control-toys

A collection of simple nonlinear dynamical systems with linear quadratic control

Dependencies

• NumPy
• SciPy
• Matplotlib
• Autograd

Instructions

1. Tweak settings.py
2. Run main.py

System definitions

• Systems are defined in systems.py
• System definitions consist of
  • dynamics function, a differentiable nonlinear map n+m → n that governs deterministic continuous-time state transitions
  • cost function, a differentiable map n+m → 1 that governs the control objective
  • disturbance function, a map n+m → n that generates stochastic additive disturbances
  • x_eq_list and u_eq_list, lists of equilibrium states and inputs to cycle thru
  • make_artist_props function, makes artist properties to draw the system in the current state-input configuration

Functionality

• Dynamics are linearized and costs quadratized around the initial equilibrum point
• Steady-state LQR gain is designed on this basis
• Control inputs are generated to track the current equilibrium point