Model Predictive Control Framework Research Articles

Dynamic-Linearization-Based Predictive Control of a Voltage-Source Inverter

In pursuit of accurate and fast trajectory tracking of power converters, an explicit model is commonly used in the finite control-set model predictive control (FCS-MPC) framework to predict precise behaviors of controlled variables. In reality, however, the model mismatch is inevitable, which causes the inherent challenges of parameter sensitivity and model uncertainties of the FCS-MPC method. This article proposes a dynamic-linearization-based predictive control architecture to circumvent such model dependence while keeping the attractive features of the conventional FCS-MPC method. By integrating the data-driven feature of the dynamic-linearization approach, the detailed model used in the FCS-MPC controller is replaced by a virtual equivalent data model, creating a data-driven predictive control architecture. The suggested method selects optimal control action solely based on the input-output data, exhibiting strong rejection against parameter variations whilst inheriting the distinctive property of the conventional FCS-MPC method. Finally, the proposed design is validated through comparative simulation and experimental results on a three-level neutral-point-clamped inverter.

Heuristic model predictive control implementation to activate energy flexibility in a fully electric school building

This paper presents a heuristic model predictive control (MPC) methodology to activate energy flexibility in fully electric school buildings in cold climates to reduce electricity demand during peak demand periods of the electric grid. To streamline the implementation of MPC, the proposed approach employs grey-box archetypes, a clustering of weather conditions to identify typical scenarios and a limited number of possible setpoint profiles. A data-driven grey-box approach is used to create archetype models for different thermal zones in a typical school building; this approach enables rapid development and requires much less calibration data than black-box models. A third-order resistance-capacitance thermal network for zones with convective heating and a fourth-order model for zones with radiant floor heating are developed and calibrated using measured data from an all-electric school building in Québec, Canada. The weather data are clustered into several categories, representing different weather conditions (6 clusters representing two ambient temperature ranges and three solar radiation ranges). The heuristic MPC strategy uses predefined optimal setpoint profiles for each cluster and weather prediction one day ahead to shift the building load from on-peak to off-peak hours. For each heuristic MPC scenario, the model runs a simulation using forecast weather data to quantify and activate energy flexibility in response to grid requirements. The developed MPC framework was implemented in the school used as the case study. Ten classrooms are investigated, with six using the MPC and four as a reference case with the reactive control system and default zone setpoint profiles. Results indicate that the school building can provide between 47% and 95% energy flexibility (load shifting relative to reference) during on-peak hours and up to 44% electricity cost reduction while satisfying acceptable temperature constraints. By implementing the proposed MPC, energy flexibility of 32 W/m2 of floor area for the zones with a convective heating system and 65 W/m2 of floor area for the zones with radiant heating can be achieved during a demand response event. The proposed strategy can be generalized and replicated in other school buildings.

A Tube Linear Model Predictive Control Approach for Autonomous Vehicles Subjected to Disturbances

The path tracking performance of autonomous vehicles is degraded by common disturbances, especially those that affect the safety of autonomous vehicles (AVs) in obstacle avoidance conditions. To improve autonomous vehicle tracking performances and their computational efficiency when subjected to common disturbances, this paper proposes a tube linear model predictive controller (MPC) framework for autonomous vehicles. A bicycle vehicle dynamics model is developed and employed in the tube MPC control design in the proposed framework. A robust invariant set is calculated with an efficient linear programming (LP) method, and it is used to guarantee that the constraints are satisfied under common disturbance conditions. The results show that the computational cost of robust positively invariant sets that are constructed by the LP method is much less than that obtained by the traditional method. In addition, all the trajectories of the tube linear MPC successfully avoided obstacles when under disturbance conditions, but only about 80% of the trajectories obtained with the traditional MPC successfully avoided obstacles under disturbance conditions. The proposed framework is effective.

Distributed multi-horizon model predictive control for network of energy hubs

The increasing penetration of renewable energy resources has transformed the energy system from a traditional hierarchical energy delivery paradigm to a distributed structure. Local energy hubs activates synergies among energy carriers rendering flexibility to the system and gives rise to possible energy trading among networked local energy hubs. Joint operation of such hubs and peer-to-peer trading between them can improve energy efficiency and support the integration of renewable energy resources. However, for such complex systems involving multiple stakeholders, both computational tractability and privacy concerns need to be accounted for. In this work, a novel multi-horizon distributed MPC framework is introduced for the control of energy hub networks. The multi-horizon approach increases the prediction horizon for MPC without compromising the time discretization or making the problem computationally intractable. The distributed scheme is based on a consensus alternating direction method of multipliers algorithm. It combines the superior performance of the centralized approach with the privacy preservation of the decentralized approach. A benchmark three-hub network is used to investigate the performance of the proposed method in simulation and compare it to the decentralized, centralized and standard model predictive control (MPC) approaches. The results show superior performance of the distributed multi-horizon MPC in terms of total cost, computational time, and robustness to demand and prices variations. Finally, the performance was also experimentally validated in real time by implementing the controller on a real energy hub system.

High‐level decision‐making for autonomous overtaking: An MPC‐based switching control approach

AbstractThe key motivation of this paper lies in the development of a high‐level decision‐making framework for autonomous overtaking maneuvers on two‐lane country roads with dynamic oncoming traffic. To generate an optimal and safe decision sequence for such scenario, an innovative high‐level decision‐making framework that combines model predictive control (MPC) and switching control methodologies is introduced. Specifically, the autonomous vehicle is abstracted and modelled as a switched system. This abstraction allows vehicle to operate in different modes corresponding to different high‐level decisions. It establishes a crucial connection between high‐level decision‐making and low‐level behaviour of the autonomous vehicle. Furthermore, barrier functions and predictive models that account for the relationship between the autonomous vehicle and oncoming traffic are incorporated. This technique enables us to guarantee the satisfaction of constraints, while also assessing performance within a prediction horizon. By repeatedly solving the online constrained optimization problems, we not only generate an optimal decision sequence for overtaking safely and efficiently but also enhance the adaptability and robustness. This adaptability allows the system to respond effectively to potential changes and unexpected events. Finally, the performance of the proposed MPC framework is demonstrated via simulations of four driving scenarios, which shows that it can handle multiple behaviours.

Nonlinear antiswing control for shipboard boom cranes with full state constraints

A nonlinear energy-based controller and a Lyapunov-based model predictive control (MPC) technology are constructed in sequence for shipboard boom cranes, while taking full state constraints into account. The mathematical model is firstly transformed to ease the explicit influences of ship rollings on the desired positions and payload swings. Barrier Lyapunov functions (BLFs) are then involved in the energy-based controller to deal with different types of state constraints, in which constraints with positive bounds are also effectively tackled with a modified BLF. By adding a contractive constraint with the energy-based controller in traditional MPC framework, Lyapunov-based MPC is then established, in which the recursive feasibility and stability is ensured effectively and easily. Asymptotical stability of two controllers is analyzed and guaranteed in theory, respectively. Compared with the energy-based controller, control performance is improved and enhanced by the Lyapunov-based MPC through solving the optimal control problem. Simulations are finally implemented, and comparisons are also carried out to demonstrate the effectiveness and features of the established controllers in this paper.

Closed loop model predictive control of a hybrid battery-hydrogen energy storage system using mixed-integer linear programming

The derivation of an efficient operational strategy for storing intermittent renewable energies using a hybrid battery-hydrogen energy storage system is a difficult task. One approach for deriving an efficient operational strategy is using mathematical optimization in the context of model predictive control. However, mathematical optimization derives an operational strategy based on a non-exact mathematical system representation for a specified prediction horizon to optimize a specified target. Thus, the resulting operational strategies can vary depending on the optimization settings.This work focuses on evaluating potential improvements in the operational strategy for a hybrid battery-hydrogen energy storage system using mathematical optimization. To investigate the operation, a simulation model of a hybrid energy storage system and a tailor-made mixed integer linear programming optimization model of this specific system are utilized in the context of a model predictive control framework. The resulting operational strategies for different settings of the model predictive control framework are compared to a rule-based controller to show the potential benefits of model predictive control compared to a conventional approach. Furthermore, an in-depth analysis of different factors that impact the effectiveness of the model predictive controller is done. Therefore, a sensitivity analysis of the effect of different electricity demands and resource sizes on the performance relative to a rule-based controller is conducted. The model predictive controller reduced the energy consumption by at least 3.9 % and up to 17.9% compared to a rule-based controller. Finally, Pareto fronts for multi-objective optimizations with different prediction and control horizons are derived and compared to the results of a rule-based controller. A cost reduction of up to 47 % is achieved by a model predictive controller with a prediction horizon of 7 days and perfect foresight.

Deep model predictive control of gene expression in thousands of single cells

Gene expression is inherently dynamic, due to complex regulation and stochastic biochemical events. However, the effects of these dynamics on cell phenotypes can be difficult to determine. Researchers have historically been limited to passive observations of natural dynamics, which can preclude studies of elusive and noisy cellular events where large amounts of data are required to reveal statistically significant effects. Here, using recent advances in the fields of machine learning and control theory, we train a deep neural network to accurately predict the response of an optogenetic system in Escherichia coli cells. We then use the network in a deep model predictive control framework to impose arbitrary and cell-specific gene expression dynamics on thousands of single cells in real time, applying the framework to generate complex time-varying patterns. We also showcase the framework’s ability to link expression patterns to dynamic functional outcomes by controlling expression of the tetA antibiotic resistance gene. This study highlights how deep learning-enabled feedback control can be used to tailor distributions of gene expression dynamics with high accuracy and throughput without expert knowledge of the biological system.

Real-world implementation of a cloud-based MPC for HVAC control in educational buildings

In their quest to enhance energy efficiency and carbon footprint management, many enterprises are turning their attention towards optimizing their facilities through amplified data monitoring and innovative control methods. In this context, this research highlights a practical solution in a commercial building located in the United States. It explains the creation, implementation, and costs of a universally applicable model predictive control (MPC) framework for the building’s heating, ventilation, and air conditioning (HVAC) system. The paper elaborates on both the hardware and software used to accumulate pertinent data and the formulation of the MPC system. This approach leverages cloud-based microservices and can be seamlessly integrated into current building management systems. In this regard, this paper presents three innovative strategies: Proportional–integral (PI)+Preheating, MPC, and occupancy-based control. These scenarios were designed to improve energy efficiency and thermal comfort significantly by reducing temperature fluctuations and adhering more closely to the setpoint temperature. The implementation of these strategies resulted in substantial energy savings, with reductions in energy consumption of 12.83%, 19.21%, and 14.98%, respectively.

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. The comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

Bilevel Predictive Control for HEVs Integrating Energy and Cabin Thermal Comfort

This paper proposes an integrated energy and cabin thermal management strategy for a connected hybrid electric vehicle that utilizes a vehicle speed preview informed by traffic connectivity. The proposed strategy employs a bilevel model predictive control framework over long and short predictive horizons to improve fuel economy while ensuring the vehicle’s traction energy and cabin thermal demands are satisfied. The cabin thermal load planning is developed with sensitivity to the vehicle speed of an air conditioning (AC) system, and the proportion of traction energy supplied between the engine and battery is optimized using the Pontryagin minimum principle. Under standard and on-road driving cycles, the simulation results indicate that over 18% and 22% reduction in fuel consumption can be saved compared to a baseline strategy and an equivalent consumption minimization strategy, respectively. Specifically, the electricity consumption of the AC system is reduced by 13% via thermal load planning of the cabin.

A robust nonlinear tracking MPC using qLPV embedding and zonotopic uncertainty propagation

In this paper, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for tracking for piece-wise constant reference signals. The main novelty is the use of quasi-Linear Parameter Varying (qLPV) embeddings in order to describe the nonlinear dynamics. Furthermore, these embeddings are exploited by an extrapolation mechanism, which provides the future behaviour of the scheduling parameters with bounded estimation error. Therefore, the resulting NMPC becomes computationally efficient (comparable to a Quadratic Programming algorithm), since, at each sampling period, the predictions are linear. Benefiting from artificial target variables, the method is also able to avoid feasibility losses due to large set-point variations. Robust constraint satisfaction, closed-loop stability, and recursive feasibility certificates are provided, thanks to uncertainty propagation zonotopes and parameter-dependent terminal ingredients. A benchmark example is used to illustrate the effectiveness of the method, which is compared to state-of-the-art techniques.

Energy flexibility quantification of a tropical net-zero office building using physically consistent neural network-based model predictive control

Building energy flexibility plays a critical role in demand-side management for reducing utility costs for building owners and sustainable, reliable, and smart grids. Realizing building energy flexibility in tropical regions requires solar photovoltaics and energy storage systems. However, quantifying the energy flexibility of buildings utilizing such technologies in tropical regions has yet to be explored, and a robust control sequence is needed for this scenario. Hence, this work presents a case study to evaluate the building energy flexibility controls and operations of a net-zero energy office building in Singapore. The case study utilizes a data-driven energy flexibility quantification workflow and employs a novel data-driven model predictive control (MPC) framework based on the physically consistent neural network (PCNN) model to optimize the building energy flexibility. To the best of our knowledge, this is the first instance that PCNN is applied to a mathematical MPC setting, and the stability of the system is formally proved. Three scenarios are evaluated and compared: the default regulated flat tariff, a real-time pricing mechanism, and an on-site battery energy storage system (BESS). Our findings indicate that incorporating real-time pricing into the MPC framework could be more beneficial to leverage building energy flexibility for control decisions than the flat-rate approach. Moreover, adding BESS to the on-site PV generation improved the building self-sufficiency and the PV self-consumption by 17% and 20%, respectively. This integration also addresses model mismatch issues within the MPC framework, thus ensuring a more reliable local energy supply. Future research can leverage the proposed PCNN-MPC framework for different data-driven energy flexibility quantification types.

Cooperative control of dynamic CAV dedicated lanes and vehicle active lane changing in expressway bottleneck areas

Bottleneck areas on expressways plague the operational efficiency of entire road systems. In mixed traffic flow environments consisting of connected and autonomous vehicles (CAVs) and connected human-driven vehicles (CHVs), it is believed that road capacity can be improved to relieve traffic congestion in bottleneck areas by setting CAV dedicated lanes (CDLs) on expressways. Existing static CDL setup methods provide fixed exclusive right-of-way for CAVs but cannot accommodate dynamic changes in traffic demand. To address this issue, utilizing lane control signals and CAV active lane-changing technology, a cooperative method involving dynamic CAV dedicated lane control (CDLC) and active lane-changing control (LCC) in the bottleneck areas of expressways is proposed in this paper. First, a fundamental diagram of traffic flow with CDLs is established based on the microscopic car-following model of mixed traffic flow, which can be used to determine the conditional thresholds for setting the CDLs of multilane expressways. Second, an expressway traffic model with CDLs is established by improving the lane-level cell transmission model. Finally, cooperative control of dynamic CAV dedicated lanes and active lane changing (CDLLC) is proposed based on the model predictive control (MPC) framework for solving the congestion problem at expressway bottlenecks in a mixed driving environment. The simulation results show that the proposed CDLLC strategy can effectively reduce the total vehicle travel time and decrease the risk of congestion propagation at expressway bottlenecks when compared to the LCC-only strategy.

Coalitional Distributed Model Predictive Control Strategy with Switching Topologies for Multi-Agent Systems

Controlling multi-agent systems (MASs) has attracted increased interest within the control community. Since the control challenge consists of the fact that each agent has limited local capabilities, our adopted solution is tailored so that a group of such entities works together and shares resources and information to fulfill a given task. In this work, we propose a coalitional control solution using the distributed model predictive control (DMPC) framework, suitable for a multi-agent system. The methodology has a switching mechanism that selects the best communication topology for the overall system. The proposed control algorithm was validated in simulation using a homogeneous vehicle platooning application with longitudinal dynamics. The available communication topologies were specifically tailored taking into account the information flow between adjacent vehicles. The obtained results show that when the platoon’s string stability is risked, the algorithm switches between different communication topologies. The resulting coalitions between vehicles ensure an increase in the overall stability of the entire system and prove the efficacy of our proposed methodology.

A Helly Model-Based MPC Control System for Jam-Absorption Driving Strategy against Traffic Waves in Mixed Traffic

Traffic waves in traffic flow significantly impact road throughput and fuel consumption and may even lead to severe safety issues. Currently, in connected and autonomous environments, the jam-absorption driving (JAD) strategy shows good performance in dissipating traffic waves. However, the previous JAD strategy has mostly focused on wave dissipation without adequately assessing traffic efficiency and safety. To address this gap, an optimal control problem for JAD in mixed traffic is proposed to reduce traffic waves. The prediction model is developed using the car-following model within a model predictive control (MPC) framework. The Helly model is selected for the manual vehicle. This is because the Helly model is a linear model that describes the car-following phenomenon accurately without delay effect. In addition, the objective function of the prediction model considers both traffic safety and efficiency while satisfying mechanical and safety constraints. Simulation results indicate that the proposed methodology can effectively reduce traffic jams and improve traffic performance on a one-lane freeway. The optimal method is more applicable to complex traffic wave scenarios, providing a new perspective for reducing traffic jams on the freeway.

Koopman fault‐tolerant model predictive control

AbstractThis paper introduces a novel data‐driven approach to develop a fault‐tolerant model predictive controller (MPC) for non‐linear systems. By adopting a Koopman operator‐theoretic perspective, the proposed method leverages historical data from the system to construct a data‐driven model that captures the non‐linear behaviour and fault characteristics. The fault influence is addressed through an online estimation of a time‐varying Koopman predictor, which allows for adjusting the MPC control law to counteract the fault effects. This estimation is performed in a higher dimensional Koopman feature space, where the dynamics behave linearly. As a result, the non‐linear fault‐tolerant MPC optimization problem can be replaced with a more practical and feasible linear time‐varying one using the approximated Koopman predictor. Moreover, by incorporating the online update procedure, the time‐varying Koopman predictor can represent the dynamics of the faulty system. Hence, the controller can adapt and compensate for the faults in real‐time, integrating the fault diagnosis module in the MPC framework and eliminating the need for a separate fault detection unit. Finally, the efficacy of the proposed approach is demonstrated through case study results, which highlight the ability of the controller to mitigate faults and maintain desired system behaviour.

Optimizing passenger vehicle travel time with Model Predictive Control in multi-region traffic networks

Abstract This study investigates the impact of truck traffic on passenger vehicles in an urban network. Utilizing the Macroscopic Fundamental Diagram (MFD), a methodology to calculate the travel time spent (TTS) by passenger vehicles has been developed. To address this issue, an optimal control problem was formulated and solved using a Model Predictive Control (MPC) approach. The MPC framework has been applied in a centralized manner, to manage accumulation for various modes. To explore different traffic management strategies, the centralized MPC technique was implemented in two distinct configurations: region-based and vehicle-based approaches. It has been tested for various vehicle mixes and multiple control scenarios to assess the effectiveness in reducing passenger travel time spent (PTTS) and vehicle accumulation. The results demonstrate that the vehicle-based MPC approach tends to minimize the number of vehicles more effectively compared to the region-based approach. However, in terms of reducing passenger travel time, the region-based approach outperforms the vehicle-based strategy. This is attributed to enhanced coordination among traffic flow controllers, highlighting the importance of strategic controller interactions in urban traffic management systems. This research enhances both the theoretical framework for optimizing traffic flow and provides valuable practical insights for city planners and engineers aiming to deploy advanced traffic management strategies. Future studies could explore the scalability of these control systems and their capability to integrate real-time traffic data.

Coordinated Operation of Virtual Coupling High-Speed Trains Under a Novel Sequential Model Predictive Control Framework

This paper deals with the coordinated control problem of the multiple high-speeds operating under the virtual coupling mode with special consideration of the coupled safety inter-train distance constraints and other independent constraints affecting train dynamics. Considering the inertial lag phenomenon within longitudinal dynamics, this study employs a third-order nonlinear control model to characterize train motion. To cope with the intricate running constraints explicitly, a centralized constrained model predictive (MPC) control problem is formulated for the regulation of the trains. Within the framework of sequential solving approach, a novel distributed model predictive control (DMPC) algorithm is designed based on a distributed train running information exchange mechanism. The algorithm decomposes the centralized MPC problem into a sequence of local problems, allowing for sequential computation and meeting the real-time control requirements. Notably, the algorithm mitigates solution conservatism arising from the distributed optimization mechanism by accounting for potential hypothetical control policies among a train’s topological neighbors when designing its control policy. The feasibility and effectiveness of the proposed results are rigorously confirmed through theoretical analysis and illustrated by numerical experiment results.

Multivariable robust tube-based nonlinear model predictive control of mammalian cell cultures

In this paper, the application of a robust nonlinear model predictive control (NMPC) framework to mammalian cell cultures is proposed, dealing with possible large kinetic parameter uncertainties. Industrial constraints formulated in view of good manufacturing practice and quality-by-design approach are also considered, namely the assurance that all state trajectories are contained within a corridor defined by lower and upper safety bounds. The latter are assimilated to the well-known tube-based paradigm which is used to formulate the corresponding robust NMPC problem. Both classical and tube-based NMPC performances are assessed in numerical simulations where specific key-species are regulated while dealing with an uncertain plant model. The capability of the tube-based method to reduce the impact of the parameter variations on the state trajectories and the violation of the constraints is highlighted, suggesting the transfer of the method on a real pharmaceutical process.