Systems and methods for monitoring and controlling a plant using extremum-seeking control. The method includes perturbing a setpoint for a controller by applying a dither signal to the setpoint. The controller uses a perturbed setpoint to generate one or more control inputs for the building equipment. Receiving, from the building equipment, an output signal and obtaining values of a performance variable based on the output signal, the values of the performance variable resulting from operating the building equipment based on the perturbed setpoint. The method includes determining 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. The method includes determining an adjustment to the setpoint predicted to drive the performance variable to an extremum based on the gradient and the Hessian of the performance variable.