Newton-based extremum-seeking control system

A method for operating and assessing performance of building equipment, the method comprising:

• perturbing a setpoint for a controller by applying a dither signal to the setpoint, resulting in a perturbed setpoint, and
• providing the perturbed setpoint to the controller, wherein the controller uses the perturbed setpoint to generate one or more control inputs for the building equipment, and the building equipment operate in accordance with the control inputs to affect a performance variable indicating a performance of the building equipment;
• receiving, from the building equipment, an output signal and obtaining values of the performance variable based on the output signal, the values of the performance variable resulting from operating the building equipment based on the perturbed setpoint;
• determining, from the values of the performance variable, a gradient of the performance variable with respect to the perturbed setpoint and a Hessian of the performance variable affected by the building equipment with respect to the setpoint;
• determining an adjustment to the setpoint predicted to drive the performance variable to an extremum based on the gradient of the performance variable and the Hessian of the performance variable.

A non-transitory computer-readable storage medium having instructions stored thereon that, upon execution by a processor, cause the processor to perform operations to operate and assess performance of building equipment , the operations comprising:

• perturbing a setpoint for a controller by applying a dither signal to the setpoint, resulting in a perturbed setpoint;
• providing the perturbed setpoint to the controller, wherein the controller uses the perturbed setpoint to generate one or more control inputs for the building equipment, and the building equipment operate in accordance with the control inputs to affect a performance variable indicating a performance of the building equipment;
• receiving, from the building equipment, an output signal and obtaining values of the performance variable based on the output signal, the values of the performance variable resulting from operating the building equipment based on the perturbed setpoint;
• determining, from the values of the performance variable, a gradient of the performance variable with respect to the perturbed setpoint and a Hessian of the performance variable affected by the building equipment with respect to the setpoint;
• and
• determining an adjustment to the setpoint predicted to drive the performance variable to an extremum based on the gradient of the performance variable and the Hessian of the performance variable.