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While going trough these slides, I wasn't able to make sense of the following on slide 32: (if only providing the url to the slides is not ok I will edit the question, but doing it like that saves a lot of time)

Why does the fact that $V_f$ is a Lyapunov function result in $$V_f(\tilde{x}_{N+1}) − V_f(x_N) + l(x_N, κ_f(x_N))\leq 0?$$

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  • $\begingroup$ Can you add a summary, because slide 32 alone does not give any context for the mentioned variables. $\endgroup$ Sep 3 '18 at 12:43
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This is simply assumption 3 on slide 29. In practice, this assumption can be ensured via suitable choice/design of the terminal cost and the terminal set.

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  • $\begingroup$ you're right - cannot believe I missed that! $\endgroup$
    – VGD
    Sep 6 '18 at 8:44

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