How to set up your personal server for projects

How to set up a server for personal web projects.

GenAI and my six degrees of separation from tensor products

My experiences getting up and running with GenAI and views on code interpretability.

AI+Building Energy Modeling: IBPSA SimBuild 2024 Notes

Notes from attending the SimBuild conference, especially sessions on data science and modeling.

Running python on air-gapped systems

How to reproducibly run python code on a system with no internet access.

Helping fix aircraft - from NLP to Bayes Nets

NLP to help aircraft mechanics reason about maintenance actions

ChatGPT x Tennis - a weekend hacking project

Using ChatGPT as my coding assistant to help me play more tennis

Remote SSH into your home desktop

Things you’ll need: A dynamic DNS service A router A local desktop A remote computer Audience for this post: people who have used SSH before. Often times I have found myself wanting to access a computer at home while I am traveling. There are options like TeamViewer, which let me control my computer’s screen from afar. But, I want something more convenient over the command line, like SSH. That way I can drop in and out of my home machine without breaking my flow.

Modern control: Solutions & state transition matrices

The state equation for a linear time-invariant system: $$ x’(t) = A x(t) + B u(t) $$ Can be solved for $x(t)$. We collect all terms in $x$: $$ x’(t) - A x(t) = B u(t) $$ Multiply equation by $e^{-At}$ $$ x’(t) e^{-At} - A x(t) e^{-At} = B u(t) e^{-At} $$ Using product rule $d(f;g) = f;dg + g;df$, where: $$ \begin{align*} df = - A e^{-At} \rightarrow & f = e^{-At} \\ dg = x'(t) \rightarrow & g = x(t) \\ \\ \therefore x'(t) e^{-At} - A x(t) e^{-At} &= d (e^{-At} x(t)) \end{align*} $$ To give:

Modern control: State space equations

In modern control approaches, systems are analyzed in time domain as a set of differential equations. Higher order differential equations are decomposed into sets of first order equations of state variables that represent the system internally. This produces three sets of variables: Input variables are stimuli given to the system. Denoted by $u$. Output variables are the result of the current system state and inputs. Denoted by $y$. State variables represent the internal state of a system which may be obscured in the output variables.

Classical control: Transfer functions

A transfer function relates the output of a system to its input when it is represented in the Laplace domain. An assumption is made that initial steady-state response is 0. If $Y(s)$ is the output of a system, $X(s)$ is the input, then the transfer function is: $$ H(s) = \frac{Y(s)}{X(s)} $$ Example - A Car A car as a system: The input is the acceleration. The output is the total distance travelled.

Classical control: Transforms

Classical control methods simplify handling of a complex system by representing it in a different domain. The equations governing system dynamics are transformed into a different set of variables. A for a function $f(t)$ in the $t$ domain, an oft used transformation is of the form: $$ \mathcal{T}(f(t)) = F(s) = \int_{Domain} f(t) \cdot g(s, t); dt $$ Mathematically, the integral removes the $t$ variable and only leaves $s$, thus converting from the $t$ domain to the $s$ domain.

Control Systems: Overview

A primer for classical control theory.