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DOE OSTI2021

Machine‐learning‐based construction of barrier functions and models for safe model predictive control

Abstract In this paper, we propose a control Lyapunov‐barrier function‐based model predictive control method utilizing a feed‐forward neural network specified control barrier function (CBF) and a recurrent neural network (RNN) predictive model to stabilize nonlinear processes with input constraints, and to guarantee that safety requirements are met for all times. The nonlinear system is first modeled using RNN techniques, and a CBF is characterized by constructing a feed‐forward neural network (FNN) model with unique structures and properties. The FNN model for the CBF is trained based on data samples collected from safe and unsafe operating regions, and the resulting FNN model is verified to demonstrate that the safety properties of the CBF are satisfied. Given sufficiently small bounded modeling errors for both the FNN and the RNN models, the proposed control system is able to guarantee closed‐loop stability while preventing the closed‐loop states from entering unsafe regions in state‐space under sample‐and‐hold control action implementation. We provide the theoretical analysis for bounded unsafe sets in state‐space, and demonstrate the effectiveness of the proposed control strategy using a nonlinear chemical process example with a bounded unsafe region.

Chen, Scarlett↗

DOE OSTI2025

HP-FLEX: Field demonstration of the semantics-driven configuration of a Model Predictive Control system to make heat pumps flexible

Model Predictive Control (MPC) has demonstrated significant potential for optimizing building operations and enabling demand flexibility. However, the widespread adoption of MPC is hindered by complex manual configuration and commissioning processes that must be conducted by control experts working alongside building operators. These challenges drive up costs and reduce scalability, particularly when technical human resources and building automation systems are limited, such as in small and medium commercial buildings (SMCBs). This paper demonstrates how semantic standards, specifically ASHRAE 223P, can accelerate the adoption of MPC applications for load flexibility in SMCBs. The authors present a replicable control framework, titled “HP-FLEX” that leverages a building’s semantic model to bootstrap the required data configuration for an MPC controller developed for optimizing heat pump systems as flexible grid resources. The semantic model helps streamline the deployment workflow, particularly for site setup, data/control commissioning, and model setup. This integration enhances portability, transferability, and scalability of the HP-FLEX MPC, which has been developed to support MPC-based supervisory HVAC controllers in SMCBs. Additionally, the paper details the required building and thermostat metadata information to enable the HP-FLEX MPC based on field demonstrations. The new workflow was tested in a small commercial building located in California, U.S., and demonstrated a load shifting performance of 9% based on a dynamic pricing signal that varies by the hour. This work provides a practical pathway for transitioning sophisticated building applications from custom to standardized semantic representations, supporting the broader adoption of advanced control strategies like MPC. The framework also establishes a foundation for evolving metadata requirements as applications mature while maintaining compatibility with industry standards.

Paul, Lazlo↗

DOE OSTI2025

HP-FLEX: Field Demonstration of the Semantics-Driven Configuration of a Model Predictive Control System to Make Heat Pumps Flexible

Paul, Lazlo↗

DOE OSTI2019

Distributed output-feedback model predictive control for multi-agent consensus

We introduce a distributed output-feedback model predictive control approach for achieving consensus among multiple agents. Each agent computes a distributed control action based on an output-feedback measurement of a local neighborhood tracking error and communicates information only to its neighbors, according to a communication network modeled as a directed graph. Each agent computes its distributed control action by solving a local min–max optimization problem that simultaneously computes a local state estimate and control input under worst-case assumptions on unmeasured input disturbances and measurement noise. Under easily verified controllability and observability assumptions, this distributed output-feedback model predictive control approach provides an upper bound on the group consensus error, thereby ensuring practical consensus in the presence of unmeasured disturbances and noise. A numerical example with four agents connected in a directed graph is demonstrated to illustrate the results.

42 ENGINEERING↗

DOE OSTI2025

Closing the loop: model-predictive control for a closed-circuit reverse osmosis system

This article presents a model-predictive controller (MPC) for the maximization of the energy efficiency of a closed-circuit desalination reverse osmosis (CCRO) system. CCRO is a process for producing drinking water that is based on a cyclic operation with the following two phases: (a) filtration and (b) drain. In this article, we test model predictive control for optimal control of this process. The most important features of our approach are as follows: (a) the selection of a model structure that enables reliable forecasts of the filtration phase (up to 3 h), (b) an on-line model calibration strategy that ensures model forecast reliability, and (c) the satisfaction of equipment safety and operational constraints on the selected setpoints. We challenge this through deliberate introduction of changes in the unmeasured feed concentration and the applied constraints. Our results indicate that frequent model parameter updates are critical to maintain model reliability for MPC purposes. In addition, we illustrate that parameter identifiability is not guaranteed and that deliberate variation in flow rates is necessary even though the process never operates in steady state. Finally, MPC can compute flow rate setpoints that maximize the energy efficiency of the CCRO process while satisfying the applicable equipment and safety constraints.

closed-circuit reverse osmosis↗

DOE OSTI2020

Development and Evaluation of Occupancy-Aware Model Predictive Control for Residential Building Energy Efficiency and Occupant Comfort

The residential sector accounts for 25% of global primary energy consumption. Two methods have previously been proposed to reduce residential energy use associated with the provision of occupant thermal comfort: 1. Occupancy-based HVAC control, operating systems only during confirmed occupancy, and 2. model predictive control (MPC), harnessing a mathematical model and forecasts to find optimal operating strategies. Previous studies estimate the average energy savings of the two methods individually in the range of 21% and 16%, respectively. The research presented herein was carried out to evaluate the energy savings potential in residential buildings by combining both approaches across different climates, house vintages, and occupancy patterns. Occupancy and eight different physical modalities (e.g. CO2 and VOC) data were collected from five homes for time periods of 4–9 weeks. Collected data sets were used to train occupancy prediction models suggested by an extensive literature survey of occupancy model types. The trained prediction models were combined with MPC and detailed EnergyPlus building simulation models to evaluate residential building performance in terms of annual energy savings and thermal comfort, along with discomfort exceedance metrics. Multiple home types and regions were analyzed to understand regional and climate-dependent potential. Based on actual field data, the occupancy models had a prediction inaccuracy between 8% and 35% across the investigated homes. Average occupancy for the collected data ranged from 56% to 86%, a typical range reported in the literature. Building simulations were conducted for three control scenarios: conventional thermostatic control, occupancy-based, and occupancy-based MPC. The results indicate that all advanced strategies improve upon the conventional control, with some scenarios cutting energy use in half with only occasional incurrence of discomfort. The findings indicate that occupancy-aware model predictive residential building control has the potential to drastically reduce energy use and associated emissions while maintaining occupant comfort for both new and existing buildings.

ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATION↗

DOE OSTI2020

Cloud-based implementation of white-box model predictive control for a GEOTABS office building: A field test demonstration

Model predictive control (MPC) has been proven in simulations and pilot case studies to be a superior control strategy for large buildings. MPC can utilize the weather and occupancy schedule forecasts, together with the system model, to predict the future thermal behavior of the building and minimize the overall energy use and maximize thermal comfort. However, these advantages come with the cost of increased modeling effort, computational demands, communication infrastructure, and commissioning efforts. Thus a typical approach is to, often rapidly, simplify the building modeling and MPC optimization problem while paying a price of not reaching the full performance potential. It has been shown that by employing accurate physics-based models, MPC performance can be notably increased closer to its theoretical performance bound. However, implementation of such high-fidelity MPC in real buildings remains a challenge, resulting in a lack of successful field test studies. This work presents the methodology and field test demonstration of a computationally efficient implementation of the white-box MPC in an office building in Belgium. The detailed model of the building is based on first-principle physical equations. The deployment and supervision of MPC operation in a practical setting are supported by an automated cloud-based communication infrastructure. The motivating factor behind the cloud-based architecture is its compatibility with a commercially appealing control as a service concept. The building is equipped with a ground source heat pump (GSHP) and thermally activated building structures (TABS), where the combination of both is also known as GEOTABS. From a control perspective, GEOTABS buildings are particularly challenging systems due to large scale, complex heating, ventilation and air conditioning (HVAC) system, and slow dynamics with time delays. On the other hand, there is an increased potential for energy savings due to the high thermal mass, which acts as thermal storage. The MPC operation is demonstrated during the challenging transient seasons (switching between heating and cooling), and its performance is compared to a traditional rule-based controller (RBC). We provide a proof of concept of real MPC operation for the most difficult seasons with notable GSHP energy use savings equal to 53.5% and thermal comfort improvement by 36.9%. Other MPC applications found in the literature describe tests for only cooling or only heating, and up to now only for a black-box or a grey-box approach.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2017

Towards a Semantically-Enabled Control Strategy for Building Simulations: Integration of Semantic Technologies and Model Predictive Control

State-of-the-art building simulation control methods incorporate physical constraints into their mathematical models, but omit implicit constraints associated with policies of operation and dependency relationships among rules representing those constraints. To overcome these shortcomings, there is a recent trend in enabling the control strategies with inference-based rule checking capabilities. One solution is to exploit semantic web technologies in building simulation control. Such approaches provide the tools for semantic modeling of domains, and the ability to deduce new information based on the models through use of Description Logic (DL). In a step toward enabling this capability, this paper presents a cross-disciplinary data-driven control strategy for building energy management simulation that integrates semantic modeling and formal rule checking mechanisms into a Model Predictive Control (MPC) formulation. The results show that MPC provides superior levels of performance when initial conditions and inputs are derived from inference-based rules.

Delgoshaei, Parastoo↗

DOE OSTI2021

Modeling and Control of an Industrial Selective Catalytic Reduction Unit with Model Predictive Control and Reinforcement Learning

Hedrick, E., K. Reynolds, V. Dwivedy, D. Bhattacharyya, S.E. Zitney, and B. Omell, "Modeling and Control of an Industrial Selective Catalytic Reduction Unit with Model Predictive Control and Reinforcement Learning," Clearwater Clean Energy Conference, Clearwater, FL, July 26-29 (2021).

Hedrick, Elijah↗

DOE OSTI2024

Practical challenges of model predictive control (MPC) for grid interactive small and medium commercial buildings

To the urgent call for mitigating climate change, substantial initiatives have been undertaken to deploy grid-interactive heating, ventilation, and air-conditioning (HVAC) controls, such as model predictive control (MPC) for buildings. These efforts typically aim to curtail peak energy demand, shift load and enhance overall energy efficiency. With the recent development of low-cost MPC technologies that don’t require extensive instrumentation or manual modeling, small and medium commercial buildings (SMCBs), which rarely utilize advanced HVAC control systems, have become candidates for grid-interactive efficient buildings (GEBs). However, despite the potential benefits and maturity of the technology itself, several practical challenges remain in real-world implementation. In this paper, we share the practical challenges that we have encountered in implementing and testing three types of MPC solutions (ON/OFF unit, dualfuel, and VRF systems) on multiple SMCB sites. We describe the MPC deployment process and discuss the lessons learned. The site selection, eligibility, and retrofit availability (e.g., utility price structure, thermostat communications, etc.) are the main discussion points at the beginning of the project. Also, the modeling automation and the best practices for interacting with endusers and handling erroneous situations are presented for successful operations.

woo Ham, Sang↗

DOE OSTI2022

Model predictive control for robust quantum state preparation

A critical engineering challenge in quantum technology is the accurate control of quantum dynamics. Model-based methods for optimal control have been shown to be highly effective when theory and experiment closely match. Consequently, realizing high-fidelity quantum processes with model-based control requires careful device characterization. In quantum processors based on cold atoms, the Hamiltonian can be well-characterized. For superconducting qubits operating at milli-Kelvin temperatures, the Hamiltonian is not as well-characterized. Unaccounted for physics (i.e., mode discrepancy), coherent disturbances, and increased noise compromise traditional model-based control. This work introduces model predictive control (MPC) for quantum control applications. MPC is a closed-loop optimization framework that (i) inherits a natural degree of disturbance rejection by incorporating measurement feedback, (ii) utilizes finite-horizon model-based optimizations to control complex multi-input, multi-output dynamical systems under state and input constraints, and (iii) is flexible enough to develop synergistically alongside other modern control strategies. We show how MPC can be used to generate practical optimized control sequences in representative examples of quantum state preparation. Specifically, we demonstrate for a qubit, a weakly-anharmonic qubit, and a system undergoing crosstalk, that MPC can realize successful model-based control even when the model is inadequate. These examples showcase why MPC is an important addition to the quantum engineering control suite.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

Model predictive control and optimization for battery charging and discharging

An apparatus for model predictive control (“MPC”) is disclosed. A method and system also perform the functions of the apparatus. The apparatus includes a measurement module that receives battery status information from one or more sensors receiving information from a battery cell, and a Kalman filter module that uses a Kalman filter and the battery status information to provide a state estimate vector. The apparatus includes a battery model module that inputs the state estimate vector and battery status information into a battery model and calculates a battery model output, the battery model representing the battery cell, and an MPC optimization module that inputs one or more battery model outputs and an error signal in a model predictive control algorithm to calculate an optimal response. The optimal response includes a modification of the error signal.

Trimboli, Michael Scott↗

DOE OSTI2022

Model Predictive Control for a Grid-interactive Efficient Thermal Storage-integrated Heat Pump System

Building heating and cooling systems can be used to overcome the mismatch between the intermittent supply of renewable power and the fluctuating demand for electricity. A novel underground thermal energy storage integrated with a dual-source heat pump has been proposed to mitigate the mismatch while meeting the thermal demand of buildings efficiently. Conventional thermostat control with heuristic rules cannot provide intelligent decisions to maximize the thermal efficiency and flexibility of the proposed system. Advanced control strategies like model predictive control (MPC) have provided a new paradigm for grid-interactive efficient building operation with the advancement of computation and sensing. This study developed an MPC for the proposed system to provide grid service for Demand Side Management and minimize the operating cost of building owners. A control-oriented dynamic model of the proposed system has been developed. Given an objective function and proper constraints, an optimization problem is formulated to determine the optimal control strategy of the system. Dynamic Programming is adopted to solve the optimization problem. A rule-based control (RBC) is also developed to achieve similar goals. Short-term simulations are conducted to compare the system performance resulting from the two controls. The simulation results indicate that the MPC performs more intelligently than the RBC in charging thermal energy storage and selecting heat pump sources by taking advantage of the predicted cooling demands of the building and the performance of the integrated system. As a result, the MPC could save energy and reduce operating costs compared with the RBC. A case study shows that, for a 3-day operation, the MPC saves 36.9% energy and reduces 38.5% operating cost compared with the RBC.

Shi, Liang↗

DOE OSTI2025

A Model Predictive Control to Improve Grid Resilience

The following article details a model predictive control (MPC) to improve grid resilience when faced with variable generation resources. This topic is of significant interest to utility power systems where distributed intermittent energy sources will increase significantly and be relied on for electric grid ancillary services. Previous work on MPCs has focused on narrowly targeted control applications such as improving electric vehicle (EV) charging infrastructure or reducing the cost of integrating Energy Storage Systems (ESSs) into the grid. In contrast, this article develops a comprehensive treatment of the construction of an MPC tailored to electric grids and then applies it integration of intermittent energy resources. To accomplish this, the following article includes a description of a reduced order model (ROM) of an electric power grid based on a circuit model, an optimization formulation that describes the MPC, a collocation method for solving linear time-dependent differential algebraic equations (DAEs) that result from the ROM, and an overall strategy for iteratively refining the behavior of the MPC. Next, the algorithm is validated using two separate numerical experiments. First, the algorithm is compared to an existing MPC code and the results are verified by a numerically precise simulation. It is shown that this algorithm produces a control comparable to existing algorithms and the behavior of the control carefully respects the bounds specified. Second, the MPC is applied to a small nine bus system that contains a mix of turbine-spinning-machine-based and intermittent generation in order to demonstrate the algorithm’s utility for resource planning and control of intermittent resources. This study demonstrates how the MPC can be tuned to change the behavior of the control, which can then assist with the integration of intermittent resources into the grid. The emphasis throughout the paper is to provide systematic treatment of the topic and produce a novel nonlinear control compatible design framework applicable to electric grids and the control of variable resources. This differs from the more targeted application-based focus in most presentations.

microgrid↗

DOE OSTI2019

An Enhanced Model Predictive Control Using Virtual Space Vectors for Grid-Connected Three-Level Neutral-Point Clamped Inverters

Reliability of power systems can be improved by the use of voltage source inverters (VSIs) with fast dynamic control, which can handle uncertainties induced by renewable energy resources and nonlinear loads. To ensure fast-dynamic response and simplified controller design, various model predictive control (MPC) methods are investigated in this paper. In the conventional MPC design for three-level VSIs, the cost function requires an additional term to ensure the balance of the neutral-point voltage (NP-V), which however can considerably impact the main goal of the MPC. To address this issue, an enhanced MPC using virtual space vectors is proposed, which allows the use of a significantly reduced weighting factor for the term in the cost function for NP-V balancing, while retaining fast-dynamic response. Additionally, the proposed MPC leads to reduced harmonic distortion in the VSI output voltage and current. Both simulation and controller hardware-in-the-loop studies are performed to demonstrate the effectiveness of the proposed enhanced MPC in an operating microgrid under both steady-state and fast-transient conditions.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2026

Near-Optimal Performance of Stochastic Model Predictive Control

Here, this article presents a regret analysis for stochastic model predictive control (SMPC) in linear systems with quadratic performance index and additive and multiplicative uncertainties. Under a finite support assumption, the problem can be cast as a finite-dimensional quadratic program, but the problem becomes quickly intractable as the problem size grows exponentially in the horizon length. SMPC aims to compute approximate solutions by solving a sequence of problems with truncated prediction horizons and committing the solution in a receding-horizon fashion. Although this approach is widely used in practice, its performance relative to the optimal solution is not well understood. This article reports for the first time a rigorous near-optimal performance guarantee of SMPC: under stabilizability and detectability conditions, the regret of SMPC is exponentially small in the prediction horizon length, allowing SMPC to achieve near-optimal performance at a substantially reduced computational expense.

93E20, 93B45↗

DOE OSTI2023

Experimental validation of model predictive control for solid oxide fuel cells

Here, this paper presents implementation of a model predictive controller (MPC) for an experimental solid oxide fuel cell (SOFC) system. The MPC controller is based on a gain-scheduled predictor with block-oriented structure that can capture important non-linear effects while still keeping the computational complexity low enough to meet real time control requirements. Experimental results show the MPC is able to regulate the SOFC cathode outlet temperature in the face of startup transients and input perturbations.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2018

Practical factors of envelope model setup and their effects on the performance of model predictive control for building heating, ventilating, and air conditioning systems

Model predictive control (MPC) for buildings is attracting significant attention in research and industry due to its potential to address a number of challenges facing the building industry, including energy cost reduction, grid integration, and occupant connectivity. However, the strategy has not yet been implemented at any scale, largely due to the significant effort required to configure and calibrate the model used in the MPC controller. While many studies have focused on methods to expedite model configuration and improve model accuracy, few have studied the impact a wide range of factors have on the accuracy of the resulting model. In addition, few have continued on to analyze these factors’ impact on MPC controller performance in terms of final operating costs. Therefore, this study first identifies the practical factors affecting model setup, specifically focusing on the thermal envelope. The seven that are identified are building design, model structure, model order, data set, data quality, identification algorithm and initial guesses, and software tool-chain. Then, through a large number of trials, it analyzes each factor's influence on model accuracy, focusing on grey-box models for a single zone building envelope. Finally, this study implements a subset of the models identified with these factor variations in heating, ventilating, and air conditioning MPC controllers, and tests them in simulation of a representative case that aims to optimally cool a single-zone building with time-varying electricity prices. It is found that a difference of up to 20%25 in cooling cost for the cases studied can occur between the best performing model and the worst performing model. The primary factors attributing to this were model structure and initial parameter guesses during parameter estimation of the model.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗