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QUANTIZATION and DELAY EFFECTS in NONLINEAR CONTROL SYSTEMS

Explore an architecture-independent approach for quantization-only systems and solutions, focusing on input-to-state stability in the presence of actuator errors. Learn about small gain arguments and dynamic quantization techniques for achieving global asymptotic stability.

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QUANTIZATION and DELAY EFFECTS in NONLINEAR CONTROL SYSTEMS

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  1. QUANTIZATION and DELAY EFFECTSin NONLINEAR CONTROL SYSTEMS Daniel Liberzon Coordinated Science Laboratory and Dept. of Electrical & Computer Eng., Univ. of Illinois at Urbana-Champaign Notre Dame, Oct 18, 2005

  2. PROBLEM FORMULATION QUANTIZER DELAY Architecture-independent approach

  3. QUANTIZATION ONLY quantization error Assume

  4. QUANTIZATION ONLY Solutions that start in enter and remain there This is input-to-state stability (ISS) w.r.t. actuator errors In time domain: [Sontag ’89] quantization error Assume

  5. QUANTIZATION and DELAY where Assuming ISS w.r.t. actuator errors as before: In time domain:

  6. SMALL–GAIN ARGUMENT if [Teel, IEEE TAC, Jul ’98] then we recover ISS w.r.t. hence ISS property becomes Small gain:

  7. FINAL RESULT Need: small gain true

  8. FINAL RESULT Need: small gain true

  9. FINAL RESULT Need: small gain true

  10. FINAL RESULT Need: small gain true

  11. FINAL RESULT solutions starting in enter and remain there Need: small gain true

  12. VARIATIONS globally asymptotically stabilizing we have Need ISS with respect to measurement errors (or work with small ) DELAY QUANTIZER • Relaxing ISS assumption Previous approach works if is sufficiently small • Different system architecture • External disturbances

  13. DYNAMIC QUANTIZATION – zooming variable Hybrid quantized control: is discrete state zoom in zoom out ISS from to small-gain condition ISS from to http://decision.csl.uiuc.edu/ liberzon Can recover global asymptotic stability [Nesic-Liberzon ’05]

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