diff --git a/README.md b/README.md index 867f374b2a020831f186e52776763fb7d8605fa4..e580aef689224865ff300ed73611abf0140b6157 100644 --- a/README.md +++ b/README.md @@ -1,2 +1,19 @@ -# rbf-approx +# Overview +This project contains supplemental Matlab code for the article: +>M. Thelander Andrén, "Using Radial Basis Functions to Appriximate the LQG-Optimal Event-Based Sampling Policy", +Submitted to European Control Conference, 2019 + +It demonstrates a numerical method using radial basis functions (RBF) to compute +an approximation of the optimal event-based sampling policy for the continuous-time +sampled-data LQG problem. The optimal policy is given by the solution to a stationary +partial differential equation (PDE) with free boundary. The PDE is given by: + +```math +-V(\tilde{x}^\intercal Q\tilde{x} - J + \tilde{x}^\intercal A^\intercal\nabla V + \frac{1}{2}\Delta V) = 0,\quad \forall \tilde{x}, +``` +```math +-V\geq 0, \quad \tilde{x}^\intercal Q\tilde{x} - J + \tilde{x}^\intercal A^\intercal\nabla V + \frac{1}{2}\Delta V\geq 0, \quad \forall \tilde{x}. +``` +The solution to this PDE is the relative value function $`V:\tilde{x}\rightarrow\mathbb{R}`$, and the optimal sampling policy is to trigger sampling whenever $`V(\tilde{x})=0`$ holds. +For more details we refer to our [article](ecc2019_paper.pdf).