A scenario-based distributed stochastic MPC for building temperature regulation

In this paper, we focus on the temperature regulation of rooms in buildings. By using the dynamic model of the thermal process, weather condition, occupancy and so on, a Stochastic Model Predictive Control (SMPC) problem is formulated to keep the temperature of rooms within a comfortable range with a predefined probability while consuming less energy. The temperature regulation problem in this paper is an optimal control problem of a linear system with additive uncertainty. To overcome the computational burden caused by the large number of rooms, a subgradient-based dual decomposition method is used to solve the SMPC problem in a distributed manner. Simulation results show the effectiveness of our results.

[1]  Francesco Borrelli,et al.  Model Predictive Control of thermal energy storage in building cooling systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[2]  R. Nelsen.  An Introduction to Copulas , 1998 .

[3]  Francesco Borrelli,et al.  Fast stochastic predictive control for building temperature regulation , 2012, 2012 American Control Conference (ACC).

[4]  Philip Haves,et al.  Model predictive control for the operation of building cooling systems , 2010, Proceedings of the 2010 American Control Conference.

[5]  Giuseppe Carlo Calafiore,et al.  Random Convex Programs , 2010, SIAM J. Optim..

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

[7]  David Q. Mayne,et al.  Robust model predictive control using tubes , 2004, Autom..

[8]  Karl Henrik Johansson,et al.  A scenario-based predictive control approach to building HVAC management systems , 2013, 2013 IEEE International Conference on Automation Science and Engineering (CASE).

[9]  John Lygeros,et al.  On the Road Between Robust Optimization and the Scenario Approach for Chance Constrained Optimization Problems , 2014, IEEE Transactions on Automatic Control.

[10]  Giuseppe Carlo Calafiore,et al.  Uncertain convex programs: randomized solutions and confidence levels , 2005, Math. Program..

[11]  Pravin K. Trivedi,et al.  Copula Modeling: An Introduction for Practitioners , 2007 .

[12]  Mia Ala-Juusela,et al.  Buildings and Climate Change: Summary for Decision-Makers , 2009 .

[13]  Giuseppe Carlo Calafiore,et al.  The scenario approach to robust control design , 2006, IEEE Transactions on Automatic Control.

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

[15]  Peter Graham,et al.  Building and climate change: A summary for decision-makers / Peter Graham and Jenny Yamamoto (eds.) , 2011 .

[16]  Petru-Daniel Morosan,et al.  Building temperature regulation using a distributed model predictive control , 2010 .

[17]  C. Sempi,et al.  Copula Theory: An Introduction , 2010 .

[18]  Manfred Morari,et al.  Use of model predictive control and weather forecasts for energy efficient building climate control , 2012 .

[19]  David E. Culler,et al.  Reducing Transient and Steady State Electricity Consumption in HVAC Using Learning-Based Model-Predictive Control , 2012, Proceedings of the IEEE.

[20]  Manfred Morari,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[21]  Francesco Borrelli,et al.  Fast stochastic MPC with optimal risk allocation applied to building control systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[22]  T. Larsson,et al.  A Lagrangean Relaxation Scheme for Structured Linear Programs With Application To Multicommodity Network Flows , 1997 .

[23]  D. Mayne,et al.  Min-max feedback model predictive control for constrained linear systems , 1998, IEEE Trans. Autom. Control..

[24]  T. Fabian,et al.  Decomposition, Pricing for Decentralization and External Economies , 1964 .

[25]  Christian Ghiaus,et al.  Optimal temperature control of intermittently heated buildings using Model Predictive Control: Part I – Building modeling , 2012 .

[26]  J. Lygeros,et al.  On the sample size of randomized MPC for chance-constrained systems with application to building climate control , 2014, European Control Conference.

[27]  Manfred Morari,et al.  Scenario-based MPC for energy-efficient building climate control under weather and occupancy uncertainty , 2013, 2013 European Control Conference (ECC).

[28]  Bourhan Tashtoush,et al.  Dynamic model of an HVAC system for control analysis , 2005 .