Problem $4$

Pick a cyber$-$physical system of your interest and perform the following tasks:

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a$)$ Describe the purpose of the system.

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b$)$ Explain why the system you chose is a cyber$-$physical system.

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c$)$ Define the physical, cyber, and interface components.

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d$)$ Derive a mathematical model for each of them. Clearly specify the parameters, inputs, outputs, states, etc.

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e$)$ Determine a property that you would like to study for this system.

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f$)$ Define the associated functions

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F and

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G$,$ and the sets

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C and

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D of a hybrid equation$/$inclusion

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g$)$ Explain what type of executions $($or solutions$)$ one would obtain for each initial condition $($and for each given input, if appropriate$)$; that is$,$ determine if they would be nontrivial, continuous, discrete, etc.