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CONTROL with LIMITED INFORMATION
Daniel Liberzon
Coordinated Science Laboratory andDept. of Electrical & Computer Eng.,Univ. of Illinois at Urbana-Champaign
CDC ’02
0
Control objectives: stabilize to 0 or to a desired set
containing 0, exit D through a specified facet, etc.
CONSTRAINED CONTROL
Constraint: – given
control commands
LIMITED INFORMATION SCENARIO
– partition of D
– points in D,
Quantizer/encoder:
Control:
for
PERTURBATION APPROACH
1. Design ignoring constraint
2. View as approximation
3. Prove that this still solves the problem
Issue:
error
Need to be robust w.r.t. measurement errors
LINEAR SYSTEMS
is asymptotically stable
9 Lyapunov function
LINEAR SYSTEMS (continued)
To have ultimate bound
we need
DYNAMIC QUANTIZATION
After ultimate bound is achievedwe can recompute partition for smaller region
Zooming in and out, we recover global asymptotic stability
zoom out zoom in
ACTIVE PROBING for INFORMATION
Can achieve GAS if we recompute often enough
. .
. . . .
..
..
Related work: Wong-Brockett, Tatikonda-Mitter, Nair-Evans, Savkin-Petersen, Hespanha
RESEARCH DIRECTIONS
• Robust control design
• Facility location algorithms
• Performance (nonstandard criteria)
• Applications