STABILIZING a NONLINEAR SYSTEM with LIMITED INFORMATION FEEDBACK

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STABILIZING a NONLINEAR SYSTEM withLIMITED
INFORMATION FEEDBACK
Daniel Liberzon
Coordinated Science Laboratory and Dept. of
Electrical Computer Eng., Univ. of Illinois at
Urbana-Champaign U.S.A.
CDC 03
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MOTIVATION

• Limited communication capacity
• many systems/tasks share network cable or
  wireless medium
• microsystems with many sensors/actuators on one
  chip

• Need to minimize information transmission
  (security)

• Event-driven actuators
• PWM amplifier
• manual car transmission
• stepping motor

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ACTIVE PROBING for INFORMATION
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LINEAR SYSTEMS
(Baillieul, Brockett-L, Hespanha et. al.,
Nair-Evans, Petersen-Savkin, Tatikonda, and
others)
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LINEAR SYSTEMS
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LINEAR SYSTEMS
Example

• is divided by 3 at the sampling time

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LINEAR SYSTEMS (continued)
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NONLINEAR SYSTEMS
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NONLINEAR SYSTEMS

• is divided by 3 at the sampling time

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NONLINEAR SYSTEMS (continued)
The norm

• grows at most by the factor in
  one period

• is divided by 3 at each sampling time

Need ISS w.r.t. measurement errors
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SUMMARY
Derived a sufficient condition for stabilization

• Similar to known results for linear systems
• Involves alphabet size, sampling period, and
  Lipschitz constant
• Relies on input-to-state stabilizability w.r.t.
  measurement errors