diff --git a/.task/backlog.data b/.task/backlog.data index 7be9eeb3..7b5be322 100644 --- a/.task/backlog.data +++ b/.task/backlog.data @@ -31,3 +31,5 @@ {"description":"Read Branicky Lyapunov paper","entry":"20250911T183429Z","modified":"20250911T200147Z","project":"Thesis","start":"20250911T200147Z","status":"pending","uuid":"f4d32147-ec74-4f68-b8d5-146c0b6f35df","tags":["reading"]} {"description":"Write first draft of state of the art","due":"20250912T040000Z","entry":"20250909T203258Z","modified":"20250911T200235Z","project":"ERLM","status":"pending","uuid":"4bec1530-18bc-43cb-9f0b-61e35dbf1730","tags":["writing"],"depends":["8e7a8e19-9197-4008-b7d9-521ffcf7ba91","96c76e6b-5c33-4f54-a156-5c59e718f01a","f4d32147-ec74-4f68-b8d5-146c0b6f35df"]} {"description":"Read Branicky Lyapunov paper","entry":"20250911T183429Z","modified":"20250911T201816Z","project":"Thesis","status":"pending","uuid":"f4d32147-ec74-4f68-b8d5-146c0b6f35df","tags":["reading"]} +{"description":"Write zettel about lipschitz continuity","entry":"20250911T211029Z","modified":"20250911T211029Z","status":"pending","uuid":"b7f68988-8c06-4d18-bf77-91d7e39fd55f","tags":["zk"]} +{"description":"Read Branicky Lyapunov paper","end":"20250911T214953Z","entry":"20250911T183429Z","modified":"20250911T214953Z","project":"Thesis","status":"completed","uuid":"f4d32147-ec74-4f68-b8d5-146c0b6f35df","tags":["reading"]} diff --git a/.task/completed.data b/.task/completed.data index 6dd6daf1..aad7aea2 100644 --- a/.task/completed.data +++ b/.task/completed.data @@ -1,3 +1,4 @@ +[description:"Read Branicky Lyapunov paper" end:"1757627393" entry:"1757615669" modified:"1757627393" project:"Thesis" status:"completed" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] [description:"Follow up with Daniel about controls bootcamp" due:"1757563200" end:"1757618582" entry:"1757449130" modified:"1757618582" project:"FSAE" status:"completed" uuid:"3eaadead-4e5e-4823-9077-16d6e1800862"] [description:"Follow up with Bajaj about writing TurboSAR paper" due:"1757563200" end:"1757618582" entry:"1757449286" modified:"1757618583" priority:"L" status:"completed" uuid:"fa2699f9-0082-433e-ae0d-cc2553db9865"] [description:"Write outline for state of the art" due:"1757476800" end:"1757516746" entry:"1757443175" modified:"1757516746" project:"ERLM" status:"completed" uuid:"8e7a8e19-9197-4008-b7d9-521ffcf7ba91"] diff --git a/.task/pending.data b/.task/pending.data index a1074898..434d3824 100644 --- a/.task/pending.data +++ b/.task/pending.data @@ -5,4 +5,4 @@ [dep_8e7a8e19-9197-4008-b7d9-521ffcf7ba91:"x" dep_96c76e6b-5c33-4f54-a156-5c59e718f01a:"x" dep_f4d32147-ec74-4f68-b8d5-146c0b6f35df:"x" depends:"8e7a8e19-9197-4008-b7d9-521ffcf7ba91,96c76e6b-5c33-4f54-a156-5c59e718f01a,f4d32147-ec74-4f68-b8d5-146c0b6f35df" description:"Write first draft of state of the art" due:"1757649600" entry:"1757449978" modified:"1757620955" project:"ERLM" status:"pending" tags:"writing" tags_writing:"x" uuid:"4bec1530-18bc-43cb-9f0b-61e35dbf1730"] [description:"get FSAE COM and track data to Matt barry for statics problem. He also wants a cad model?" due:"1758254400" entry:"1757515988" modified:"1757515988" status:"pending" uuid:"48f997bf-b686-4c0b-bee5-ac8e5f874ad9"] [description:"Read Opportunities, Challenges, and Research Needs for Remote Microreactor Operations" entry:"1757516723" modified:"1757516723" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"96c76e6b-5c33-4f54-a156-5c59e718f01a"] -[description:"Read Branicky Lyapunov paper" entry:"1757615669" modified:"1757621896" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] +[description:"Write zettel about lipschitz continuity" entry:"1757625029" modified:"1757625029" status:"pending" tags:"zk" tags_zk:"x" uuid:"b7f68988-8c06-4d18-bf77-91d7e39fd55f"] diff --git a/.task/undo.data b/.task/undo.data index 3804958d..1efcd4bc 100644 --- a/.task/undo.data +++ b/.task/undo.data @@ -109,3 +109,10 @@ time 1757621896 old [description:"Read Branicky Lyapunov paper" entry:"1757615669" modified:"1757620907" project:"Thesis" start:"1757620907" status:"pending" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] new [description:"Read Branicky Lyapunov paper" entry:"1757615669" modified:"1757621896" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] --- +time 1757625029 +new [description:"Write zettel about lipschitz continuity" entry:"1757625029" modified:"1757625029" status:"pending" tags:"zk" tags_zk:"x" uuid:"b7f68988-8c06-4d18-bf77-91d7e39fd55f"] +--- +time 1757627393 +old [description:"Read Branicky Lyapunov paper" entry:"1757615669" modified:"1757621896" project:"Thesis" status:"pending" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] +new [description:"Read Branicky Lyapunov paper" end:"1757627393" entry:"1757615669" modified:"1757627393" project:"Thesis" status:"completed" tags:"reading" tags_reading:"x" uuid:"f4d32147-ec74-4f68-b8d5-146c0b6f35df"] +--- diff --git a/Zettelkasten/Permanent Notes/20250829114522-hybrid-systems.md b/Zettelkasten/Permanent Notes/20250829114522-hybrid-systems.md index 4e1e49db..a2eb0430 100644 --- a/Zettelkasten/Permanent Notes/20250829114522-hybrid-systems.md +++ b/Zettelkasten/Permanent Notes/20250829114522-hybrid-systems.md @@ -3,22 +3,55 @@ id: 20250829114522 title: Hybrid Systems type: permanent created: 2025-08-29T15:45:22Z -modified: 2025-08-29T15:48:22Z +modified: 2025-09-11T21:46:53Z tags: [] --- # Hybrid Systems -Hybrid systems are those that mix continuous dynamics with -discrete dynamics. This can mean physical phenomena -controlled by something discrete like a logic based -controller, or more interestingly controllers that switch -control laws based on different circumstances. +I'm borrowing a lot from +[[multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems]]. + +Hybrid systems are those that combine continuous and +discrete dynamics together. This is usually some sort of +finite automata + differential equations. + +Hybrid systems can be written like: + +$$\dot{x}(t) = \xi(t), \quad t\geq 0$$ + +where $x(t)$ is the continuous component of the state. +$\xi(t)$ is a vector field that depends on $x(t)$ and the +hybrid dynamics. + +Switching between modes (aka discontinuities in $\xi(\cdot)$) +can happen in one of two ways: + +1. **Autonomous Switching** - Autonomous switches happen + depending on state values of $x(t)$. + +2. **Controlled Switching** - $\xi(\cdot)$ changes abruptly + in response to a control command. + +One may write a continuous time autonomous hybrid system +like this: + +$$\dot{x}(t) = f(x(t), q(t))$$ +$$q(t) = \nu(x(t), q(t^-))$$ + +where: +- $x(t) \in R^n$ +- $q(t) \in Q \simeq {1,...,N}$ +- $f(\cdot,q): R^n \rightarrow R^n,q \in Q$, with each +[[lipschitz-continuous]]. These are the *continuous +dynamics*. +- $\nu: R^n \times Q \rightarrow Q$ is the *finite dynamics* + +A controlled system might be written as: +$$\dot{x}(t) = f(x(t), q(t), u(t))$$ +$$q(t) = \nu(x(t), q(t^-), u(t))$$ + +where: +- $u(t) \in R^m$ + -Gemini AI says a good example of a hybrid controller is a -robot that uses a movement controller until it reaches a -target, and then switching to a force controller thereafter. -The continuous dynamics and physics have not changed, but -the derived model of the physics has entirely in a discrete -way. This kind of 'mode' switching is called being -event-driven. diff --git a/Zettelkasten/Permanent Notes/20250911165736-switched-systems.md b/Zettelkasten/Permanent Notes/20250911165736-switched-systems.md new file mode 100644 index 00000000..341b5f31 --- /dev/null +++ b/Zettelkasten/Permanent Notes/20250911165736-switched-systems.md @@ -0,0 +1,35 @@ +--- +id: 20250911165736 +title: Switched Systems +type: permanent +created: 2025-09-11T20:57:36Z +modified: 2025-09-11T21:09:55Z +tags: [] +--- + +# Switched Systems + +Switched systems are those that mix continuous and discrete +dynamics. They are systems that are 'multimodal'. This means +that they can have different continuous dynamic modes. + +I'm borrowing form +[[multiple-lyapunov-functions-and-other-analysis-tools-for-swtiched-and-hybrid-systems]], +but here's a short description of how they work. + +A prototypical switched system is as follows: +$$\dot{x}(t)=f_i ( x(t)), \quad i \in Q \simeq {1,...,N}$$ + +with two conditions: +1. Each $f_i$ is globally [[Lipschitz Continuous]] +2. The i's are picked in a way that there are finite + switches in finite time. + + +There's also this thing called a *continuous switched +system*. A continuous switched system is one that does not +change continuous states when a switch occurs. That is to +say when switching from $i$ to $i'$: + +$$f_i(x(t_i),t_i) = f_{i'}(x(t_{i'}),t_{i'})$$ + diff --git a/Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md b/Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md new file mode 100644 index 00000000..d6ecdfa6 --- /dev/null +++ b/Zettelkasten/Permanent Notes/20250911170650-lipschitz-continuous.md @@ -0,0 +1,10 @@ +--- +id: 20250911170650 +title: Lipschitz Continuous +type: permanent +created: 2025-09-11T21:06:50Z +modified: 2025-09-11T21:06:50Z +tags: [] +--- + +# Lipschitz Continuous 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 b8567819..5a5b8a6a 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: 2025-09-11T20:55:15Z +modified: 2025-09-11T21:53:20Z citekey: --- @@ -46,4 +46,7 @@ Complex ideas written simply. Easy to read. **Weak Points? Strong Points?** ## Zettels Created +[[Switched Systems]] +[[hybrid-systems]] +[[lipschitz-continuous]]