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

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Related work: Wong-Brockett, Tatikonda-Mitter, Nair-Evans, Savkin-Petersen, Hespanha

RESEARCH DIRECTIONS

• Robust control design

• Facility location algorithms

• Performance (nonstandard criteria)

• Applications