1 / 11

QUANTIZED OUTPUT FEEDBACK CONTROL of NONLINEAR SYSTEMS

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. 1 of 11. QUANTIZED OUTPUT FEEDBACK.

kendraj
Download Presentation

QUANTIZED OUTPUT FEEDBACK CONTROL of NONLINEAR SYSTEMS

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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 1of 11

  2. QUANTIZED OUTPUT FEEDBACK PLANT QUANTIZER CONTROLLER • 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 2 of 11

  3. QUANTIZER Encoder Decoder QUANTIZER finite set Output space is divided into quantization regions Assume such that: 1. 2. is the range, is the quantization error bound For , the quantizer saturates 3 of 11

  4. LINEAR SYSTEM Luenberger observer-based controller: quantization error Closed-loop system: or in short where is Hurwitz if and are Hurwitz [Brockett-L] Plant: 4 of 11

  5. LINEAR SYSTEM (continued) For we have Recall: level sets of V Solutions go from the larger level set to the smaller one Hurwitz 5 of 11

  6. INPUT-TO-STATE STABILITY (ISS) [Sontag] is of class if • for each fixed Example: class function • as for each ISS: where Equivalent Lyapunov characterization: when for some 6 of 11

  7. NONLINEAR SYSTEM Dynamic controller: Closed-loop system: quantization error or in short Assume: this is ISS w.r.t. quantization error (so in particular, should have GAS when ) Plant: 7of 11

  8. NONLINEAR SYSTEM (continued) Lyap. function and class function s.t. level sets of V Solutions go from the larger level set to the smaller one ISS Can recover GAS using dynamic quantization 8of 11

  9. ISS ASSUMPTION: CLOSER LOOK if for some we have 1. and 2. Reason: cascade argument Can extend this via a small-gain argument (need ) Closed-loop system is ISS 9of 11

  10. ISS CONTROLLER DESIGN This is ISS property of control law w.r.t. observation errors: Closed-loop system: 1. • 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] 10of 11

  11. ISS OBSERVER DESIGN • This property can be achieved for with detectable and globally Lipschitz, very restrictive Closed-loop system: 2. 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! 11of 11

More Related