Stability proof of nominal MPC with terminal cost and constraint
Clash Royale CLAN TAG#URR8PPP
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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
$$V_f(tildex_N+1) â V_f(x_N) + l(x_N, ú_f(x_N))leq 0?$$
control-theory optimal-control stability-theory
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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
$$V_f(tildex_N+1) â V_f(x_N) + l(x_N, ú_f(x_N))leq 0?$$
control-theory optimal-control stability-theory
Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
â Kwin van der Veen
Sep 3 at 12:43
add a comment |Â
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
$$V_f(tildex_N+1) â V_f(x_N) + l(x_N, ú_f(x_N))leq 0?$$
control-theory optimal-control stability-theory
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
$$V_f(tildex_N+1) â V_f(x_N) + l(x_N, ú_f(x_N))leq 0?$$
control-theory optimal-control stability-theory
control-theory optimal-control stability-theory
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.
â Kwin van der Veen
Sep 3 at 12:43
add a comment |Â
Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
â 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.
â 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.
â Kwin van der Veen
Sep 3 at 12:43
add a comment |Â
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.
you're right - cannot believe I missed that!
â VGD
Sep 6 at 8:44
add a comment |Â
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.
you're right - cannot believe I missed that!
â VGD
Sep 6 at 8:44
add a comment |Â
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.
you're right - cannot believe I missed that!
â VGD
Sep 6 at 8:44
add a comment |Â
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.
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.
answered Sep 3 at 17:03
Nukular
15518
15518
you're right - cannot believe I missed that!
â VGD
Sep 6 at 8:44
add a comment |Â
you're right - cannot believe I missed that!
â VGD
Sep 6 at 8:44
you're right - cannot believe I missed that!
â VGD
Sep 6 at 8:44
you're right - cannot believe I missed that!
â VGD
Sep 6 at 8:44
add a comment |Â
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Can you add a summary, because slide 32 alone does not give any context for the mentioned variables.
â Kwin van der Veen
Sep 3 at 12:43