ISS of Switched Systems and Application to Adaptive Control

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ISS of Switched Systems andApplication to
Adaptive Control

• Linh Vu, Debasish Chatterjee, Daniel Liberzon

CDC 2005
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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)
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Slow switching

• Average dwell-time switching

Hespanha-Morse. Stability of switched systems
with average dwell-time. (99)
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Main result
Theorem 1

• Suppose that there exist
  such that

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Application Supervisory Control

• A parameterized plant with unknown parameters

Goal stabilize the plant when and
guarantee bounded when is bounded.
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fixed
Plant
Controller
Multi- estimator
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A2 The injected systems satisfy ISS hypotheses
of Theorem 1 with respect to
(criteria for controllers multi-estimator
design)
then
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• 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

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• Example

Controllers
Multi-estimator
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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