS under COMMUNICATION CONSTRAINTS


1
CONTROL of NONLINEAR SYSTEMS under
COMMUNICATION CONSTRAINTS
Daniel Liberzon
Coordinated Science Laboratory and Dept. of
Electrical Computer Eng., Univ. of Illinois at
Urbana-Champaign
Caltech, Apr 1, 2005
2
LIMITED INFORMATION SCENARIO
3
OBSTRUCTION to STABILIZATION
Asymptotic stabilization is usually lost
4
BASIC QUESTIONS
  • What can we say about a given quantized system?
  • How can we design the best quantizer for
    stability?
  • What can we do with very coarse quantization?
  • What are the difficulties for nonlinear systems?

5
STATE QUANTIZATION LINEAR SYSTEMS
quantization error
6
NONLINEAR SYSTEMS
For linear systems, we saw that if
gives then
automatically gives
when
This is robustness to measurement errors
7
LOCATIONAL OPTIMIZATION

Bullo-L
Compare mailboxes in a city, cellular base
stations in a region
8
MULTICENTER PROBLEM

This is the center of enclosing sphere of
smallest radius
9
LOCATIONAL OPTIMIZATION REFINED APPROACH
Only applicable to linear systems
10
WEIGHTED MULTICENTER PROBLEM
on not containing 0 (annulus)
Lloyd algorithm as before
11
DYNAMIC QUANTIZATION
Can recover global asymptotic stability
12
ACTIVE PROBING for INFORMATION
13
LINEAR SYSTEMS
(Baillieul, Brockett-L, Hespanha et. al.,
Nair-Evans, Petersen-Savkin, Tatikonda, and
others)
14
LINEAR SYSTEMS
15
LINEAR SYSTEMS
Example
  • is divided by 3 at the sampling time

16
LINEAR SYSTEMS (continued)
17
NONLINEAR SYSTEMS
  • is divided by 3 at the sampling time

18
NONLINEAR SYSTEMS (continued)
The norm
  • grows at most by the factor in
    one period
  • is divided by 3 at each sampling time

19
ROBUSTNESS of the CONTROLLER
ISS w.r.t. measurement errors quite
restrictive...
20
SOME RESEARCH DIRECTIONS
  • Applications
  • Other?
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