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STABILIZING a NONLINEAR SYSTEM with LIMITED INFORMATION FEEDBACK

STABILIZING a NONLINEAR SYSTEM with LIMITED INFORMATION FEEDBACK. Daniel Liberzon. Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign U.S.A. CDC ’03. MOTIVATION. finite subset of. Encoder. Decoder. QUANTIZER.

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STABILIZING a NONLINEAR SYSTEM with LIMITED INFORMATION FEEDBACK

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  1. 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

  2. MOTIVATION finite subset of Encoder Decoder QUANTIZER • 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

  3. ACTIVE PROBING for INFORMATION PLANT QUANTIZER CONTROLLER dynamic (time-varying) dynamic (changes at sampling times) Encoder Decoder very small

  4. LINEAR SYSTEMS (Baillieul, Brockett-L, Hespanha et. al., Nair-Evans, Petersen-Savkin, Tatikonda, and others)

  5. LINEAR SYSTEMS Example: Zoom out to get initial bound sampling times Between sampling times, let

  6. LINEAR SYSTEMS Between sampling times, let Consider The norm • grows at most by the factor in one period Example: • is divided by 3 at the sampling time

  7. LINEAR SYSTEMS (continued) The norm • grows at most by the factor in one period • is divided by 3 at each sampling time Pick small enough s.t. sampling frequency vs. open-loop instability amount of static info provided by quantizer 0 where is Hurwitz

  8. NONLINEAR SYSTEMS Example: Zoom out to get initial bound sampling times Between samplings

  9. NONLINEAR SYSTEMS Example: Between samplings Let where is Lipschitz constant of The norm • grows at most by the factor in one period • is divided by 3 at the sampling time

  10. NONLINEAR SYSTEMS (continued) Pick small enough s.t. 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

  11. SUMMARY Research directions: • Relaxing the ISS assumption (De Persis) • Outputs: how many variables to transmit? • Necessary conditions for stabilization • Performance 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

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