dstuemk / nonlinear-ctrl

Stabilizing a non-linear system with backstepping and lyapunov based control

Non-Linear Control

In this MATLAB-Script two feedback controllers for stabilizing a non-linear dynamical system are compared. The system is described by the following differential equation:

Control strategies

Backstepping control

Recursive design where in each step one state variable get's controled. The resulting closed loop system leads to asymptotic stability.

Finally substitude back and into the control law.

Lyapuov based control

A positive definite "pseudo-energy" energy function is defined. The control law aims to make the derivative of this function negative (semi-)definite. This leads to a closed loop system which loses energy over time.

Phase portrait