Extremum seeking control system and a method for controlling a system

An extremum seeking control method for controlling a subject system, wherein the method uses a processor coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out at least some steps of the method, comprising:

• receiving a tracking error, consecutive measurements of a system output of the subject system, and consecutive measurements of a cost function of the subject system, wherein the tracking error is a difference between a set-point of the subject system and a measurement of the system output;
• estimating a gradient indicating a direction of change of the set-point of the subject system, based on the tracking error, the consecutive measurements of the system output, and the consecutive measurements of the cost function of the subject system;
• determining a weight based on the tracking error and a difference between the consecutive measurements of the system output;
• determining a covariance of the gradient, based on the weight and the difference between the consecutive measurements of the system output;
• determining a step-size based on a ratio of the covariance of the gradient to the gradient wherein the step-size corresponds to a magnitude of the change of the set-point of the subject system;
• determining a set-point optimizing performance of the subject system, based on the direction of the change of the set-point of the subject system, and the magnitude of the change of the set-point of the subject system;
• generating one or more control commands defining one or more operational parameters of the subject system, based on the determined set point;
• and
• controlling the system according to the one or more control commands.

A non-transitory computer-readable storage medium embodied thereon a program executable by a processor for performing a method, the method comprising:

• receiving a tracking error, consecutive measurements of a system output, and consecutive measurements of a cost function of the subject system, wherein the tracking error is a difference between a set-point of the subject system and a measurement of the system output;
• estimating a gradient indicating a direction of change of the set-point of the subject system, based on the tracking error, the consecutive measurements of the system output, and the consecutive measurements of the cost function of the subject system;
• determining a weight based on the tracking error and a difference between consecutive measurements of the system output;
• determining a covariance of the gradient, based on the weight and the difference between the consecutive measurements of the system output;
• determining a step-size based on a ratio of the covariance of the gradient to the gradient, wherein the step-size corresponds to a magnitude of the change of the set-point of the subject system;
• determining a set-point optimizing performance of the subject system, based on the direction of the change of the set-point of the subject system, and the magnitude of the change of the set-point of the subject system;
• generating one or more control commands defining one or more operational parameters of the subject system based on the determine d set point;
• and
• controlling the system according to the one or more control commands.