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#README.md

This directory contains a tutorial for using matlab to stabilize a trajectory of a non-linear system, using a finite-horizon continuous-time Linear Quadratic Regulator (LQR).

Entry-point function for the primary demo, using the full non-linear plant

• Plots vector field for non-linear system
• Generate a nominal trajectory
• Approximate trajectory using polynomial curve fitting
• Solve LQR along the trajectory
• Approximate gains using polynomial curve fitting
• Compare the gains obtained from finite vs infinite horizon lqr
• Run simulations to demonstrate controller's stabilizing properties

Solves the finite-horizon continuous-time LQR problem for a time-varying plant (stabilize a non-linear trajectory)

Derives the dynamics equations and writes function files for the non-linear plant.

A quick little demo to find the finite-horizon continuous-time LQR gains for a linear plant, and then comparing the solutions to the infinite-horizon version, generated using Matlab's lqr command.

Solves the finite-horizon continuous-time LQR problem for a linear time-invariant plant.