Method and system for devising an optimum control policy

A method for automatically tuning a multivariate PID controller for controlling a system, said method comprising:

• configuring the multivariate PID controller with a random control policy for controlling the system, said random control policy having at least one parameter that characterizes said random control policy;
• controlling the system with the multivariate PID controller based on said random control policy;
• devising an optimum control policy for the multivariate PID controller for controlling the system by
• optimizing said at least one parameter that characterizes said random control policy;
• using a Gaussian process model to model expected dynamics of the system, wherein said optimization optimizes a cost function which depends on said random control policy and said Gaussian process model with respect to said at least one parameter;
• and
• carrying out said optimization by evaluating at least one gradient of said cost function with respect to said at least one parameter to generate at least one optimized parameter of said optimum control policy,
• wherein for an evaluation of said cost function a temporal evolution of a state of the system is computed using said random control policy and said Gaussian process model, and
• wherein said cost function depends on an evaluation of an expectation value of a cost function under a probability density of an augmented state at time steps,
• tuning the multivariate PID controller by changing said at least one parameter to said at least one optimized parameter;
• and
• controlling the system with the tuned multivariate PID controller based on the optimum control policy.