- Research
- Open Access
Using personal environmental comfort systems to mitigate the impact of occupancy prediction errors on HVAC performance
- Milan Jain^{1}Email author,
- Rachel K. Kalaimani^{2},
- Srinivasan Keshav^{3} and
- Catherine Rosenberg^{3}
- Received: 6 September 2018
- Accepted: 1 November 2018
- Published: 12 December 2018
Abstract
Heating, Ventilation and Air Conditioning (HVAC) consumes a significant fraction of energy in commercial buildings. Hence, the use of optimization techniques to reduce HVAC energy consumption has been widely studied. Model predictive control (MPC) is one state of the art optimization technique for HVAC control which converts the control problem to a sequence of optimization problems, each over a finite time horizon. In a typical MPC, future system state is estimated from a model using predictions of model inputs, such as building occupancy and outside air temperature. Consequently, as prediction accuracy deteriorates, MPC performance–in terms of occupant comfort and building energy use–degrades. In this work, we use a custom-built building thermal simulator to systematically investigate the impact of occupancy prediction errors on occupant comfort and energy consumption. Our analysis shows that in our test building, as occupancy prediction error increases from 5 to 20% the performance of an MPC-based HVAC controller becomes worse than that of even a simple static schedule. However, when combined with a personal environmental control (PEC) system, HVAC controllers are considerably more robust to prediction errors. Thus, we quantify the effectiveness of PECs in mitigating the impact of forecast errors on MPC control for HVAC systems.
Keywords
- HVAC
- Control
- Optimisation
- Error analysis
- Thermal modelling
- Simulation
Introduction
Commercial buildings account for about one-third of global energy consumption, with HVAC (Heating Ventilating and Air-Conditioning) units being the major contributor. An HVAC typically comprises of few Air Handling Units (AHUs), which heat or cool the air to a specified setpoint temperature, and Variable Air Volume (VAV) units that control the volume of air flowing into each thermal zone. In most commercial buildings, HVAC maintains a desired set point temperature during working hours (9 AM to 6 PM) and a set back temperature during non-working hours. Unfortunately, given the stochastic nature of building occupancy, a static schedule either leads to energy wastage or occupant discomfort (Dawson-Haggerty et al. 2013; Erickson et al. 2013).
HVAC energy optimization is an active area of research. In the literature, studies have proposed several control strategies which broadly fall into two categories: reactive and predictive (Balaji et al. 2013; Erickson et al. 2011; Gyalistras et al. 2010; Oldewurtel et al. 2010). In a reactive controller, AHUs and VAVs respond to measured occupancy in a zone. Here, occupancy is measured using motion, CO_{2} sensors, or by monitoring building’s WiFi infrastructure (Trivedi et al. 2017). Since buildings typically take some time to respond to control inputs, better performance can be obtained using predictive control strategy where the controller selects the optimal trajectory of set points for a finite time horizon. Of the predictive control techniques, perhaps the best-known approach is Model Predictive Control (MPC) (Garcia et al. 1989).
In a typical MPC, a known building thermal model estimates the future system state using forecasts of model inputs, such as building occupancy and outside air temperature. However, the effectiveness of this approach depends on the accuracy of the predictions. As prediction accuracy deteriorates, MPC performance - in terms of occupant comfort and building energy use - degrades and may get even worse than conventional techniques. In recent work, Oldewurtel et al. (2011) extensively studied the influence of errors in weather forecast on HVAC energy consumption and occupants’ comfort and quantified the impact of mis-predictions. However, the work neither addressed errors in occupancy prediction nor studied the ways to mitigate the influence of prediction errors.
In this paper, we address this gap. We study the influence of occupancy errors on MPC performance using a custom-built building simulator. We also model and analyze the impact of personal environmental control system (PEC) in the presence of prediction errors. A PEC could be an off-the-shelf desktop fan or a heater to provide individual thermal comfort (Brager et al. 2015). We find that PEC when used with model predictive control, can reduce both - the variability in energy consumption and the occupants’ discomfort.
- 1
We present the design and development of a building thermal simulator that models conventional schedule-based, reactive occupancy-based, and predictive MPC-based HVAC controllers.
- 2
We extend the MPC-based control strategy proposed by Kalaimani et al. (2018) and allow PEC to react between any two consecutive states of the system.
- 3
We quantify the impact of occupancy prediction errors on two MPC-based control strategies - with and without PEC. For analysis, we use occupancy data from forty-five volunteers over three months and simulations of a test building in both heating and cooling seasons.
- 4
It is important that occupancy forecast errors are realistic; thus, we propose a method to systematically introduce realistic occupancy errors into MPC predictions using real-world occupancy data.
The rest of the paper is organized as follows. “Related work” section discusses the literature and studies conducted in the past. In “HVAC control strategies” section, we outline the control strategies studied in the paper. In “Simulator software architecture” section, we present the detailed architecture and design of the thermal simulator followed by detailed analysis in “Evaluation” section. In “Discussion and conclusion” section, we discuss several limitations and possible future directions of the study and conclude the paper.
Related work
Central HVAC controllers
In the past, researchers have extensively studied the optimization of HVAC controllers to minimize the aggregate energy consumption and maximize user comfort. Agarwal et al. (2011) studied aggressive duty cycling of HVAC based on occupancy patterns within the building. Lu et al. (2010) proposed a smart thermostat to automate HVAC control by sensing occupancy and sleeping patterns in residential buildings. The occupancy-based control allows buildings to operate outside of comfort regimes when unoccupied, thus reducing energy usage (Erickson et al. 2011). Henceforth, several other studies also explored the use of occupancy information to optimize the HVAC energy operations (Aswani et al. 2012; Balaji et al. 2013; Erickson et al. 2011, 2013; Iyengar et al. 2015; Kleiminger et al. 2014; Koehler et al. 2011; Nest 2012; Scott et al. 2011; Yang and Newman 2012). However, centralized HVAC controllers divide a building into thermal zones comprising of private and shared spaces. Within each zone, these control strategies maintain ASHRAE standard while assuming each zone as either occupied or unoccupied; thus, ignoring individual comfort requirements.
Personal environmental control
For personalized comfort, studies proposed to use personal environmental control systems (PECs), especially in shared spaces (Brager et al. 2015; Bauman et al. 1998; Zhang et al. 2013; Gao and Keshav 2013b; 2013a; Rabbani and Keshav 2016). Unlike conventional centrally-controlled HVAC system, where people share the same set point temperature (Dear et al. 2013), PEC systems can meet the comfort requirements of all occupants, albeit at the cost of additional energy expenditure. Kalaimani et al. (2018) merged PEC with model predictive control to further minimize the HVAC energy consumption and maximize the user comfort.
Though advanced predictive control strategies (such as MPC) have the potential to optimize HVAC operations significantly, none of the studies mentioned above quantify the influence of the prediction errors on the energy consumption of HVAC and on the occupants’ comfort.
Error analysis
Oldewurtel et al. (2011) studied the influence of errors in weather forecast on MPC-controlled HVAC operations, and their results indicate that the quality of weather predictions highly correlates with the performance of the model predictive controller. However, the study only focused on prediction errors in the weather forecast and the evaluation was limited to “pure” MPC-based HVAC controller. Given that occupancy prediction is also an input to MPC, it is essential to analyze the influence of occupancy prediction errors on HVAC operations. Besides, the study (Oldewurtel 2011) is limited to HVAC and does not incorporate the impact of PECs in satisfying the comfort requirements of occupants.
In this paper, we extend the work in (Oldewurtel 2011) and in (Kalaimani et al. 2018) by first analyzing the effect of prediction errors in occupancy and later exploring the benefits of PECs in mitigating (or minimizing) the influence of prediction errors on HVAC operations. Our study indicates that predictive control strategies make HVAC operations highly unreliable. High variability has discouraged building managers to use advanced HVAC control strategies, and thus, they have continued using conventional HVAC controllers.
HVAC control strategies
In a typical commercial building, spaces are either private (such as offices) or shared (such as cafeteria, corridor), and a set of private and shared spaces constitutes a zone. Within each zone, there exists a VAV unit that takes air from AHU at a particular temperature (u(t)) and supplies it across the rooms at a specific rate (v^{ij}(t)) to maintain the room temperature close to the set point temperature. Here, j indicates the room number in the i^{th} zone of the building. To ensure a consistent supply of fresh air, AHU recirculates only a limited amount of used air (r(t)) and ejects the remaining air in the open environment.
List of HVAC control variables
Symbol | Description | Unit |
---|---|---|
u(t) | Supply air temperature at time t | ^{∘}C |
v^{ij}(t) | Rate of flow of supply air in room j of a VAV zone i at time t | m^{3}/s |
Schedule-based control
In a schedule-based control of HVAC, the building manager starts the HVAC at a fixed time in the morning and shuts it down in the evening (typically 9 AM to 6 PM). On any day, AHU supplies air at a static temperature which is chosen based on the season (summer/winter), and the set point temperature does not vary within a day. Based on ASHRAE standards^{1}, we set the supply air temperature (u^{(t)}) to 15^{∘}C for summers and 20^{∘}C for winters. For both seasons, the ratio of reuse air (r) and rate of flow of supply air (v^{(t)}) is constant at 0.8 and 0.236 m^{3}/s, respectively. The approach is naive but widely used by building managers in commercial buildings.
Reactive control
In reactive control strategies, VAV cools or heats the space only if people are present in the corresponding VAV zone. In the past, studies have suggested several direct and indirect HVAC control strategies to estimate occupancy; we use the occupancy data and implement the strategy proposed by Ardakanian et al. (2016) for benchmarking.
Model predictive control
List of symbols used in the thermal model
Symbol | Description | Default | Unit |
---|---|---|---|
ρ | Density of air | 1.204 | kg/m^{3} |
σ | Specific heat of air | 1.003 | kJ/(kg.K) |
τ | Sampling interval | − | s |
n _{ z} | Total number of VAV zones in a building | − | − |
\(n_{r}^{i}\) | Total number of rooms in VAV zone i | − | − |
O^{ij}(t) | Occupancy in room j of zone i at time t | − | − |
T^{ij}(t) | Temperature in room j of zone i at time t due to HVAC | − | ^{∘} C |
T_{ex}(t) | External temperature at time t | − | ^{∘} C |
C ^{ i j} | Thermal capacity of room j in zone i | 2000 | kJ/K |
\(\alpha _{ex}^{ij}\) | Heat transfer coefficient between outside and room j in zone i | 0.048 | kJ/(K.s) |
\(Q_{ap}^{ij}\) | Heat load due to heating/cooling equipments in room j of zone i | 0.1 | kW |
\(Q_{oc}^{ij}\) | Heat load due to occupant in room j of zone i | 0.1 | kW |
V(t) depicts the total air supplied across all the rooms within a building, η_{h} and η_{c} indicate the efficiency of the heating and cooling unit, respectively. T_{cu}(t) and T_{mx}(t) denote the temperature of air coming from the cooling and mixing unit, respectively. η_{f} is the efficiency of the VAV fan which is supplying air to the room. Details about the power consumed by the supply fan can be found in Reference (Rabbani and Keshav 2016).
The optimization problem constraints the comfort index to remain within the specified bounds to ensure user comfort. In this study, we use widely used metric PMV - Predicted Mean Vote, to measure user comfort (Fanger 1973). Other constraints include time-scale limitations, thermal dynamics (Eq. 1), and constraints dictated by the system setup (such as thermal comfort and HVAC operation should remain within a desired range). In this paper, we implemented MPC with two time-scales where the controller updates the supply air temperature every hour and the supply air volume every 10 min. The above time-scales are typically determined by the physical limitation of an HVAC unit. For more details about this specific formulation of the optimization problem, please refer to Kalaimani et al. (2016).
MPC with personal environment controller
Recently, Kalaimani et al. (2018) proposed a hybrid HVAC controller and combined MPC with a personal environmental control system. In the study, (Kalaimani et al. 2018) used SPOT - an off-the-shelf desktop fan/heater with local temperature sensing and a computer-controlled actuator to provide individual thermal comfort. Assuming perfect prediction of occupancy and outside temperature, the study shows that combining MPC with SPOT is effective in reducing the total energy consumption by choosing appropriate thermal setbacks during the intervals of sparse occupancy.
In the proposed approach, we assume that room is divided into two regions: occupied- the part of the room where the occupant is present; and unoccupied - the other part of the room.
Notations used in the revised thermal model
Symbol | Description | Default | Unit |
---|---|---|---|
\(T_{hv}^{ij}{(t)}\) | Temperature in room j of zone i at time t due to HVAC | − | ^{∘} C |
\(\Delta _{oc}^{ij}{(t)}\) | Change in temperature of occupied region of room j in zone i at time t | − | ^{∘} C |
\(T_{oc}^{ij}{(t)}\) | Temperature in occupied region of room j in zone i at time t | − | ^{∘} C |
\(T_{un}^{ij}{(t)}\) | Temperature in unoccupied region of room j in zone i at time t | − | ^{∘} C |
\(C_{oc}^{ij}\) | Thermal capacity of occupied region of room j in zone i | 200 | kJ/K |
α _{ in} | Heat transfer coefficient between occupied and unoccupied regions of room j in zone i | 0.1425 | kJ/(K.s) |
\(Q_{he}^{ij}\) | Heat load due to SPOT in room j of zone i | 0.7 | kW |
The controller determines HVAC control parameters (Table 1) on a 10-min timescale and in between, fan/heater (of SPOT) reacts to occupancy every 30 s. By doing so, SPOT assists the controller in regulating the discomfort that might arise due to mis-predictions; thus ensuring both - personalized comfort and minimal influence of prediction errors on HVAC operations. Next, we discuss the simulator.
Simulator software architecture
- 1Master - to handle data I/O and preprocessing,
- 2
Error Management - to inject unbiased errors in the occupancy streams,
- 3
Simulator - to simulate room temperature for a given thermal model and control logic, and
- 4
Analyser - to compute energy consumption, occupant comfort, and analyze simulated data streams.
In the current version, Simulator module incorporates AMPL (2014) – an algebraic modeling language for the mathematical programming – to compute the control parameters.
Master module
Modeling occupancy prediction errors
ThermalSim represents occupancy data for a day as a string of consecutive 0’s (for unoccupied workspaces) and 1’s (for occupied spaces). We consider only two states of occupancy because a majority of occupancy prediction algorithms use occupancy as a two-state variable. We call this string an occupancy string. The length of a single occupancy string depends upon the sampling rate of the occupancy data. Data sampled every ten minutes will generate an occupancy string of length 144 characters, and if the sampling rate is thirty seconds, the string will be 2880 characters long.
Error matrix
It is important that occupancy forecast errors be realistic. For example, it does not make sense to randomly flip occupancy states, since this may result in forecasting occupancy during the middle of the night, which is very unlikely. Our key insight is that a likely outcome of an errored forecast is to forecast another valid occupancy string, with the observation that the higher the error rate, the larger the distance, in an appropriate metric space, between the true and the errored strings.
We use the following approach: For a dataset with n occupancy strings, each cell of an error matrix depicts the Hamming Distance between any two occupancy strings – the number of mismatching characters (Hamming 1950). To normalize, we divide value in each cell by the length of occupancy string. The error matrix is a symmetric matrix of size n^{2} which helps in systematically injecting unbiased errors in the occupancy data.
To illustrate, consider a scenario where we want to analyze different control strategies with 10% prediction error in the occupancy data. The error management module will refer error matrix for an occupancy string which is closest to the day of analysis. We term the selected occupancy string as the reference string. The module will then look into the error matrix to find all those strings that have 10% error as compared to the reference string and randomly select one. We call the selected one an erroneous string. If the day (reference string) was 30% occupied, then the occupancy in the erroneous string may fall anywhere in between 20-40%.
Simulator
- 1
thermal model - depicts various thermal interactions occurring within a room, and
- 2
control module - to compute the control parameters.
- 1
schedule-based,
- 2
reactive,
- 3
model predictive control (no SPOT device present), and
- 4
SPOT-aware model predictive control.
In the rest of the paper, we will use NS as an acronym for No-SPOT model predictive control and SA for SPOT-Aware MPC.
Simulator validation
- 1
thermal capacity of the room (C),
- 2
heat transfer coefficient between outside and room (α_{ex}),
- 3
coefficient of heating/cooling (ρσ)
- 4
heat load due to occupants (Q_{ac}), and
- 5
heat load due to heating/cooling appliances (Q_{ac}).
Metrics
Energy consumption
Equation 9 computes the total energy consumption of a building for a day. Here, Po(t) denotes the power consumption of HVAC and other heating/cooling devices, τ is the sampling rate, and n_{t} is the number of daily samples.
Occupant discomfort
Robustness
Prediction errors are stochastic in nature and their impact on energy consumption and occupant comfort depends on two factors:
Nature of the error: If the prediction algorithm mispredicts occupancy for short time intervals (say for a minute or so), we term the prediction errors as point errors, otherwise we call them burst errors. For a particular error percentage, an erroneous occupancy string can have point errors, burst errors, or a mix of both; resulting in different values of energy consumption and occupants’ discomfort for the same error percentage.
Timing of the error: The occupancy prediction algorithm can make errors at any time of the day - such as during peak or non-peak time. Consider the situation where the occupancy prediction has 15% error during the peak hours and the controller assumes one of the five rooms to be occupied though it was unoccupied. In this situation there is a high chance that the HVAC might be already running during that time. Given the fact that the other four rooms are occupied, this particular prediction error will have an insignificant impact on the HVAC operations. However, during night time, the same error percentage might waste significant energy. This illustrates that the timing of the prediction errors has a significant impact on both comfort and energy consumption.
Note that the circles (NS) are more scattered than the triangles (SA). In the case of NS, the system decides the control parameters such that the desired room temperature (which is the same for each room) is achieved across all the rooms. In case of a sudden change in the occupancy, NS updates the control parameters, but it takes significant time to re-attain the energy-discomfort tradeoff setpoint. In contrast, in SA, the controller knows the current state of SPOT; thus, the controller chooses a set point such that HVAC provides a certain level of comfort to the occupants and SPOT provides the necessary additional offset. SPOT, being responsive in nature, keeps the comfort level of individuals within the desired range with insignificant increase in aggregate energy consumption. Therefore, even if the error percentage increases, the energy and discomfort stays close to the perfect prediction for SA whereas NS becomes highly unstable.
For concreteness, we use ± 20 kWh and ± 5% as the acceptable limits for energy consumption and occupants’ discomfort, respectively, as shown by the rectangles in the figure. For the given scenario (in Fig. 5), when the error percentage is increasing from 5 to 20%, NS is less robust towards the prediction error (60%→0%), however, SA remains consistent (100%→93%). For a predictive control strategy, a PEC system (like SPOT) mitigates the effect of prediction errors to make the HVAC operations more reliable and robust. Whenever there is an unexpected occupancy in the room, SPOT can react quickly as compared to central HVAC system which has a slower time-scale.
Evaluation
Test building description
Dataset
ThermalSim requires real-world occupancy data to generate an error matrix. We leveraged an existing deployment from our university campus and gathered occupancy data (along with other information) from more than fifty volunteers – including students, faculty, and the staff members every 30 seconds for a year.
Evaluation setup
Our research hypothesis is that the benefits of using a PEC system like SPOT along with HVAC controller mitigates the influence of prediction errors on MPC-based HVAC operation.
We validate this hypothesis assuming occupants in all the five rooms have similar comfort requirements: [23^{∘}C,25^{∘}C] in summers and [21^{∘}C,23^{∘}C] in winters. For the given setup, we compare the performance of predictive and non-predictive HVAC controllers for 25 days, both in summers and winters.
For each day, we select an occupancy string from the error matrix that deviates (from the current day) by the error percentage specified in the system. For instance, if we wish to introduce 10% error in the current day occupancy string, we search for another occupancy string in historical data where 288 out of 2880 instances (for a data sampled every 30 seconds) have a mismatch with the current day occupancy string. ThermalSim utilizes both actual and erroneous occupancy string to simulate the building (depicted in Fig. 6) for all the four control strategies and compare their performance.
To mitigate any bias in the selection of erroneous occupancy strings, ThermalSim evaluates fifteen different erroneous occupancy patterns for each day and error percentage. Furthermore, a separate analysis for each of the two seasons provides better understanding of the influence of seasonal variations.
Insights updated the title and text of this whole section
User experience
The schedule-based and reactive controllers can make occupants uncomfortable and yet consume significant energy, even with perfect prediction. When set to follow a fixed schedule, HVAC supplies air at a constant flow and temperature, and does not consider occupants’ schedules or daily temperature changes. For pictorial representation, we use energy-discomfort plot where x-axis denotes the daily energy consumption of the building and y-axis represents the total discomfort for the users. Consequently, with a schedule-based control strategy, user experience lies in the top-right corner of the energy-discomfort plot with maximum energy consumption along with notable discomfort for both the seasons (see Figs. 8, 9). On the other hand, a reactive controller with occupancy information is marginally better or equivalent to the schedule-based controller. Model predictive control (with no SPOT) shows significant improvement in minimizing both energy consumption and occupants’ discomfort. Given the weather forecast and occupancy prediction, MPC keeps updating the temperature and volume of supply air at regular time intervals.
As central HVAC unit cannot cater to the dynamic schedule of the occupants, discomfort in NS is slightly higher than the hybrid control strategy that integrates SPOT with MPC to satisfy the comfort requirements of each individual in the building. In SA, the central HVAC system is aware of the SPOT system, therefore, the controller choses the set point temperature such that HVAC can provide minimal comfort, and SPOT can offset the individual comfort requirements. This results in additional savings in energy when there is partial occupancy is in line with the results from previous study by Rachel et al. (2018). Next, we observed that the discomfort is negligible for summer as opposed to winter. The fan assists the occupant in quickly achieving her desired comfort level as opposed to a heater which takes comparatively more time to increase the temperature to provide the offset. In conclusion, irrespective of the season, both SA and NS strategies improve comfort and energy compared to schedule-based and reactive, with SA outperforming NS.
Error analysis
Discussion and conclusion
In this work, we analysed the influence of prediction errors in occupancy on the HVAC operations while leveraging a custom-built building simulator - ThermalSim. In this section, we summarize our results, discuss various limitations of the study followed by research questions which are open for the community.
Our insights include the following: First, our dataset indicates that aggregate energy consumption is higher in winters than in summers. Second, integrating a PEC like SPOT with a predictive HVAC controller is definitely better or comparable than a pure MPC based approach. Third, for SA controller, fast reactive device (such as fan) is 20% better than the heater, in terms of occupants discomfort. Finally, NS typically fails to satisfy the comfort requirements on any day.
Our work suffers from two main limitations. First, while the thermal model (of ThermalSim) considered the effect of numerous sources (such as weather, occupancy) affecting the room temperature, there still exist various other factors (such as humidity) which are critical for such analysis. We plan to explore such factors and enrich the data for a deeper analysis in future.
Second, we carried out the study through a dataset collected from a particular part of the world. Climate, users’ attitude (towards energy savings), and many other factors differ significantly across the geographies. Though the results indicate that SA is more robust than NS, there can be considerable discrepancy across (and within) the countries. A real-world implementation of the technology is critical to understand its effectiveness in achieving the desired goals.
We find that mitigating the effect of prediction errors possess considerable potential in optimising the HVAC operations with predictive controllers. While model predictive control (MPC) is one of the most promising state of the art HVAC control strategies, its performance is limited by the accuracy of the weather and occupancy predictions. Therefore, we designed a custom-built building simulator – ThermalSim – to analyse the influence of prediction errors on HVAC operations. We also proposed a method to introduce realistic errors in occupancy for the analysis. Our initial analysis indicates that prediction error (in occupancy) of 20% can make the HVAC operations highly unstable in terms of both energy consumption and occupants’ comfort. Recent literature shows that it is feasible to use a personal thermal comfort system – SPOT – along with predictive strategy to ensure personalised comfort in personal and shared spaces. We observed that while SPOT is effective in attaining better personalised comfort, it also strengthens the predictive strategies by mitigating the influence of predictions errors on energy consumption and occupants’ comfort because it works at a finer time-scale than the MPC-based HVAC. Employing a personal thermal comfort system, such as SPOT, we stay in the acceptable region 95% of the times as oppose to 83% of the times even for the prediction errors as high as 20%, in the occupancy; thus, motivating a reliable control strategy across the commercial buildings.
American Society of Heating, Refrigeration and Air-Conditioning - a global organisation that publishes standards and guidelines related to HVAC.
Declarations
Acknowledgements
We would like to acknowledge Alimohammad Rabbani (then a Masters student at University of Waterloo) and Costin Ograda-Bratu (currently a lab technician at University of Waterloo) for collecting and sharing occpancy data. We would also like to acknowledge the volunteers who participated (and are even now participating) in data collection.
Funding
This work was supported by Cisco Systems Canada and the Canadian Natural Sciences and Engineering Research Council under a Cooperative Research and Development grant. The funding body played no role in the design of the study, collection, analysis, and interpretation of data, and in writing the manuscript.
Availability of data and materials
On request, the authors will supply occupancy data to interested researchers. The simulator is open source and available at https://github.com/milanjain81/SBS_MakefileProject.
Authors’ contributions
Together, all the authors devised the project, the main conceptual ideas and outline for the analysis. MJ carried out the implementation and analysed the data. Prof. RKK, Prof. SK, and Prof. CR worked out the optimisation problem for Model Predictive Control and helped in writing the manuscript. All authors read and approved the final manuscript.
Competing interests
The author(s) declare(s) that they have no competing interests.
Publisher’s Note
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Authors’ Affiliations
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