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Continuous-Time, Finite-Horizon LQR

version (42 KB) by Matthew Kelly
Derivation and implementation of continuous-time finite-horizon Linear Quadratic Regulator


Updated 21 Feb 2016

GitHub view license on GitHub

A tutorial for using matlab to stabilize a trajectory of a non-linear system, using a finite-horizon continuous-time Linear Quadratic Regulator (LQR). The function trajectoryLqr.m solves the finite-horizon continuous-time LQR problem for a time-varying plant. This is used to generate a trajectory tracking controller. Includes multiple example files to show usage.
The image shows an estimation of the backward-reachable set of states along the trajectory which can be stabilized to the target along the trajectory of choice using the finite-horizon continuous-time LQR controller.

Cite As

Matthew Kelly (2019). Continuous-Time, Finite-Horizon LQR (, GitHub. Retrieved .

Comments and Ratings (7)


Mark Tinker

My primary reference for continuous time-varying LQR was the paper "LQR-Trees: Feedback Motion Planning via Sums-of-Squares Verification" by Russ Tedrake at MIT. You can find a pdf here:

The reachability calculation is not from any specific paper. The technique is generally known as "Front Propagation", and it is entirely based on simulation, although this is a very simplistic implementation (typically you need to re-mesh the front as time progresses).

You might be interested in the Level-Set Toolbox by Ian Mitchell at UBC, which uses level-set methods to compute reachable sets.

I hope that this helps!


Thanx, Matthew for the link. I have managed to download. I am doing masters thesis on optimal control. Can you suggest me some documents which you followed for analyzing the reachability trajectory..

AMRITAM DAS -- The "Download Zip" link seems to work fine for me. You can't preview the files because this submission is actually a GitHub repository:

If you're still having download problems, then you can download directly from GitHub, and also preview the source code on that website.

Best of luck, and let me know if you have any questions or comments about the code!


Why can't I download this file ?

Matthew Sheen


improved title, summary, and image.

MATLAB Release Compatibility
Created with R2012a
Compatible with any release
Platform Compatibility
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