Auto sync: 2025-09-16 17:33:55 (7 files changed)
M .task/backlog.data M .task/completed.data M .task/pending.data M .task/undo.data A Writing/ERLM/research-approach/outline.md M "Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md" M "Zettelkasten/Permanent Notes/Literature Notes/LIT-20250911143337-multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems.md"
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{"description":"Research Approach Outline","entry":"20250916T203752Z","modified":"20250916T203826Z","project":"ERLM","status":"pending","uuid":"e6cc0b14-6db4-4935-b19f-674c812aeda3","tags":["writing"],"depends":["56c9b3cc-078e-4155-b4cd-f982ae23bd36","c008dbde-ec2a-42f7-a34c-a6038e9d8cd4"]}
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old [description:"Write research approach" due:"1758513600" entry:"1758055048" modified:"1758055048" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"56c9b3cc-078e-4155-b4cd-f982ae23bd36"]
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new [dep_c008dbde-ec2a-42f7-a34c-a6038e9d8cd4:"x" dep_e6cc0b14-6db4-4935-b19f-674c812aeda3:"x" depends:"c008dbde-ec2a-42f7-a34c-a6038e9d8cd4,e6cc0b14-6db4-4935-b19f-674c812aeda3" description:"Write research approach" due:"1758513600" entry:"1758055048" modified:"1758055281" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"56c9b3cc-078e-4155-b4cd-f982ae23bd36"]
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---
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old [description:"Research Approach First Draft" entry:"1758055095" modified:"1758055188" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"c008dbde-ec2a-42f7-a34c-a6038e9d8cd4"]
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new [dep_e6cc0b14-6db4-4935-b19f-674c812aeda3:"x" depends:"e6cc0b14-6db4-4935-b19f-674c812aeda3" description:"Research Approach First Draft" entry:"1758055095" modified:"1758055295" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"c008dbde-ec2a-42f7-a34c-a6038e9d8cd4"]
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---
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28
Writing/ERLM/research-approach/outline.md
Normal file
28
Writing/ERLM/research-approach/outline.md
Normal file
@ -0,0 +1,28 @@
|
|||||||
|
Okay so here's how things will go:
|
||||||
|
|
||||||
|
Integrate V design into the workings here
|
||||||
|
|
||||||
|
1. Requirement identification and translation
|
||||||
|
1. Point towards hardens lando thing
|
||||||
|
2. we're going to do a nuclear start up sequence
|
||||||
|
|
||||||
|
2. Synthesize requirements into a discrete automata
|
||||||
|
1. this makes up our mode switching behavior
|
||||||
|
2. There's probably going to be a serious amount of
|
||||||
|
refinement required here
|
||||||
|
3. Figure out by the structure of the nodes what the
|
||||||
|
purpose of the mode is
|
||||||
|
1. Do all traces leave? Do any traces leave? What
|
||||||
|
does this mean for the FUNCTION of the node?
|
||||||
|
|
||||||
|
3. Build controllers that satisfy each mode requirement
|
||||||
|
1. Reachability to ensure valid input and output sets?
|
||||||
|
2. We can ensure zeno behavior won't happen by looking
|
||||||
|
at the interface between modes
|
||||||
|
3. We should also see based on reachability that a well
|
||||||
|
built controller ONLY can enter the modes as
|
||||||
|
specified by the discrete automata
|
||||||
|
4. Contract based methods?
|
||||||
|
|
||||||
|
4. Fuck it man, that's like your provability or whatever
|
||||||
|
man.
|
||||||
@ -3,8 +3,22 @@ id: 20250911170650
|
|||||||
title: Lipschitz Continuous
|
title: Lipschitz Continuous
|
||||||
type: permanent
|
type: permanent
|
||||||
created: 2025-09-11T21:06:50Z
|
created: 2025-09-11T21:06:50Z
|
||||||
modified: 2025-09-11T21:06:50Z
|
modified: 2025-09-16T16:32:37Z
|
||||||
tags: []
|
tags: []
|
||||||
---
|
---
|
||||||
|
|
||||||
# Lipschitz Continuous
|
# Lipschitz Continuous
|
||||||
|
|
||||||
|
Lipschitz continuous functions are a special case of
|
||||||
|
continuous functions. Lipschitz continuity means that a cone
|
||||||
|
can be created with slope less than some real number
|
||||||
|
$K$.
|
||||||
|
|
||||||
|
Fora a real valued function in one dimension, Lipschitz
|
||||||
|
continuity is defined as:
|
||||||
|
|
||||||
|
$$| f(x_1) - f(x_2)| \leq K|x_1 - x_2|$$
|
||||||
|
|
||||||
|
Lipschitz continuity can be expanded to vector fields. From
|
||||||
|
here, we can say that ODE trajectories do NOT intersect, and
|
||||||
|
that every trajectory is unique.
|
||||||
|
|||||||
@ -3,7 +3,7 @@ id: LIT-20250911143337
|
|||||||
title: Multiple Lyapunov Functions and Other Analysis Tools for Swtiched and Hybrid Systems
|
title: Multiple Lyapunov Functions and Other Analysis Tools for Swtiched and Hybrid Systems
|
||||||
type: literature
|
type: literature
|
||||||
created: 2025-09-11T18:33:37Z
|
created: 2025-09-11T18:33:37Z
|
||||||
modified: 2025-09-11T21:53:20Z
|
modified: 2025-09-16T17:23:17Z
|
||||||
citekey:
|
citekey:
|
||||||
---
|
---
|
||||||
|
|
||||||
|
|||||||
Loading…
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Reference in New Issue
Block a user