QUANTIZED OUTPUT FEEDBACK CONTROL of NONLINEAR SYSTEMS

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QUANTIZED OUTPUT FEEDBACK CONTROL of
NONLINEAR SYSTEMS
Daniel Liberzon
Coordinated Science Laboratory and Dept. of
Electrical Computer Eng., Univ. of Illinois at
Urbana-Champaign
Mediterranean Control Conference, Athens, Greece,
Jun 2007
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QUANTIZED OUTPUT FEEDBACK

• Motivation
• limited communication between sensor and
  actuator
• trade-off between communication and computation

• Objectives
• analyze effect of quantization on system
  stability
• design controllers robust to quantization errors

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QUANTIZER
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LINEAR SYSTEM
Brockett-L
Plant
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LINEAR SYSTEM (continued)
Hurwitz
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NONLINEAR SYSTEM
Plant
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NONLINEAR SYSTEM (continued)
ISS
Can recover GAS using dynamic quantization
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ISS ASSUMPTION CLOSER LOOK
Closed-loop system
is ISS
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ISS CONTROLLER DESIGN
Closed-loop system
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• Not always possible to achieve Freeman 95, Fah
  99

• Results exist for classes of systems Freeman
  Kokotovic 93,
• 96, Freeman 97, Fah 99, Jiang et al. 99,
  Sanfelice Teel 05

• ISS assumption is fundamental in quantized
  control of
• nonlinear systems L 03

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ISS OBSERVER DESIGN
Closed-loop system
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This is ISS property of observer w.r.t. additive
output errors

• No results on design of such ISS observers exist

More research on this problem is needed!
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