Title: CONTROL of NONLINEAR SYSTEMS under COMMUNICATION CONSTRAINTS
1CONTROL 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
2LIMITED INFORMATION SCENARIO
3OBSTRUCTION to STABILIZATION
Asymptotic stabilization is usually lost
4BASIC 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?
5STATE QUANTIZATION LINEAR SYSTEMS
quantization error
6NONLINEAR 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
8MULTICENTER PROBLEM
This is the center of enclosing sphere of
smallest radius
9LOCATIONAL OPTIMIZATION REFINED APPROACH
Only applicable to linear systems
10WEIGHTED MULTICENTER PROBLEM
on not containing 0 (annulus)
Lloyd algorithm as before
11DYNAMIC QUANTIZATION
Can recover global asymptotic stability
12ACTIVE PROBING for INFORMATION
13LINEAR SYSTEMS
(Baillieul, Brockett-L, Hespanha et. al.,
Nair-Evans, Petersen-Savkin, Tatikonda, and
others)
14LINEAR SYSTEMS
15LINEAR SYSTEMS
Example
- is divided by 3 at the sampling time
16LINEAR SYSTEMS (continued)
17NONLINEAR SYSTEMS
- is divided by 3 at the sampling time
18NONLINEAR SYSTEMS (continued)
The norm
- grows at most by the factor in
one period
- is divided by 3 at each sampling time
19ROBUSTNESS of the CONTROLLER
ISS w.r.t. measurement errors quite
restrictive...
20SOME RESEARCH DIRECTIONS