**8. List of notations**



these results show how the effectiveness of the MPC control of complex environment relies on the power and on the flexibility of the Bayesian predictor and of the Bayesian Inference

In this Chapter we have shown that the role of Bayesian predictors may be critical in order to implement predictive control of buildings. This kind of control is one of the most effective ones currently being developed by researchers, because it is able to smooth control actions and to trigger them in advance. However, it cannot be applied without a reliable predictor of the expected state of the controlled domain. Such a predictor must be queried in real-time, which

In other words, computationally demanding software programs cannot be used to produce predictions at run time, but they can be run to generate datasets and these datasets may be used to transfer knowledge into Bayesian Networks. At this juncture, Bayesian inference may be performed: in fact, inputs by the controller (i.e. input variables describing the current state of the domain plus candidate arrays of control values) are instantiated in Bayesian Networks in the form of a set of evidences; then, inference algorithms are propagated and expected future values describing the energy and thermal state of the domain might be estimated. This procedure can be repeated thousands of times at each control step and it makes the imple‐

When implemented in a real case, the results from inferences were shown to be very accurate with low deviations from the values estimated by means of more complex numerical models. In addition, our testing of the use predictive Bayesian Networks embedded in a wider MPC framework to support the ranking of concurrent control policies was successful, too. So Bayesian Networks proved to be able to solve the problem of reducing complex models into more manageable tools for performing cumbersome inferences through limited computational

is feasible just in case a reasonable computational effort is required.

32 Dynamic Programming and Bayesian Inference, Concepts and Applications

paradigm.

**7. Conclusions**

mentation of MPC feasible.

**8. List of notations**

*BN* Bayesian Network

*DBN* Dynamic Bayesian Network

*AF-BN* Air Flow Prediction Bayesian Network

*General*

efforts, while getting highly accurate results.

**Nomenclature Meaning**

*TP-DBN* Temperature Prediction Dynamic Bayesian Network


*DFreSF1, DFreSF2, DFreTF1,*

*PElSF1, PElSF2, PElTF1,*

*Sub-section 5.2*

*X*

*X*

tunnels, respectively

*GaiTr1* Internal gain supplied by trains approaching on railway 1

respectively

*DTePL3* Variation of temperature in platform PL3

*X\_p01* Denotes one step ahead value for a variable X

*\_* Desired reference value for a certain variable *X*

*~* Normalisation factor for a certain variable *X*

α Weights of terms in cost function

respectively

*XMin, XMax* Minimum and maximum values allowed for a certain variable *X*

*X +, X -* Function that gets the absolute value of the positive and negative values of variableX,

This work is part of the EU-funded research SEAM4US. Also, we are very grateful to our colleagues Engs. Roberta Ansuini and Sara Ruffini, who helped us develop the models.

, Massimo Vaccarini and Alberto Giretti

Università Politecnica delle Marche, Department of Civil and Building Engineering and Ar‐

\*Address all correspondence to: alessandro.carbonari@univpm.it

chitecture, Via Brecce Bianche, Ancona, Italy

*J* Cost function to be minimized by MPC

*H* Prediction horizon

**Acknowledgements**

**Author details**

Alessandro Carbonari\*

*NPeSta* Number of people in the station *TemPL3* Temperature in platform PL3

*DTeOut* Variation of outdoor temperature *HFlOut* Heat flux coming from outdoor air

*TOuMet* Outdoor temperature

Discretized frequencies that drive the two fans in the station and the two fans in the

Bayesian Networks for Supporting Model Based Predictive Control of Smart Buildings

http://dx.doi.org/10.5772/58470

35

Electric power absorbed by the two fans in the station and the two fans in the tunnels,

*DFreTF2*

*PElTF2*

