Stability proof of nominal MPC with terminal cost and constraint

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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
$$V_f(tildex_N+1) − V_f(x_N) + l(x_N, κ_f(x_N))leq 0?$$










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  • Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
    – Kwin van der Veen
    Sep 3 at 12:43














up vote
1
down vote

favorite












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
$$V_f(tildex_N+1) − V_f(x_N) + l(x_N, κ_f(x_N))leq 0?$$










share|cite|improve this question





















  • Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
    – Kwin van der Veen
    Sep 3 at 12:43












up vote
1
down vote

favorite









up vote
1
down vote

favorite











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
$$V_f(tildex_N+1) − V_f(x_N) + l(x_N, κ_f(x_N))leq 0?$$










share|cite|improve this question













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
$$V_f(tildex_N+1) − V_f(x_N) + l(x_N, κ_f(x_N))leq 0?$$







control-theory optimal-control stability-theory






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asked Sep 3 at 11:50









VGD

678




678











  • Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
    – Kwin van der Veen
    Sep 3 at 12:43
















  • Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
    – Kwin van der Veen
    Sep 3 at 12:43















Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
– Kwin van der Veen
Sep 3 at 12:43




Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
– Kwin van der Veen
Sep 3 at 12:43










1 Answer
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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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  • you're right - cannot believe I missed that!
    – VGD
    Sep 6 at 8:44










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










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.






share|cite|improve this answer




















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














up vote
1
down vote



accepted










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.






share|cite|improve this answer




















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












up vote
1
down vote



accepted







up vote
1
down vote



accepted






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.






share|cite|improve this answer












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.







share|cite|improve this answer












share|cite|improve this answer



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answered Sep 3 at 17:03









Nukular

15518




15518











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
















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















you're right - cannot believe I missed that!
– VGD
Sep 6 at 8:44




you're right - cannot believe I missed that!
– VGD
Sep 6 at 8:44

















 

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