Smriti Chopra ECE Ph.D. Candidate Georgia Tech

Control of Mobile Robots: Glue Lectures

Instructor:

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Glue Lecture 5: Hybrid Automata Pay attention, this lecture will help you all with Quiz 5!

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For example,

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Zeno Phenomenon

x = f1 x = f2

g(x) < 0

g(x) � 0

When is it Type 1 Zeno?

g(x) = 0

Lf1g < 0 ^ Lf2g > 0

Must induce sliding mode

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Example …

x = 6� x

x = 5x

x < 10

x � 10

Example …

g(x) = 0

Lf1g < 0 ^ Lf2g > 0

Check :

g(x) = 0 ) x = 10

Lf1g = 6� x < 0 ) x > 6

Lf2g = 5x > 0 ) x > 0

Must do sliding control !!!

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In general form … dg

dt= 0

(to find dynamics)

To find sliding mode dynamics …

dg

dt= 0 ) x = 0

x =1

Lf2g � Lf1g(Lf2gf1 � Lf1gf2)

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To find sliding mode dynamics …

x =1

Lf2g � Lf1g(Lf2gf1 � Lf1gf2)

Lf1g = 6� x = f1

Lf2g = 5x = f2

) x = 0

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All together …

x = 10 x = 10

x < 10

x =1

Lf2g � Lf1g(Lf2gf1 � Lf1gf2)

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x > 10

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Check the forums, and good luck with Quiz 5!