Time-Varying Newton Based Extremum Seeking for Optimization of Vapor Compression Systems

In applications such as home air conditioners and building chillers, optimizing a vapor compression system's energy consumption may lead to significant operational cost savings for the entire HVAC system. Model-free extremum seeking has recently been investigated as a means of real-time nonlinear programming for HVAC equipment. For mass produced vapor compression systems, gradient descent extremum seeking may incur a high manual tuning cost because knowledge of the performance index function's curvature is required for algorithm deployment. Using Newton descent extremum seeking is a possible remedy for replacing manual tuning with automatic tuning of optimization gains. However, Newton descent extremum seeking requires estimation of the Hessian inverse, leading to an increase in the number of estimated parameters. Thus, a well-tuned gradient descent controller that incorporates prior knowledge of the Hessian inverse may converge at a faster rate. This paper proposes a discrete-time extremum seeking algorithm that extends previous approaches from the literature and addresses the Newton descent convergence rate issue by leveraging the recursive least-squares algorithm's potential for achieving fast parameter estimation. Using a moving boundary vapor compression system simulation model, the strengths and weaknesses of the proposed approach are evaluated against its gradient descent and LTI filter based extremum seeking counterparts. Results confirm that Newton descent is robust to Hessian uncertainty, while the convergence rate improvement from using recursive least-squares estimation helps the proposed approach compete with gradient descent extremum seeking.