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Microgrids are a development trend and have attracted a lot of attention worldwide. The control system plays a crucial role in implementing these systems and, due to their complexity, artificial intelligence techniques represent some enabling technologies for their future development and success. In this paper, we propose a novel formulation of an economic model predictive control (economic MPC) applied to a microgrid designed for a faculty building with the inclusion of a predictive model to deal with the energy demand disturbance using a recurrent neural network of the long short‐term memory (RNN‐LSTM). First, we develop a framework to identify an RNN‐LSTM using historical data registered by a smart three‐phase power quality analyzer to provide feedforward power demand predictions. Next, we present an economic MPC formulation that includes the prediction model for the disturbance within the optimization problem to be solved by the MPC strategy. We carried out simulations with different scenarios of energy consumption, available resources, and simulation times to highlight the results obtained and analyze the performance of the energy management system. In all cases, we observed the correct operation of the proposed control scheme, complying at all times with the objectives and operational restrictions imposed on the system. [ABSTRACT FROM AUTHOR]

Tunnel boring machines (TBMs) are usually the first choice for tunneling construction with its advantages on high safety, time saving, and less operators. Cutterhead system is an important component for TBMs since it is used to excavate rocks and soil. It is difficult to guarantee both the boring efficiency and energy saving under the excavating rock disturbances and the constraints on the driving motors in TBMs by manual operation. To deal with this problem, it is necessary to develop advanced control algorithms for the cutterhead system. Thus, we investigate an economic model predictive control (EMPC) structure for cutterhead system in TBMs. A generalized nonlinear dynamic model of TBM cutterhead system is built based on the first principle method. An economic cost is constructed with the boring efficiency and energy cost to evaluate the tunnel construction quality. EMPC algorithms are designed to optimize the constructed economic cost for a cutterhead system to guarantee good economic performance. It is shown that EMPC can improve the economic performance of the cutterhead system. [ABSTRACT FROM AUTHOR]

The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set (VCTS) at a minimal but safe distance. To guarantee collision avoidance, the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking (EB) trajectories of two successive units during the whole EB process. In this case, the minimal safety distance is usually numerically calculated without an analytic formulation. Thus, the constrained VCTS control problem is hard to address with space-time separation, which is still a gap in the existing literature. To solve this problem, we propose a Distributed Economic Model Predictive Control (DEMPC) approach with computation efficiency and theoretical guarantee. Specifically, to alleviate the computation burden, we transform implicit safety constraints into explicitly linear ones, such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently. For theoretical analysis, sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC, employing compatibility constraints, tube techniques and terminal ingredient tuning. Moreover, we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS. Finally, experimental results demonstrate the performance and advantages of the proposed approaches.

This article proposes a two‐layer framework to maximize economic performance through dynamic process economics optimization while addressing fluctuating real‐world economics and enhancing cyberattack resilience via encryption in the feedback control layer for nonlinear processes. The upper layer employs a Lyapunov‐based economic model predictive control scheme, receiving updated economic information for each operating period, while the lower layer utilizes an encrypted linear feedback control system. Encrypted state information is decrypted in the upper layer to determine the economically optimal dynamic operating trajectory through nonlinear optimization. Conversely, the lower layer securely tracks this trajectory in an encrypted space without decryption. To mitigate the cyber vulnerability of the upper layer, we integrate a cyberattack detector that utilizes sensor‐derived data for attack detection. We quantify the errors stemming from quantization, disturbances, and sample‐and‐hold controller implementation. Simulation results of a nonlinear chemical process highlight the robustness and economic benefits of this new control architecture. [ABSTRACT FROM AUTHOR]

To establish a stable hydrogen economy in Germany, continuously new regulatory schemes for hydrogen systems are developed. Recently, a subsidy scheme was included in the Renewable Energy Act (EEG), which provides boundary conditions for hydrogen-based energy storage systems (HBESSs) design and operation. Therefore, regulation constraints need to be included into technical control to show the actual influence on the operation of the HBESS. This work provides a generic framework to consider economic parameters for power set point assignment of HBESSs and enables the comparison of the different control strategies, rule-based control (RBC) and economic model predictive control (EMPC). The Hydrogen Lab Bremerhaven (HLB) and the EEG serve as use case for the application, which was implemented in MATLAB Simulink. While the revenue was optimized, also the components utilization rate and the grid-supporting operation were evaluated. The economic results show that the new EEG subsidy enables profitable operation of HBESS for the first time, by guaranteeing a use case specific electricity price of 94.81 e/MWh. Also, the supervisory control method is crucial since the EMPC generates higher revenues than a simple RBC. Utilization rates show that by the current subsidy scheme the monetary incentive to store energy is missing. Also, the revenue as objective for the EMPC leads to lower times of grid-supporting operation, compared to the RBC. Overall, the method of including a regulation scheme into technical control for HBESS could be successfully demonstrated.

Based on the hierarchical control structure, optimization and control problems of large‐scale and multivariate plants are solved sequentially. The economic performance of the plant plays an essential role in the plant‐wide modern industry. The optimal operating conditions will change as the economic criteria changes throughout the operation of the plant as the result of variations in raw material prices, product prices, production demand, market fluctuations, disturbances, and so forth. In reality, soft constraints are frequently used to denote the production requirements of various operating conditions. In order to improve economic performance and guarantee feasibility for the entire plant operation, a novel economic model predictive control (EMPC) strategy is proposed to control the constrained multi‐variable process system with varying economic performance criteria under soft constraints. By incorporating the transient steady‐state and two categories of slack variables for soft constraints, a modified economic performance index is optimized to cope with the changing criteria. In addition, a contractive constraint is added to the closed‐loop system to guarantee stability for non‐dissipative stage costs. This approach ensures recursive feasibility and asymptotic stability. The effectiveness of the proposed method is demonstrated by numerical examples and the fluid catalytic cracking unit (FCCU) process. [ABSTRACT FROM AUTHOR]

At present, the new energy industry represented by photovoltaics has become the main force to realize the optimization of China's energy structure and the goal of "double carbon"; with the absence of land resources, the waterborne bifacial photovoltaic has ushered in a new opportunity. Therefore, in order to address the problem that the maximum power point tracking (MPPT) of photovoltaics (PV) could not take into account, the dynamic economic performance in the control process, an economic model predictive control (EMPC), is proposed in this work to realize the MPPT of the waterborne bifacial PV power generation system. Firstly, the model of the bifacial PV module is constructed by combining the ray-tracing irradiance model and considering the effect of water surface albedo on the irradiance absorbed by the module. Secondly, the EMPC controller is designed based on the state-space model of the system to maximize the power generation as the economic performance index, and to solve the optimal input variables time by time to achieve a rolling optimization with the operational requirements of the system itself as the constraints. Thirdly, the MATLAB/Simulink (R2022a) simulation experimental results verify that the EMPC strategy could be utilized to achieve MPPT of the waterborne bifacial PV power generation system, according to the changes of environment. Finally, it is also demonstrated that the bifacial PV power generation system that employed the EMPC strategy outperformed the traditional MPPT algorithm, with respect to both output power tracking velocity and accuracy, and the power generation could be improved by about 6% to 14.5%, which significantly enhances the system's dynamic process economics. [ABSTRACT FROM AUTHOR]

Tracking model predictive control (MPC) and economic model predictive control (EMPC) are essential techniques in process control. Economic model predictive control with zone tracking offers an effective means of concurrently addressing both tracking MPC and EMPC objectives. However, the aggregated conflicting objectives do not always align with the prioritization of critical tasks, such as safety, stability, quality, and economy. To address this issue, this study introduces a lexicographic approach for EMPC with zone tracking, which aims at balancing the competing zone tracking and economic objectives. The work also explores a generalized lexicographic multi-objective MPC (MoMPC) formulation and presents lexicographic zone economic model predictive control to accommodate multiple tracking and economic objectives. The advantages, disadvantages, and effectiveness of the proposed approach are validated and showcased through extensive simulation experiments. • A lexicographic zone economic model predictive control (ZEMPC) method is proposed. • Lexicographic ZEMPC encompassing multiple zone and economic objectives is developed. • The effectiveness of the proposed approach is supported by extensive experiments. [ABSTRACT FROM AUTHOR]

Agriculture accounts for approximately 70% of the world’s freshwater consumption. Furthermore, traditional irrigation practices, which rely on empirical methods, result in excessive water usage. This, in turn, leads to increased working hours for irrigation pumps and higher electricity consumption. The main objective of this study is to develop and evaluate periodic model predictive control structures that explicitly account for on-off irrigation, a characteristic of drip irrigation systems where watering can be turned on and off, but flow cannot be regulated. While both proposed control structures incorporate an economic upper layer (Real Time Optimizer, RTO), they differ in the costs associated with the lower layer. The first structure, called Model Predictive Control for Tracking (MPCT), focuses on tracking effectiveness, while the second structure, called Economic Model Predictive Control for Tracking (EMPCT), incorporates the economic cost into the tracking term. These proposed structures are tested in a realistic case study, specifically in a strawberry greenhouse, and both show satisfactory performance. The choice of the best option will depend on specific conditions.

Economic model predictive control (EMPC) has attracted an abundance of interest in both academic and industrial communities in recent years because it is able to increase the economic profits of dynamic systems. For greater computational efficiency, two-layer EMPC schemes are applied in some complex process control. However, the performance of two-layer EMPC is significantly influenced by the accuracy of the chosen process model. Reinforcement learning (RL) has been studied as a model-free strategy of model-based control approaches, but its safety and stability remain a concern. In order to estimate the model parameters of nonlinear dynamic systems in real time, this work introduces a unique scheme for merging two-layer EMPC and RL. In this scheme, the two-layer EMPC technique maintains closed-loop stability and recursive feasibility while operating the closed-loop dynamic system optimally. And the RL agent continually compares the observed states to the predictions made by the EMPC and modifies the time-varying parameters as necessary. The usability of the proposed scheme is shown on a chemical process of ethylene oxide production in dynamic environment. This work enables online and continuous control, optimization, and model correction, and makes process production optimization more feasible and profitable. [Display omitted] A two-layer economic model predictive control scheme is considered. A RL agent is integrated to estimate the time-varying parameters. Lyapunov-based stability analysis is provided. A chemical production simulation is utilized to verify the efficiency. [ABSTRACT FROM AUTHOR]

This paper focuses on vehicle tracking control issues with consideration of energy efficiency, ride comfort and tracking performance. To address this issue, an economic model predictive control (EMPC) framework is proposed by taking average performance into account and introducing a time‐varying terminal set. We integrate an economic model predictive controller and a terminal controller with a feedback gain related to the time‐varying terminal set into the proposed EMPC framework. An acceleration‐dependent average constraint is designed and incorporated into the MPC optimization problem to facilitate the convergence of the actual acceleration to the desired one, which enables the vehicle to implement a smooth driving style that boosts energy economy. A tuning factor in the average constraint has the capacity to balance energy consumption and control performance. Under the premise of invariance constraints, a dynamic terminal set is constructed by solving a dynamic programming problem online, which enables an arbitrary location and scale of the terminal set at each iteration by taking the current and predicted tracking errors into account. This allows a reduction in the conservativeness of an economic model predictive controller in the sense of both the region of attraction and the cost bound. Recursive feasibility of the MPC optimization problem and the terminal set dynamic programming is ensured, and average performance is not worse than the performance with an optimal steady‐state operation. Moreover, the convergence of the closed‐loop tracking error to the optimal steady‐state is guaranteed by using the dissipativity theory. The effectiveness of the proposed algorithm is verified by numerical comparisons with different controller parameters and standard EMPC. [ABSTRACT FROM AUTHOR]

The wave energy converter (WEC) control problem aims to make the best use of wave excitation to maximize energy capture and ensure safe operation across a broad range of sea states. This falls into the recently developed economic model predictive control (EMPC) framework, subject to wave excitation being treated as a predictable additive disturbance in the control problem. However, there are few theoretical developments on EMPC theory that can be directly used, as the persistent disturbances bring nontrivial problems to optimal operation, safety etc. Whilst the disturbance is beneficial for the energy production objective, it may cause safe operation problems. This article develops a systematic WEC EMPC design approach for WECs with essential linear hydrodynamical characteristics. By introducing terminal weight and terminal state constraint design into the WEC EMPC structure, important features such as convexity, satisfaction of safety constraints, and recursive feasibility can be guaranteed. Contrary to our intuition, we show that (1) the proposed EMPC with a terminal weight provides an unbiased estimate of the ideal conceptual infinite horizon solution, and (2) the WEC operational range, in terms of the operational sea states, is extended by imposing a terminal constraint. Finally, numerical simulations are provided to verify the efficacy of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a finite-time economic model predictive control (MPC) algorithm that can be used for frequency regulation and optimal load dispatch in multi-area power systems. Economic MPC can be used in a power system to ensure frequency stability, real-time economic optimization, control of the system and optimal load dispatch from it. A generalized terminal penalty term was used, and the finite-time convergence of the system was guaranteed. The effectiveness of the proposed model predictive control algorithm was verified by simulating a power system, which had two areas connected by an AC tie line. The simulation results demonstrated the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Demand responsive industrial loads with high thermal inertia have potential to provide ancillary service for frequency regulation in the power market. To capture the benefit, this study proposes a new hierarchical framework to coordinate the demand responsive industrial loads with thermal power plants in an industrial park for secondary frequency control. In the proposed framework, demand responsive loads and generating resources are coordinated for optimal dispatch in two-time scales: (1) the regulation reserve of the industrial park is optimally scheduled in a day-ahead manner. The stochastic regulation signal is replaced by the specific extremely trajectories. Furthermore, the extremely trajectories are achieved by the day-ahead predicted regulation mileage. The resulting benefit is to transform the stochastic reserve scheduling problem into a deterministic optimization; (2) a model predictive control strategy is proposed to dispatch the industry park in real time with an objective to maximize the revenue. The proposed technology is tested using a real-world industrial electrolysis power system based upon Pennsylvania, Jersey, and Maryland (PJM) power market. Various scenarios are simulated to study the performance of the proposed approach to enable industry parks to provide ancillary service into the power market. The simulation results indicate that an industrial park with a capacity of 500 MW can provide up to 40 MW ancillary service for participation in the secondary frequency regulation. The proposed strategy is demonstrated to be capable of maintaining the economic and secure operation of the industrial park while satisfying performance requirements from the real world regulation market.

Demand responsive industrial loads with high thermal inertia have potential to provide ancillary service for frequency regulation in the power market. To capture the benefit, this study proposes a new hierarchical framework to coordinate the demand responsive industrial loads with thermal power plants in an industrial park for secondary frequency control. In the proposed framework, demand responsive loads and generating resources are coordinated for optimal dispatch in two-time scales: (1) the regulation reserve of the industrial park is optimally scheduled in a day-ahead manner. The stochastic regulation signal is replaced by the specific extremely trajectories. Furthermore, the extremely trajectories are achieved by the day-ahead predicted regulation mileage. The resulting benefit is to transform the stochastic reserve scheduling problem into a deterministic optimization; (2) a model predictive control strategy is proposed to dispatch the industry park in real time with an objective to maximize the revenue. The proposed technology is tested using a real-world industrial electrolysis power system based upon Pennsylvania, Jersey, and Maryland (PJM) power market. Various scenarios are simulated to study the performance of the proposed approach to enable industry parks to provide ancillary service into the power market. The simulation results indicate that an industrial park with a capacity of 500 MW can provide up to 40 MW ancillary service for participation in the secondary frequency regulation. The proposed strategy is demonstrated to be capable of maintaining the economic and secure operation of the industrial park while satisfying performance requirements from the real world regulation market.

The aim of this document is to present an efficient and systematic method of model‐based predictive control synthesis. Model predictive control requires using a model of a dynamical system, that can be linear, time‐varying, non‐linear, or identified from data. Finding a model that is both precise and simulatable at low computational cost can be challenging and time consuming due to requiring extensive knowledge of the system and physics as well as a large volume of data with relevant scenarios and sometimes a complicated identification work. (filtering noises and bias, data formatting, etc.) The proposed methodology begins with fine‐scale multi‐physics modeling, which is possible thanks to open model libraries (see Modelica). The obtained model is then simulated by considering ad hoc scenarios to generate data, which are then used to identify a neural network, that will support the predictive control syntheses. The systematic methodology is detailed and applied to the widely used control benchmark known as the quadruple tanks process. Results show that the methodology is accurately applied to optimize hyperparameters in finding a neural network model and to control the quadruple tanks process with the predictive controller. [ABSTRACT FROM AUTHOR]

Economic model predictive control (EMPC) is an effective control strategy for wastewater treatment plants (WWTPs), which are crucial for preventing water pollution and improving the water quality. However, industrial processes typically involve large-scale nonlinear and strongly coupled systems, and it is computationally expensive to solve nonlinear optimization problems based on nonlinear prediction models such as EMPC. In this study, to facilitate the application of EMPC to large-scale nonlinear systems such as WWTPs, the lattice trajectory piecewise linear (PWL) model is used to approximate the nonlinear system with a predefined error bound. The resulting optimization problem can be expressed as a continuous PWL programming problem if the cost function of the EMPC is linear. Therefore, an iterative descent algorithm is proposed to transform the PWL programming problem into a series of linear programming problems. The stability of the nonlinear system operating under EMPC is analyzed. The EMPC scheme based on the lattice trajectory PWL model is applied to a WWTP benchmark problem, in which the state is 78-dimensional and the EMPC cost is linear. The proposed strategy outperforms the EMPC schemes based on the nonlinear prediction model and trajectory PWL prediction model. Overall, the EMPC scheme based on the lattice trajectory PWL prediction model can improve the computational efficiency of optimization problems while ensuring control performance. • Lattice trajectory piecewise linear approximation of the wastewater process. • A novel descent algorithm is proposed for piecewise linear programming problem. • Stability of the nonlinear wastewater process is proved. • The efficacy of the proposed strategy is shown through simulation. [ABSTRACT FROM AUTHOR]

This work studies a distributed economic model predictive control (DEMPC) approach for multi-stage belt conveyor (BC) systems based on a novel low-order model. First, the existing BC finite element dynamic model is reduced to a low-order model with five micro-element segments. In describing the speed and acceleration range of the BC, the low-order model is consistent with the original model. Then, a DEMPC method is proposed for multi-stage BC systems. In this method, the state information of the adjacent BCs is used to express the collaborative cost function for the local optimization control problem. By using the obtained method, the economic performance is improved, and the energy consumption is reduced. Finally, hardware-in-the-loop simulation tests are utilized to demonstrate the benefits of the results gained. • A low-order dynamical model is proposed for the single belt conveyor. • A collaborative cost function is constructed for the multistate belt conveyor. • A distributed economic model predictive control of multistage belt conveyor is given. • A hardware-in-the-loop experiment system is designed to verify the proposed methods. [ABSTRACT FROM AUTHOR]

The study proposes a robust algorithm for batch-to-batch optimization in the presence of model-mismatch. Robustness is achieved by the implementation of the following features: i — the gradient correction step is modified to consider the gradients of the cost function and constraints at both final and intermediate points, ii — Economic Model Predictive Control is applied to mitigate the impact of unmeasured disturbances on the optimum, and iii — an optimal design of experiments is performed to expedite convergence. Significant improvements of the proposed algorithm in convergence to the process optimum and robustness to noise, unmeasured disturbances, and model error are demonstrated using a fed-batch fermentation for penicillin production. • Traditional batch-to-batch optimization algorithm was enhanced by incorporating 3 novel steps. • Proposed gradient correction reduced noise sensitivity and improved optima. • Economic predictive control is used to reject unmeasured disturbances in the batch. • Application of optimal experimental design reduced costs and time to achieve the optimum. • Fed-batch penicillin process was used to show the improvements in performance. [ABSTRACT FROM AUTHOR]

Recent advances have been made in self-stabilizing Economic Nonlinear Model Predictive Control (eNMPC) formulation without pre-calculated setpoints, which leverages norm-based steady-state optimality conditions to enhance system robustness. To enable practical implementation, a generalized time-domain formulation is proposed, accommodating the discrete-time nature of control instrumentation and the continuous-time nature of first-principles models. A case study involving a modular membrane reactor illustrates the applicability of self-stabilizing eNMPC in real-world industrial scenarios. • Explores self-stabilizing eNMPC for automation without predetermined setpoint. • Lyapunov constraint penalizes distance from optimality conditions, not solutions. • Proposes time-domain formulation to bridge discrete-time control and continuous models. • Tuning stabilizing constraints enhances closed-loop control and system adaptability. • Examines eNMPC in a membrane reactor, highlighting real-time control and efficiency. [ABSTRACT FROM AUTHOR]

Mineral processing plants remain nowadays infamous for their low energy efficiency. Economic model predictive control (EMPC), by directly considering the energy costs, could possibly help reduce their footprint, but its environmental benefits are yet to be clearly quantified. In an attempt to cast some light on this topic, this paper compares the response to a given ore feed size and hardness disturbance sequence of an EMPC to that of basic and advanced regulatory control systems using the profits and the specific energy (power draw/ore feed rate) as metrics. The simulated circuit comprises a high-pressure grinding rolls (HPGR), a ball mill, and a flotation circuit. It is based on population balance modeling and is an extension of previous works. The basic regulatory control (BRC) system comprises only single-input–single-output control loops with proportional–integral (PI) controllers and operates at a fixed feed rate. The advanced regulatory control (ARC) system consists of PI controllers maximizing the plant feed rate with override constraint handling. The results show that (1) ARC generates more revenue and maintains a lower circuit specific energy consumption than BRC, (2) ARC can produce the same economic performance as EMPC because the constraints of the system define the economic optimum, and (3) EMPC can trade revenues for a lower circuit specific energy with a hybrid criterion that penalizes power draw. • The work compares different control systems on an HPGR grinding circuit. • A decentralized PI control system can generate equivalent revenues to an EMPC. • EMPC can trade revenues for a lower circuit specific energy. [ABSTRACT FROM AUTHOR]

This work focuses on the development of a Lyapunov-based economic model predictive control (LEMPC) scheme that utilizes recurrent neural networks (RNNs) with an online update to optimize the economic benefits of switched non-linear systems subject to a prescribed switching schedule. We first develop an initial offline-learning RNN using historical operational data, and then update RNNs with real-time data to improve model prediction accuracy. The generalized error bounds for RNNs updated online with independent and identically distributed (i.i.d.) and non-i.i.d. data samples are derived, respectively. Subsequently, by incorporating online updating RNNs within LEMPC, probabilistic closed-loop stability, and economic optimality are achieved simultaneously for switched non-linear systems accounting for the RNN generalized error bound. A chemical process example with scheduled mode transitions is used to demonstrate that the closed-loop economic performance under LEMPC can be improved using an online update of RNNs. [ABSTRACT FROM AUTHOR]

Wastewater Treatment Plants (WWTPs) are industrial facilities, which are important for the protection of the environment, because they remove pollutants from wastewater, before it reaches natural bodies of water. WWTPs consist of complex physical, chemical, and biological energy-intensive processes, which are subject to significant disturbances and uncertainties, due to large variations in the load and quality of the influent. Rising energy prices and increasingly stringent effluent requirements have amplified the need of developing more efficient control schemes for WWTPs. In this paper a novel Economic Dynamic Matrix Control (EDMC) configuration is proposed for WWTPs, where the objective is to minimize the plant's operating costs in terms of energy savings, while maintaining the effluent quality within acceptable regulatory limits. The novelty of the proposed scheme lies in the combination of the standard Dynamic Matrix Control (DMC) methodology, with economic oriented control strategies. The EDMC predictive models are derived from the application of step tests on the COST/IWA Benchmark Simulation Model No. 1 (BSM1). Based on the BSM1 model, the proposed method is compared to standard Multiple Input–Multiple Output (MIMO) DMC controllers, to the default BSM1 control strategy and to other economic control methods, which have been proposed in the literature. The results illustrate that the proposed EDMC scheme is superior to alternative control strategies in terms of minimizing the energy consumption while, the effluent quality of the plant is maintained at acceptable levels. • We propose a novel control method combining conventional DMC with concepts from Economic MPC. • The method is particularly tailored to the control of Waste Water Treatment Plants. • The method is based on data-driven models derived from step tests, so it can be applied easily in real-life scenarios. • Feasibility is tested on a benchmark model and compared to several other control methods proposed in the literature. [ABSTRACT FROM AUTHOR]

This paper considers the multi-objective platooning control problem of a group of connected and automated vehicles (CAVs) with bidirectional topologies. A new distributed economic model predictive control (DEMPC) algorithm is presented to reconcile the conflict of the control objectives of tracking, safety, stability and fuel economy of the heterogeneous vehicle platoon with guaranteed string stability. Using transient engine energy efficiency indices and cooperative performance of tracking and string stability, two distributed receding horizon optimal control problems are orderly formulated by a Lyapunov-based coupling constraint. Moreover, a new concept of $\gamma $ -string stability is defined for the platoon with bidirectional topologies. Some distributed terminal conditions are then derived to guarantee the recursive feasibility and asymptotic stability of the DEMPC as well as $\gamma $ -string stability of the platoon in the presence of constraints. Compared to traditional platooning control, the new DEMPC has a 4.2% energy-saving of vehicles while achieving the cooperative tasks of the platoon in several simulation scenarios. [ABSTRACT FROM AUTHOR]

Electric microgrids have become an interesting tool to facilitate the inclusion of renewable energies. Its architecture and control system plays a fundamental role in the implementation of these systems. This paper proposes a control strategy for the management of energy resources in a residential microgrid. The system is made up of a set of solar panels as renewable resource, a storage system formed by a lithium-ion battery bank and a consumption profile according to a residence. The microgrid will be connected to the main electrical grid and the proposed management strategy consists in the implementation of a suitable Economic Model Predictive Control, where it considers the costs of use for the different components of the microgrid, thus contemplating the participation of the system as an active agent in the electricity market. Simulations were carried out with different scenarios of available resources and prediction times. In all cases, the objectives fulfilling by satisfying the restrictions operational and technical imposed on the system. • Modelling of a residential microgrid. • Participation in the electrical market of microgrids. • Economic Model Predictive Control as a Energy Management System in microgrids. [ABSTRACT FROM AUTHOR]

In this paper, a technique that integrates methods of dynamic economic optimization and real-time control by including economic model predictive control and closed-loop predictive control has been developed, using a two-layer structure. The upper layer, which consists of an economic nonlinear MPC (NMPC), makes use of the updated state information to optimize some economic cost indices and calculates in real time the economically optimal trajectories for the process states. The lower layer uses a closed-loop nonlinear GPC (NCLGPC) to calculate the control actions that allow for the outputs of the process to follow the trajectories received from the upper layer. This paper also includes the theoretical demonstration proving that the deviation between the state of the closed-loop system and the economically time varying trajectory provided by the upper layer is bounded, thus guaranteeing stability. The proposed approach is based on the use of nonlinear models to describe all the relevant process dynamics and cover a wide operating range, providing accurate predictions and guaranteeing the performance of the control systems. In particular, the methodology is implemented in the N-Removal process of a WWTP and the results demonstrate that the method is effective and can be used profitably in practical cases such as the chemical, refinery and petrochemical process industries. [ABSTRACT FROM AUTHOR]

(Economic) nonlinear model predictive control ((e)NMPC) requires dynamic models that are sufficiently accurate and computationally tractable. Data-driven surrogate models for mechanistic models can reduce the computational burden of (e)NMPC; however, such models are typically trained by system identification for maximum prediction accuracy on simulation samples and perform suboptimally in (e)NMPC. We present a method for end-to-end reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC. We apply our method to two applications derived from an established nonlinear continuous stirred-tank reactor model. The controller performance is compared to that of (e)NMPCs utilizing models trained using system identification, and model-free neural network controllers trained using reinforcement learning. We show that the end-to-end trained models outperform those trained using system identification in (e)NMPC, and that, in contrast to the neural network controllers, the (e)NMPC controllers can react to changes in the control setting without retraining. • Task-optimal Koopman models for control learned using reinforcement learning. • Reinforcement learning of Koopman models outperforms system identification. • Reinforcement learned Koopman MPCs adapt to environment changes without retraining. [ABSTRACT FROM AUTHOR]

This work proposes an economic model predictive control (EMPC) strategy in the linear parameter varying (LPV) framework for the control of dissolved oxygen concentrations in the aerated reactors of a wastewater treatment plant (WWTP). A reduced model of the complex nonlinear plant is represented in a quasi-linear parameter varying (qLPV) form to reduce computational burden, enabling the real-time operation. To facilitate the formulation of the time-varying parameters which are functions of system states, as well as for feedback control purposes, a moving horizon estimator (MHE) that uses the qLPV WWTP model is proposed. The control strategy is investigated and evaluated based on the ASM1 simulation benchmark for performance assessment. The obtained results applying the EMPC strategy for the control of the aeration system in the WWTP of Girona (Spain) show its effectiveness. [ABSTRACT FROM AUTHOR]

Advanced process control can benefit to the operation efficiency and quality of tablets produced by wet granulation lines. Following the development of a new fully continuous fluidized bed reactor as a potential substitute for the current batch dryer design, this paper examines the energy and product quality performances of two predictive control strategies using an experimentally validated simulator. The first one proposes an economic model predictive controller explicitly minimizing the dryer energy consumption. The second one follows the same objective, but uses a simpler classical predictive control framework implementing targets on manipulated variables to drive them toward low energy consumption operating points. Both controllers lead to similar performances, and consume about 20% less energy than a reference feedback scheme without manipulated variable setpoints. Results also show that tracking the product quality attribute significantly benefits from a feedforward action because of the long residence time. This article addresses a subject little explored by the literature, the control of continuous fluidized bed dryers, and clearly demonstrates that a standard linear strategy can reduce the operating costs with an appropriate design. • Predictive control is applied on a simulated continuous fluidized bed dryer. • An economic model predictive controller (EMPC) minimizes the energy consumption. • A more standard predictive controller (MPC) also aims for low-energy actions. • Both EMPC and MPC results in low-energy operations. • Feedforward compensation improves the product quality in both cases. [ABSTRACT FROM AUTHOR]

In this paper, the tuning of economic model predictive control (EMPC) applied to drinking water transport networks (DWTNs) is addressed using multi-objective optimization approaches. The tuning strategies are based on Pareto front calculations of the underlying multi-objective problem. This feature represents an improvement with respect to the standard EMPC approach for weight tuning based on trial and error. Different multi-objective optimization methods with corresponding normalization approaches of the controller objectives are first studied to explore the dynamic nature of the Pareto fronts. An automated decision-making strategy is proposed to select the preferred controller parameters as a function of different disturbance values. The tuning requires an offline training phase and an online application phase. During the offline phase, the controller parameters are selected for different disturbances using the decision-making strategy. During the online phase, two approaches are evaluated: (i) exploiting the controller parameters with the highest frequency in the resulting histogram or (ii) using a regression model between the controller parameters and the disturbances. The proposed tuning strategies are applied to a real-life simulation case study based on the Barcelona DWTN. The simulation results show that the proposed tuning strategies outperform the baseline results by exploiting the periodicity of the water demands profile. [ABSTRACT FROM AUTHOR]

[Display omitted] • An economic model predictive control is applied to a fluid catalytic cracking unit. • The plant-model mismatch of the riser is addressed by the modifier adaptation. • Multi-model controllers are constructed to guarantee the stability. • A fluid catalytic cracking simulation is utilized to demonstrate the efficiency. The fluid catalytic cracking (FCC) unit is a typical multi-timescale system. Its operational performance will make a significant difference in the overall economic benefits of the oil refining factory. Classical model-based optimization approaches may not always be completely satisfied due to unmeasurable disturbances and model-plant structure mismatch. A distributed economic MPC with pseudo-steady state modifier adaptation (DEMPC-MA) is proposed to cope with the difficulties. The strategy divides the plant into two parts, i.e., the slow dynamic part and pseudo-steady state part. The output modifier adaption is adopted to modify the model function according to the pseudo-steady state characteristics of the riser. Lyapunov stable constraints are added to the EMPC problem to guarantee a safe operation, while the feasibility of the algorithm is ensured by a set of auxiliary controllers, which are constructed offline based on the multi-model approach. The overall control optimization problem is solved in a distributed formulation through the alternating direction method of multipliers (ADMM) to improve the calculation performance. The proposed algorithm was applied to an industrial FCC unit model based on a refinery factory in Jiujiang, China. The results showed that the method obtained better economic benefits and finally reached the optimal steady-state operating point even if the model structure and parameter of the prediction model were mismatched. [ABSTRACT FROM AUTHOR]

This paper proposes a stabilizing distributed gradient-based economic MPC strategy for cooperative control of constrained linear systems. This strategy is based on quadratic programming to limit the computational cost, and one key feature is the evaluation of an economically optimal steady-state directly in the control law, leading the closed-loop system towards it. The control law includes three ingredients to enlarge its domain of attraction and potentially avoid feasibility problems, namely: artificial steady-state, slack variables, and terminal equality constraints solely on non-stable states. A four-tank system is used to address the properties of the formulation, especially its stability in the nominal case, the capacity to track the desired target for a nonlinear performance economic function, and tackle unmeasured and persistent unmeasured disturbances. • Quadratic programming-oriented distributed economic MPC. • Improved feasibility of the MPC control law through slacked terminal constraints. • Enlargement of the domain of attraction through slacked terminal constraints. • Economically optimal steady-state computed directly in the control law. [ABSTRACT FROM AUTHOR]

The controllers for a cyber-physical system may be impacted by sensor measurement cyberattacks, actuator signal cyberattacks, or both types of attacks. Prior work in our group has developed a theory for handling cyberattacks on process sensors. However, sensor and actuator cyberattacks have a different character from one another. Specifically, sensor measurement attacks prevent proper inputs from being applied to the process by manipulating the measurements that the controller receives, so that the control law plays a role in the impact of a given sensor measurement cyberattack on a process. In contrast, actuator signal attacks prevent proper inputs from being applied to a process by bypassing the control law to cause the actuators to apply undesirable control actions. Despite these differences, this manuscript shows that we can extend and combine strategies for handling sensor cyberattacks from our prior work to handle attacks on actuators and to handle cases where sensor and actuator attacks occur at the same time. These strategies for cyberattack-handling and detection are based on the Lyapunov-based economic model predictive control (LEMPC) and nonlinear systems theory. We first review our prior work on sensor measurement cyberattacks, providing several new insights regarding the methods. We then discuss how those methods can be extended to handle attacks on actuator signals and then how the strategies for handling sensor and actuator attacks individually can be combined to produce a strategy that is able to guarantee safety when attacks are not detected, even if both types of attacks are occurring at once. We also demonstrate that the other combinations of the sensor and actuator attack-handling strategies cannot achieve this same effect. Subsequently, we provide a mathematical characterization of the “discoverability” of cyberattacks that enables us to consider the various strategies for cyberattack detection presented in a more general context. We conclude by presenting a reactor example that showcases the aspects of designing LEMPC.

The reliable control of the large-scale wind farm is crucial for the stability and security of the renewable power system with high wind power penetration. Due to the uncertain and variable nature of wind power, the traditional control strategy is difficult to work. Regarding the large-scale, geographically dispersed wind farm, an efficient distributed economic model predictive control strategy is proposed, which integrates the power tracking and economic optimization of the wind farm into one optimal control framework. By adopting the global economic cost function, the Nash optimal solutions under distributed framework approach the Pareto optimum. Thus, the reference power from the transmission system operator is accurately tracked, while the global dynamic economic optimality is guaranteed. The simulation results under step wind speed and practical wind speed variations verify the efficiency and reliability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Economic model predictive control in microgrids combined with dynamic pricing of grid electricity is a promising technique to make the power system more flexible. However, to date, each individual microgrid requires major efforts for the mathematical modelling, the implementation on embedded devices, and the qualification of the control. In this work, a field-suitable generalised linear microgrid model is presented. This scalable model is instantiated on field-typical hardware and in a modular way, so that a class of various microgrids can be easily controlled. This significantly reduces the modelling effort during commissioning, decreases the necessary qualification of commissioning staff, and allows for the easy integration of additional microgrid devices during operation. An exemplary model, derived from an existing production facility microgrid, is instantiated, and the characteristics of the results are analysed. [ABSTRACT FROM AUTHOR]

In this paper performance indices for economic model predictive controllers (MPC) are considered. Since existing relative performance measures, designed for stabilizing controllers, fail in the economic setting, we propose alternative absolute quantities. We show that these can be applied to assess the performance of the closed loop trajectories on-line while the controller is running. The advantages of our approach are demonstrated by simulations involving a convection-diffusion-system. The method is also combined with proper orthogonal decomposition, thus demonstrating the possibility for both efficient and performant MPC for systems governed by partial differential equations. [ABSTRACT FROM AUTHOR]

Used water treatment plays a pivotal role in advancing environmental sustainability. Economic model predictive control holds the promise of enhancing the overall operational performance of the water treatment facilities. In this study, we propose a data-driven economic predictive control approach within the Koopman modeling framework. First, we propose a deep learning-enabled input–output Koopman modeling approach, which predicts the overall economic operational cost of the wastewater treatment process based on input data and available output measurements that are directly linked to the operational costs. Subsequently, by leveraging this learned input–output Koopman model, a convex economic predictive control scheme is developed. The resulting predictive control problem can be efficiently solved by leveraging quadratic programming solvers, and complex non-convex optimization problems are bypassed. The proposed method is applied to a benchmark wastewater treatment process. The proposed method significantly improves the overall economic operational performance of the water treatment process. Additionally, the computational efficiency of the proposed method is significantly enhanced as compared to benchmark control solutions. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of different control strategies to solve the gas-lift optimization (GLO) problem of offshore rigs. GLO consists of distributing the compressed gas between the wells to maximize oil production, considering several operational and process aspects such as the cost of flaring, price fluctuations, measurable noise, external disturbances, and plant-model mismatches. We compare and evaluate the performance of economic nonlinear model predictive control (ENMPC), Modifier-based EMPC (EMPC-Mod), EMPC with Local Linearization on Trajectory (EMPC-LLT), the static Real-Time Optimizer with Parameter Adaptation (ROPA), and the Active Constraint Control (ACC) based on feedback controllers. The study points out the advantages and drawbacks of each approach being useful for engineers to choose the most appropriate strategy. Moreover, the results show that the linear EMPCs and ROPA have similar performance to the theoretical optimal while maintaining minimal computational burden, and also that ACC is satisfactory for this case study. • Comparison of economic model predictive controllers (EMPC) for gas-lift optimization. • Deep evaluation including accuracy of solutions, computational costs, and simplicity. • Presentation of advantages and drawbacks of each strategy, useful for practitioners. • Formulation of an economic recipe based on local linearization on trajectory model. • MPCs tested in realistic scenarios with disturbances, noise, and modeling errors. [ABSTRACT FROM AUTHOR]

We consider the problem of dynamic regulation with an economic cost function to control unknown linear systems, in which improving the economic performance and guaranteeing the stability of economical optimal equilibrium point are control objectives. A data-driven economic MPC scheme is presented using measured input-output trajectories without a prior system identification step. Our method uses Hankel matrices which include one input-output data trajectory for prediction in economic MPC, while persistently exciting of the input generating the data is needed. One of the novelties of the presented framework is directly verifying the strong duality property from input-output trajectory with the general cost function, considered as the supply rate. This is used to find a Lyapunov function for data-driven economic MPC. Under the strong duality assumption, asymptotic stability of the economical optimal equilibrium point for the closed-loop system with terminal equality constraint is guaranteed. The proposed data-driven economic MPC approach needs only persistently exciting data trajectory along with an upper bound on the system order and need no model description and no online parameter estimation. The proposed scheme applicability compared to the existing model-based economic MPC and data-driven MPC is illustrated for continuous stirred tank reactor (CSTR) and a numerical example and the robustness of the proposed scheme is evaluated in the case of measurement noise, as well as nonlinear model for CSTR system. • Proposing a data-driven EMPC for unknown linear time-invariant (LTI) systems. • Using past measured data for the prediction and obtaining the optimal equilibrium. • Presenting a novel approach to verify the data-driven strong duality in data-driven. • Guaranteeing closed-loop asymptotic stability of the economical optimal equilibrium. • Illustrating the proposed data-driven EMPC applicability by CSTR example. [ABSTRACT FROM AUTHOR]

Smart home scheduling, facilitated by advanced metering, monitoring, and manipulation technology, plays an important role in the energy transition in terms of accommodating intermittent renewable energy and improving energy consumption efficiency. The key functionalities of home energy scheduling are usually implemented by leveraging the flexibility of household appliances, such as thermostatically controlled loads (TCLs) and energy storage units, to improve the peak-to-average ratio for utilities and reduce energy bills for customers. However, the consumption patterns of appliances are greatly influenced by a variety of factors, including real-time tariffs, ambient temperature profiles, indoor activities, and solar irradiance. Hence, smart home energy scheduling is a challenging task because most of these impacting factors are stochastic and difficult to predict. To properly model and manage the uncertainty factors associated with smart home appliance scheduling, an economic model predictive control (MPC)-based bilevel smart scheduling scheme is proposed in this paper. The comprehensive modeling of distributed generation and household appliances is performed at the single-household level. The home energy scheduling problem is formulated on two levels, with the upper level emphasizing the economic impact and the lower level focusing on capturing TCL responses. The correlations among different TCLs and their performance under the influence of various uncertainty factors, such as environmental impacts and user behaviors, are considered. The efficiency of the proposed MPC-based bilevel optimization model and the effectiveness of the home energy scheduling strategy in managing uncertainties are validated and illustrated in numerical studies.

Control of wet limestone flue gas desulfurisation (WFGD) system is critical for pollution reduction of the coal-fired power plant. To fulfill the environmental requirements with the least cost, economic model predictive control (EMPC) is utilized in this paper to tackle the difficulties of WFGD, such as nonlinearity, couplings and trade-off between efficiency and safety. First, a comprehensive first-principle model is developed to describe the overall nonlinear characteristics of WFGD, with special considerations on Gas-to-liquid contact zone and slurry pool module. Second, four objectives are formulated to evaluate the economic criterion from different perspectives, including cost, safety, control efforts and performance. Utopia strategy, combined with NSGA-II, is used to solve the EMPC problem and obtain the Pareto front of the multi-objective optimization. Simulation results show that the proposed strategy is able to efficiently ensure the emission requirement and reduce the economic cost simultaneously, regardless of load disturbance, adjustment of emission lower limit and fluctuation of limestone market price. [ABSTRACT FROM AUTHOR]

In this article, a robust distributed economic model predictive control (DEMPC) approach is developed for plant‐wide chemical processes. The proposed approach achieves arbitrary feasible setpoints that may vary frequently, attenuates the plant‐wide effects of unknown disturbances and minimizes a plant‐wide economic cost. In this approach, a plant‐wide process is represented as a network of process units and each process unit is controlled by an individual controller which shares a plant‐wide optimization economic objective and stability conditions through the network. To ensure the convergence of process variables to arbitrary setpoints, a contraction condition is developed for the DEMPC, based on the contraction theory. To deal with the effects of interactions among process units, the concept of dissipativity is adopted. Using sum‐separable control contraction metrics, a reference‐independent robust stability condition is developed to ensure the plant‐wide disturbance effects (under interactions among process units) to be attenuated in terms of differential ℒ2 gain and represented by a plant‐wide differential dissipativity condition, which is converted into the differential dissipativity conditions that individual controllers need to satisfy. This approach facilitates the optimization of plant‐wide economic costs with global constraints in a distributed way, allowing efficient implementation of alternating direction method of multipliers (ADMM). The proposed approach is illustrated using a reactor‐separator process. [ABSTRACT FROM AUTHOR]