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ISS of Switched Systems and Application to Adaptive Control

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ISS of Switched Systems and Application to Adaptive Control Linh Vu, Debasish Chatterjee, Daniel Liberzon Coordinated Science Laboratory, University of Illinois ... – PowerPoint PPT presentation

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Title: ISS of Switched Systems and Application to Adaptive Control


1
ISS of Switched Systems andApplication to
Adaptive Control
  • Linh Vu, Debasish Chatterjee, Daniel Liberzon

CDC 2005
2
Switched Nonlinear Systems
  • where

is a switching signal
and is some index set
LTI systemsHespanha-Morse. Stability of
switched systems with average dwell-time. (99)
3
Slow switching
  • Average dwell-time switching

Hespanha-Morse. Stability of switched systems
with average dwell-time. (99)
4
Main result
Theorem 1
  • Suppose that there exist
    such that

5
Application Supervisory Control
  • A parameterized plant with unknown parameters

Goal stabilize the plant when and
guarantee bounded when is bounded.
6
fixed
Plant
Controller
Multi- estimator
7
A2 The injected systems satisfy ISS hypotheses
of Theorem 1 with respect to
(criteria for controllers multi-estimator
design)
then
8
(No Transcript)
9
  • Theorem 2
  • Suppose that
  • the plant satisfies A3
  • the controllers and the multi-estimator satisfy
    A1 and A2.
  • Then under the scaled-independent hysteresis
    switching logic, all continuous states of the
    closed-loop systems are bounded for arbitrary
    initial conditions and bounded disturbance.
  • Further, if then can make

10
  • Example

Controllers
Multi-estimator
11
Conclusion
  • ISS type properties of switched system under
    average dwell-time switching
  • Application to supervisory control of nonlinear
    uncertain systems in the presence of disturbances
  • Future work
  • Relax the requirement of the existence of a
    constant for nonlinear systems
  • Include unmodeled dynamics (non-exact matching)
  • Use other slow switching mechanisms
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