Mean-Field Control for Improving Energy Efficiency

In this chapter, we describe a mean-field control method to improve energy efficiency for operating the heating, ventilation, and air conditioning (HVAC) systems. To illustrate the idea of this method, we consider a distributed set-point temperature regulation problem for building HVAC systems. With a large number of zones in large buildings, the problem becomes intractable with standard control approaches due to the large state space dimension of the dynamic model. To mitigate complexity, we apply the mean-field control approach to large-scale control problems in buildings. The mean-field here represents the net effect of the entire building envelope on any individual zone. Rather than solving the large-scale centralized problem, we explore distributed game-theoretic solution approaches that work by optimizing with respect to the mean-field. The methodology is illustrated with a numerical example in a simulation environment.

[1]  Minyi Huang,et al.  Nash Certainty Equivalence in Large Population Stochastic Dynamic Games: Connections with the Physics of Interacting Particle Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[2]  George J. Pappas,et al.  Receding-horizon supervisory control of green buildings , 2011, Proceedings of the 2011 American Control Conference.

[3]  P. Lions,et al.  Mean field games , 2007 .

[4]  Michael R. Brambley,et al.  Advanced Sensors and Controls for Building Applications: Market Assessment and Potential R&D Pathways , 2005 .

[5]  M Morari,et al.  Energy efficient building climate control using Stochastic Model Predictive Control and weather predictions , 2010, Proceedings of the 2010 American Control Conference.

[6]  Francesco Borrelli,et al.  A distributed predictive control approach to building temperature regulation , 2011, Proceedings of the 2011 American Control Conference.

[7]  Sean P. Meyn,et al.  Synchronization of Coupled Oscillators is a Game , 2010, IEEE Transactions on Automatic Control.

[8]  M. M. Gouda,et al.  Building thermal model reduction using nonlinear constrained optimization , 2002 .

[9]  Andrew G. Alleyne,et al.  Optimal control architecture selection for thermal control of buildings , 2011, Proceedings of the 2011 American Control Conference.

[10]  Petru-Daniel Morosan,et al.  A distributed MPC strategy based on Benders' decomposition applied to multi-source multi-zone temperature regulation , 2011 .

[11]  Minyi Huang,et al.  Large-Population Cost-Coupled LQG Problems With Nonuniform Agents: Individual-Mass Behavior and Decentralized $\varepsilon$-Nash Equilibria , 2007, IEEE Transactions on Automatic Control.

[12]  Prabir Barooah,et al.  Identification of multi-zone building thermal interaction model from data , 2011, IEEE Conference on Decision and Control and European Control Conference.

[13]  Prabir Barooah,et al.  A Method for model-reduction of nonlinear building thermal dynamics , 2011, Proceedings of the 2011 American Control Conference.

[14]  Sean P. Meyn,et al.  Building thermal model reduction via aggregation of states , 2010, Proceedings of the 2010 American Control Conference.