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description:"Research Approach First Draft" entry:"1758055095" modified:"1758055295" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"c008dbde-ec2a-42f7-a34c-a6038e9d8cd4"] +--- diff --git a/Writing/ERLM/research-approach/outline.md b/Writing/ERLM/research-approach/outline.md new file mode 100644 index 000000000..1f2e4ab48 --- /dev/null +++ b/Writing/ERLM/research-approach/outline.md @@ -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. diff --git a/Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md b/Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md index d6ecdfa64..9497617cb 100644 --- a/Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md +++ b/Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md @@ -3,8 +3,22 @@ id: 20250911170650 title: Lipschitz Continuous type: permanent created: 2025-09-11T21:06:50Z -modified: 2025-09-11T21:06:50Z +modified: 2025-09-16T16:32:37Z tags: [] --- # 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. diff --git a/Zettelkasten/Permanent Notes/Literature Notes/LIT-20250911143337-multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems.md b/Zettelkasten/Permanent Notes/Literature Notes/LIT-20250911143337-multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems.md index 5a5b8a6a3..88cd41816 100644 --- a/Zettelkasten/Permanent Notes/Literature Notes/LIT-20250911143337-multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems.md +++ b/Zettelkasten/Permanent Notes/Literature Notes/LIT-20250911143337-multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems.md @@ -3,7 +3,7 @@ id: LIT-20250911143337 title: Multiple Lyapunov Functions and Other Analysis Tools for Swtiched and Hybrid Systems type: literature created: 2025-09-11T18:33:37Z -modified: 2025-09-11T21:53:20Z +modified: 2025-09-16T17:23:17Z citekey: ---