An Improved Formulation of Hybrid Model Predictive Control With Application to Production-Inventory Systems
Open accessAbstract
We consider an improved model predictive control (MPC) formulation for linear hybrid systems described by mixed logical dynamical (MLD) models. The algorithm relies on a multiple-degree-of-freedom parametrization that enables the user to adjust the speed of setpoint tracking, measured disturbance rejection and unmeasured disturbance rejection independently in the closed-loop system. Consequently, controller tuning is more flexible and intuitive than relying on objective function weights (such as move suppression) traditionally used in MPC schemes. The controller formulation is motivated by the needs of nontraditional control applications that are suitably described by hybrid production-inventory systems. Two applications are considered in this paper: adaptive, time-varying interventions in behavioral health, and inventory management in supply chains under conditions of limited capacity. In the adaptive intervention application, a hypothetical intervention inspired by the Fast Track program, a real-life preventive intervention for reducing conduct disorder in at-risk children, is examined. In the inventory management application, the ability of the algorithm to judiciously alter production capacity under conditions of varying demand is presented. These case studies demonstrate that MPC for hybrid systems can be tuned for desired performance under demanding conditions involving noise and uncertainty.
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Model predictive control, recommender systems, agent-based modeling, or Bayesian network analysis are plausible personalization algorithm strategies.
“Model predictive control [40–43], recommender systems [44], agent-based modeling [45], or Bayesian network analysis [46] are all plausible personalization algorithm strategies.”
From Agile science: creating useful products for behavior change in the real world (2016) · cites this paper as [41]
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Agile science: creating useful products for behavior change in the real world
Hekler, E. B., Klasnja, P., Riley, W. T., Buman, M. P., Huberty, J., Rivera, D. E., & Martin, C. A. (2016) · Translational Behavioral Medicine · doi:10.1007/s13142-016-0395-7 · Cited by 208 · see citing works
Self-citationAdvancing Models and Theories for Digital Behavior Change Interventions
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“These methods include strategies such as system identification (Ljung, 1999), and model-predictive control (Nandola & Rivera, 2013).”
MethodA dynamical systems model of Social Cognitive Theory
Martín, C. A., Rivera, D. E., Riley, W. T., Hekler, E. B., Buman, M. P., Adams, M. A., & King, A. C. (2014) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2014.6859463 · Cited by 83 · see citing works
“The proposed model can ultimately serve a role as the controller model in a “just-intime” adaptive intervention using MPC [15].”
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“…to various real-world decision making problems including risk management in semiconductor manufacturing and irrigation canals (Zafra-Cabeza et al., 2008, 2011), inventory management in supply chains (Nandola and Rivera, 2013), and maintenance planning of railway infrastructures (Su et al., 2015).”
BackgroundMartín, C. A., Rivera, D. E., Hekler, E. B., Riley, W. T., Buman, M. P., Adams, M. A., & Magann, A. B. (2018) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2018.2873538 · Cited by 54 · see citing works
“interventions as control systems, this dual definition of the type of signals yields to the use of techniques as HMPC [22] where continuous and discrete signals are considered at the same time using the SCT model.”
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BackgroundA Dynamical Systems Approach to Understanding Self-Regulation in Smoking Cessation Behavior Change
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Self-citationExploring Behavioral Markers of Long-Term Physical Activity Maintenance
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“…utilization of these mathematical models in the creation of “closed-loop control systems,” which are central for systems that tailor an intervention relying on individual response, thus providing increasingly personalized and adaptive interventions (Nandola & Rivera, 2013; Rivera et al., 2007).”
Self-citationA Hybrid Dynamical Approach for Allocating Materials in a Dry Bulk Terminal
Xin, J., Negenborn, R. R., & van Vianen, T. (2018) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2017.2784483 · Cited by 32 · see citing works
“This control methodology has been successfully used in the domain of transportation and logistics [20]–[22], [29]–[31].”
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Self-citationA framework for hybrid model predictive control in mineral processing
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“Adaptive, timevarying interventions constitute feedback control systems [8] and are amenable to hybrid model predictive control approaches [9].”
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Self-citationHybrid model predictive control for optimizing gestational weight gain behavioral interventions
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“Though traditional interventions appear to reduce the risk of adverse pregnancy outcomes among normal weight women [5], [6], these have been less effective for overweight and obese women.”
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Self-citationA control engineering approach for designing an optimized treatment plan for fibromyalgia
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Self-citationOptimized treatment of fibromyalgia using system identification and hybrid model predictive control
Deshpande, S., Nandola, N. N., Rivera, D. E., & Younger, J. (2014) · Control Engineering Practice · doi:10.1016/j.conengprac.2014.09.011 · Cited by 22 · see citing works
“In a control engineering approach to adaptive interventions (Rivera et al., 2007; Zafra-Cabeza et al., 2011; Nandola & Rivera, 2013), the controller assigns dosages to each participant as dictated by model dynamics, problem constraints, and disturbances (both measured and unmeasured).”
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“The optimizer uses the model and current measurements y(k) to compute future states through an observer/filter as is described with details in [12].”
BackgroundMethodInfluentialSelf-citationLee, S., & Prabhu, V. V. (2014) · IEEE Transactions on Automation Science and Engineering · doi:10.1109/tase.2014.2339281 · Cited by 19 · see citing works
“Some approaches have also been suggested for coupled systems: production with inventory, and production with capacity [22]–[26].”
BackgroundControl Engineering Methods for the Design of Robust Behavioral Treatments
Bekiroglu, K., Lagoa, C. M., Murphy, S. A., & Lanza, S. T. (2016) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2016.2580661 · Cited by 19 · see citing works
“Some extend studies use controller design methods to design adaptive interventions for special problems in behavioral science [7]–[9].”
Continuous-time system identification of a smoking cessation intervention
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“Ultimately, self-regulatory models similar to those estimated here could inform novel treatment strategies (Nandola & Rivera, 2013; Riley et al., 2011; Rivera, 2012; Timms et al., 2013).”
BackgroundMethodInfluentialSelf-citationControl systems engineering for understanding and optimizing smoking cessation interventions
Timms, K. P., Rivera, D. E., Collins, L. M., & Piper, M. E. (2013) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2013.6580123 · Cited by 19 · see citing works
“, pre-determined medication dosages) and hard- and soft-constraints makes it an advantageous intervention framework [16].”
BackgroundSelf-citationA Hybrid Model Predictive Control strategy for optimizing a smoking cessation intervention
Timms, K. P., Rivera, D. E., Piper, M. E., & Collins, L. M. (2014) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2014.6859466 · Cited by 19 · see citing works
“Ensuring manipulated variable assignments adhere to predetermined discrete levels means the algorithmic structure of a control-oriented intervention must consider hybrid systems [10].”
InfluentialSelf-citationIntegrated Vendor-Managed Time Efficient Application to Production of Inventory Systems
Shah, B. K., Kedia, V., & Jha, R. K. (2021) · International Conference on Inventive Computation Technologies (ICICT) · doi:10.1109/icict50816.2021.9358504 · Cited by 18 · see citing works
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Self-citationKhan, O., Mistiri, M. E., Banerjee, S., Hekler, E. B., & Rivera, D. E. (2024) · Control Engineering Practice · doi:10.1016/j.conengprac.2024.106171 · Cited by 16 · see citing works
Self-citationDong, Y., Deshpande, S., Rivera, D. E., Downs, D. S., & Savage, J. S. (2014) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.1109/acc.2014.6859462 · Cited by 16 · see citing works
“The HMPC formulation relies on the use of Mixed Logical Dynamical (MLD) framework for the control of hybrid systems developed in [11], and implements the improved three-degree-of-freedom (3 DoF) tuning formulation of Nandola and Rivera [5].”
InfluentialSelf-citationPiña, A., Holly, L. E., Zerr, A. A., & Rivera, D. E. (2014) · Journal of Clinical Child & Adolescent Psychology · doi:10.1080/15374416.2014.888667 · Cited by 14 · see citing works
“…composition (Navarro-Barrientos et al., 2011), physical activity among older adults (Hekler et al., 2013), glucose-insulin (Bequette, 2009), substance misuse (Nandola & Rivera, 2013; Rivera et al., 2007), and smoking cessation (Timms, Rivera, Collins, & Piper, 2013) have appeared in the literature.”
BackgroundSelf-citationModel predictive control for inventory management in biomass manufacturing supply chains
Álvarez-Rodríguez, D. A., Normey-Rico, J. E., & Flesch, R. C. C. (2017) · International Journal of Production Research · doi:10.1080/00207543.2017.1315191 · Cited by 12 · see citing works
Dealing with observational data in control
Wilson, E. D., Clairon, Q., Henderson, R., & Taylor, C. J. (2018) · Annual Reviews in Control · doi:10.1016/j.arcontrol.2018.05.001 · Cited by 12 · see citing works
“…to individuals to achieve health behaviour change, where MPC has been applied to behavioural research to develop controller-design-based interventions (Bekiroglu, Lagoa, Murphy, & Lanza, 2017; Deshpande, Nandola, Rivera, & Younger, 2014; Nandola & Rivera, 2013; Rivera, Pew, & Collins, 2007).”
Control Systems Engineering for Optimizing Behavioral mHealth Interventions
Rivera, D. E., Martín, C. A., Timms, K. P., Deshpande, S., Nandola, N. N., & Hekler, E. B. (2017) · Springer eBooks · doi:10.1007/978-3-319-51394-2_24 · Cited by 10 · see citing works
“In [34], Mixed Logical Dynamical (MLD) models are used to represent linear hybrid systems which feature real and integer states, inputs and constraints [4]:”
BackgroundMethodInfluentialSelf-citationHejri, M., Giua, A., & Mokhtari, H. (2018) · International Journal of Robust and Nonlinear Control · doi:10.1002/rnc.4278 · Cited by 10 · see citing works
“23 38 In these applications, the MPC problem in 24 - 31 , 35 - 38 has Obtaining MLD models for a given hybrid system can be a tedious and tricky.”
BackgroundGuo, P., Rivera, D. E., Dong, Y., Deshpande, S., Savage, J. S., Hohman, E. E., Pauley, A. M., Leonard, K. S., & Downs, D. S. (2022) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2022.107721 · Cited by 10 · see citing works
Self-citationModel Predictive Control for Maintenance Operations Planning of Railway Infrastructures
Su, Z., Núñez, A. A., Jamshidi, A. A., Baldi, S., Li, Z., Dollevoet, R. P. B. J., & Schutter, B. D. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-24264-4_46 · Cited by 10 · see citing works
“See [18] for an application of hierarchical distributed MPC to risk management of a network of irrigation canals, and [19] for applications of hybrid MPC to interventions in behavioral health and inventory management in supply chains.”
Mistiri, M. E., Khan, O., Martín, C. A., Hekler, E. B., & Rivera, D. E. (2025) · IEEE Open Journal of Control Systems · doi:10.1109/ojcsys.2025.3538263 · Cited by 9 · see citing works
“Hence, a hybrid model predictive control (HMPC) strategy [13], [40] is examined and applied to this problem, as it accounts for hybrid dynamics via MLD representation; this allows for incorporating the natural constraints and logical arguments associated with the problem as part of the prediction…”
Self-citationKhan, O., Mistiri, M. E., Rivera, D. E., Martin, C. A., & Hekler, E. B. (2022) · IEEE Conference on Decision and Control (CDC) · doi:10.1109/cdc51059.2022.9992932 · Cited by 9 · see citing works
“E5 ≥ E2δ̄k + E3Zk + E1Uk + E4Xflt,k + EdDflt,k − E41uk−1 − E42δk−1 − E43zk−1 − E4ddflt,k−1 (31) The matrices Φ, H1, H2, H3, Hd, Hi1 ∀ i = 1, 2, 3, d in (24), matrices Ēi ∀ i = 1, 2, 3, 4, d in (30), and matrices E1, E2, E3, E4, E5, Ed, E4i, i = 1, 2, 3, d in (31) can be found in [4].”
BackgroundMethodSelf-citationBanerjee, S., Khan, O., Mistiri, M. E., Nandola, N. N., & Rivera, D. E. (2024) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2024.08.565 · Cited by 8 · see citing works
Self-citationMove blocking strategy applied to re-entrant manufacturing line scheduling
Jung, T. Y., Jang, H., & Lee, J. H. (2015) · International Journal of Control Automation and Systems · doi:10.1007/s12555-014-0243-9 · Cited by 7 · see citing works
“This is because customer demands are typically simplified into piecewise constant profiles [9].”
BackgroundMethodLeveraging intensive longitudinal data to better understand health behaviors
Timms, K. P., Martín, C. A., Rivera, D. E., Hekler, E. B., & Riley, W. T. (2014) · Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) · doi:10.1109/embc.2014.6945211 · Cited by 7 · see citing works
“Dynamical systems models describing behavior change via an SCT-based mechanism stem from a connection to production-inventory systems [1], [4], [9]: Fig.”
BackgroundSelf-citationBanerjee, S., Kha, R. T., Rivera, D. E., & Hekler, E. B. (2024) · Journal of Process Control · doi:10.1016/j.jprocont.2024.103242 · Cited by 5 · see citing works
Self-citationA control engineering approach for optimizing physical activity behavioral interventions
Martín, C. A., Rivera, D. E., & Hekler, E. B. (2016) · IEEE Ecuador Technical Chapters Meeting (ETCM) · doi:10.1109/etcm.2016.7750851 · Cited by 5 · see citing works
“The intervention is designed using Hybrid Model Predictive Control (HMPC) ideas [9].”
MethodInfluentialSelf-citationSwitching Control of Closed-loop Supply Chain Systems withMarkovian Jumping Parameters
Li, Q., Mei, L., & Jia, X. (2015) · Acta Automatica Sinica · Cited by 4 · see citing works
Artificial Neural Network Approach to Modeling of Polypropylene Reactor
Karas, P., & Kozák, Š. (2017) · International Journal of Advances in Chemistry · doi:10.5121/ijac.2017.3401 · Cited by 3 · see citing works
A receding horizon event-driven control strategy for intelligent traffic management
Lúcia, W., Franzè, G., & Famularo, D. (2021) · Discrete Event Dynamic Systems · doi:10.1007/s10626-020-00337-7 · Cited by 3 · see citing works
Downs, D. S., Pauley, A. M., Rivera, D. E., Savage, J. S., Moore, A. M., Shao, D., Chow, S., Lagoa, C. M., Pauli, J. M., Khan, O., et al. (2025) · JMIR Research Protocols · doi:10.2196/66637 · Cited by 2 · see citing works
Self-citationA Novel Engineering Approach to Modeling and Optimizing Smoking Cessation Interventions
Timms, K. P. (2014) · Cited by 2 · see citing works
Advanced control based on MPC ideas for offshore hydrogen production
Serna, Á., Tadeo, F., & Normey-Rico, J. E. (2020) · Jornadas de Automática · doi:10.17979/spudc.9788497497749.0167 · Cited by 1 · see citing works
“This optimization solver has been used for predictive control in different works [13, 14].”
MethodValdiviezo, D. A. C., Martín, C. A., Mistiri, M. E., Rivera, D. E., & Hekler, E. B. (2022) · Revista Iberoamericana de Automática e Informática Industrial RIAI · doi:10.4995/riai.2022.16798 · Cited by 1 · see citing works
Self-citationDiversity Guided Production Inventory Control in Automobile Manufacturers
Tao, L., Chen, W., Wang, G., Su, L.-J., Yang, Y., & Dong, Y. (2022) · IEEE International Conference on Automation Science and Engineering (CASE) · doi:10.1109/case49997.2022.9926437 · Cited by 1 · see citing works
Murray, T., Hekler, E. B., Spruijt‐Metz, D., Rivera, D. E., & Raij, A. B. (2016) · Advances in intelligent systems and computing · doi:10.1007/978-3-319-41627-4_25
Self-citationTópicos em gestão da produção: volume 5
Tristão, H. M. (2018) · doi:10.5935/978-85-93729-33-1.2018b001
A Control Engineering and System Identification Approach to Improve a Cocoa Biofertilization Process
Gallino, V., Martín, C. A., Sosa, D., & Barcos-Arias, M. (2018) · Proceedings of the ... American Control Conference/Proceedings of the American Control Conference · doi:10.23919/acc.2018.8431481
“The dosage procedure can be re-designed using different advanced control strategies such as Hybrid Model Predictive Control [15] that allows the use of discrete levels of concentrations under realistic constraints.”
MethodSu, Z., Jamshidi, A. A., Núñez, A. A., Baldi, S., & Schutter, B. D. (2019) · Springer eBooks · doi:10.1007/978-3-030-05645-2_18
Model for Predictive Production
Sharma, B., Das, I., Pandey, M., & Rautaray, S. S. (2019) · Advances in intelligent systems and computing · doi:10.1007/978-981-32-9186-7_8
Sutrisno, S., Widowati, W., & Tjahjana, R. H. (2021) · Indonesian Journal of Electrical Engineering and Computer Science · doi:10.11591/ijeecs.v22.i3.pp1748-1753
“For review time from day 30 to 50 and day 80 to 100, the inventory level is closed to the set point as shown in Figure 2 in [30], [11].”
MethodFreigoun, M. T., Tsakalis, K. S., & Raupp, G. B. (2021) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2021.08.330
2013 Index IEEE Transactions on Control Systems Technology Vol. 21
(2013) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2013.2286231
Huang, C., Chen, J., Deng, S., & Ge, H. L. (2025) · International Journal of Energy Research · doi:10.1155/er/4099569
“The application fi elds of HMPC cover control systems of behavioral medical devices [47], production inventory systems [48], HVAC systems [49], power electronic converters [50], and more, demonstrating exceptional control performances.”
Hybrid model predictive control with explicit policy integration via extended MLD models
Campregher, F., Guzmán, J. L., Milanesi, M., Rivera, D. E., & Visioli, A. (2026) · Journal of the Franklin Institute · doi:10.1016/j.jfranklin.2026.109103
Self-citationThe robustness of inventory levels and power support in business and energy grid administration
Weinmann, A., & Vöhr, G. (2013) · e+i Elektrotechnik und Informationstechnik · doi:10.1007/s00502-013-0159-8
“Production inventory systems and the appropriate modified model predictive control is a topic of arising interest in its dynamical details (e.g., Nandola and Rivera [27], among many others).”
Background
- Authors
- Nandola, N. N., & Rivera, D. E.
- Affiliations
- ABB (India) (IN)
- Arizona State University (US)
- Venue
- IEEE Transactions on Control Systems Technology
- Published
- 2013-01
- Volume
- 21
- Issue
- 1
- Pages
- 121-135
- ISSN
- 1063-6536 (ISSN-L)
- 1558-0865
- PMC
- PMC3859541
- OpenAlex
- W2037886542
- Cited by
- 64
- References
- 44
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 3 · 2022: 5 · 2021: 4 · 2020: 1 · 2019: 3 · 2018: 8 · 2017: 6 · 2016: 6 · 2015: 4 · 2014: 10 · 2013: 7 · 2012: 2
- FWCI
- 10.20
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- IEEE Transactions on Control Systems Technology (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute on Drug Abuse (R21DA024266, K25DA021173)
- Topics
- Physical Sciences › Engineering › Control and Systems Engineering › Advanced Control Systems Optimization
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Keywords
- hybrid model predictive control, reference tracking, disturbance rejection, controller tuning, production-inventory systems, behavioral health interventions, conduct disorder, inventory management, supply chain capacity
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