Input selection for multivariable extremum seeking control with application to real-time optimization of a chilled-water plant

Extremum Seeking Control (ESC) has been recognized as a potential model-free control solution for applications where model acquisition is difficult and/or cost prohibitive, e.g. for building HVAC systems. Such systems have large numbers of candidate inputs that could be used for ESC, however, it is not economically necessary to include all of them as manipulated inputs. This study presents a Hessian estimation based automatic input selection strategy for multi-variable ESC. The Hessian estimation strategy in the Newton based ESC is applied, and the singular values of the estimated Hessian matrix are used to decide the subset of inputs for the underlying ESC. The finite impulse response (FIR) filter is used for isolating the Hessian elements with faster transient performance than the infinite impulse (IIR) filter. Also, an optimal dither frequency design is performed to avoid undesirably close spacing between the associated frequency components and the use of large roll-off filters. The proposed approach is illustrated with a three-input numerical example, and the simulation is under way for a Modelica model for a chilled-water plant.