Linear System Control

Controllability Gramians - CG Directory

• CG.py - Basic problem, has the option to do N-1 sum or Lyapunov Equatio
• CG_Bounded.py - Same problem, but runs a small optimization problem to keep U within bounds. This is because in a real-world problem, U would have to be within the bounds of the actuator.
• CG_AVL.py - This is a more difficult problem, where the system had to be transferred from continuous to discrete. Additionally, the state vector is 12 components, so a much higher dimensionality problem.

LQR Controller - LQR Directory

• Cart_Pole.py - Simple cart pole problem that uses ARE to solve for optimal controls.

MPC Controller - MPC Directory

• driver_SD.py - Simple spring dashpot mass system.
• driver_AVL.py - AVL example using MPC controller.
• NL_Drag.py - A nonlinear drag model, which demonstrates how a nonlinear model would have to be linearized at each step prior to MPC.
• src Directory - Contains the utils and background functions for MPC.