Dynamic system control using deep machine learning

A method comprising:

• defining a nonlinear dynamic control system by a set of equations that include a state vector z and one or more control inputs u;
• via a machine learning method, deriving a sub-optimal controller that stabilizes the nonlinear dynamic control system at an equilibrium point;
• and
• retraining the sub-optimal controller to be used as a stabilizing controller for the nonlinear dynamic control system under general operating conditions, wherein retraining the sub-optimal controller comprises a model predictive control (MPC) approach in which a parameterized, state-dependent control map is learned by solving a sequence of finite horizon optimal control problems.

A system comprising:

• a controlled apparatus comprising a dynamic, closed-loop, stabilizing controller used to control a state of the controlled apparatus;
• and
• a computer comprising a memory coupled to a processor, the memory comprising instructions that cause the processor to:
• define a dynamic control system by a set of equations that include a state vector z of the controlled apparatus and one or more control inputs u of the controlled apparatus;
• via a machine learning method, derive a sub-optimal controller that stabilizes the controlled apparatus at an equilibrium point;
• retrain the sub-optimal controller to be used as a stabilizing controller for the controlled apparatus under general operating conditions;
• and
• facilitate transferring the stabilizing controller to the controlled apparatus.