Title: ISS of Switched Systems and Application to Adaptive Control
1ISS of Switched Systems andApplication to
Adaptive Control
- Linh Vu, Debasish Chatterjee, Daniel Liberzon
CDC 2005
2Switched Nonlinear Systems
is a switching signal
and is some index set
LTI systemsHespanha-Morse. Stability of
switched systems with average dwell-time. (99)
3Slow switching
- Average dwell-time switching
Hespanha-Morse. Stability of switched systems
with average dwell-time. (99)
4Main result
Theorem 1
- Suppose that there exist
such that
5Application Supervisory Control
- A parameterized plant with unknown parameters
Goal stabilize the plant when and
guarantee bounded when is bounded.
6fixed
Plant
Controller
Multi- estimator
7A2 The injected systems satisfy ISS hypotheses
of Theorem 1 with respect to
(criteria for controllers multi-estimator
design)
then
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9- 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
10Controllers
Multi-estimator
11Conclusion
- 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