Model Predictive Control Optimization Problem Research Articles

Robust security‐based model predictive control for nonlinear cyber‐physical system under random occurring deception attacks and actuator saturation

AbstractThis article presents a robust security‐based model predictive control (MPC) framework for a class of discrete‐time nonlinear cyber‐physical systems (CPSs) suffering random deception attacks and persistent actuator saturation. In CPSs, the attacks can significantly degrade the control performance. Naturally, a larger degree of control is required, prompting the consideration of actuator saturation in CPS's structure. In our work, the cyberattacks on the controller‐actuator (C‐A) channel are described as a stochastic process with specific probability and bounded energy. The security‐related constraint is introduced to improve the resistance and robustness against attacks. Mean‐square quadratic boundedness is derived to estimate the robustly invariant set. By placing the saturated input into a convex hull, a robust security‐based MPC optimization problem is addressed less conservatively with linear matrix inequality technique. Furthermore, the feasibility of the proposed method is proved recursively, and the stability and security of the closed‐loop system are established in mean‐square sense. In the end, the laboratory tank and reactor‐separator process are applied to validate the effectiveness of the proposed algorithm.

Analysis of Model Predictive Control-Based Energy Management System Performance to Enhance Energy Transmission

A supervisory control system using Model Predictive Control (MPC) has been designed to evaluate the efficiency of wind and solar power and is consistent with the cost function in the supervisory MPC optimization problem. A two-layer Economic Model Predictive Control (EMPC) framework has been developed and has improved results such as cost reductions compared to recent advanced methods. A speed Generalized Predictive Control (GPC) scheme intended for wind energy conversion systems was developed last year, with simulation results indicating superior performance over previous models. A Hierarchical Distributed Model Predictive Control (HDMPC) can work under different weather conditions with improved economic performance and keep a good balance between power delivery and load demand. An energy management system (EMS), built on the basis of MPC, can be quite lucrative for the sphere in the present climate scenario, with the selection and testing of suitable algorithms, controlled processes, cost functions, and a set of constraints as well as with proper optimizations carried out. Previous research indicates that an MPC-based EMS has the potential to be a good solution to manage energy well and also introduced it to the world experimentally. The key intention of this research study is to explore the existing advances that have been introduced and to analyze their performance in terms of cost function, different sets of constraints, variant conversion processes, and scalability to achieve more optimized operation of MPC-based EMS.

An improved state space model predictive control for linear systems with input disturbance

This paper presents an improved model predictive control (MPC) algorithm for linear systems with input disturbance. Based on the developed extended non-minimum state space input disturbance (ENMSS-ID) model, the input disturbance model structure is incorporated into the MPC framework and the objective function of the MPC optimization problem is improved to weigh the system output increments. This enables the algorithm simultaneously to achieve good input disturbance rejection performance for systems with known input disturbances and reduce the controllers’ sensitivity to model mismatch. An existing optimal estimation method is introduced to estimate the input disturbance, together with the proposed strategy to improve estimation convergence. Offset-free property is also proven to show the steady-state performance of the designed control scheme. Finally, two benchmark plants are studied to illustrate the effectiveness and advantages of the proposed algorithm.

A metaheuristic algorithm for model predictive control of the oil-cooled motor in hybrid electric vehicles

The current energy management methods for hybrid vehicles are primarily focused on matching the power flow between the engine and the motor. In order to further reduce overall energy consumption and extend the vehicle's lifespan, this paper utilizes model predictive control (MPC) in the energy management of hybrid vehicles to control the energy consumption and temperature of the oil-cooled motor, with a focus on studying the algorithm for solving the optimization problem in MPC. The main work includes: Establishing a simplified model for the oil-cooled motor and training the working condition prediction model based on the worldwide harmonized light vehicles test cycle (WLTC) conditions utilizing long short-term memory (LSTM) recurrent neural network technology. Furthermore, proposing a novel metaheuristic algorithm based on the temporal nature of the problem, multiple hierarchical clustering algorithm (MHCA). In comparison with typical metaheuristic algorithms, the MPC optimized using MHCA exhibits significantly reduced computation time, with an average time of 0.1967s, indicating that using MHCA can theoretically achieve real-time control and eliminate lag in actual control processes. Furthermore, compared to other optimization algorithms, the MHCA algorithm demonstrates the lowest correlation between computation time and operational conditions, highlighting its high robustness in ensuring the safety of practical control.

Controller Design for Air Conditioner of a Vehicle with Three Control Inputs Using Model Predictive Control

Fuel consumption optimization is a critical field of research within the automotive industry to meet consumer expectations and regulatory requirements. A reduction in fuel consumption can be achieved by reducing the energy consumed by the vehicle. Several subsystems contribute to the overall energy consumption of the vehicle, including the air conditioning (A/C) system. The loads within the A/C system are mainly contributed by the compressor, condenser fan, and underhood aerodynamic drag, which are the components targeted for overall vehicle energy use reduction in this paper. This paper explores a new avenue for A/C system control by considering the power consumption due to vehicle drag (regulated by the condenser fan and active grille shutters (AGS)) to reduce the energy consumption of the A/C system and improve the overall vehicle fuel economy. The control approach used in this paper is model predictive control (MPC). The controller is designed in Simulink, where the compressor clutch signal, condenser fan speed, and AGS open-fraction are inputs. The controller is connected to a high-fidelity vehicle model in Gamma Technologies (GT)-Suite (which is treated as the real physical vehicle) to form a software-in-the-loop simulation environment, where the controller sends actuator inputs to GT-Suite and the vehicle response is sent back to the controller in Simulink. Quadratic programming is used to solve the MPC optimization problem and determine the optimal input trajectory at each time step. The results indicate that using MPC to control the compressor clutch, condenser fan, and AGS can provide a 37.6% reduction in the overall A/C system energy consumption and a 32.7% reduction in the error for the air temperature reference tracking compared to the conventional baseline proportional integral derivative control present in the GT-Suite model.

Model Predictive Control for Energy Optimization of HVAC Systems Using EnergyPlus and ACO Algorithm

The deployment of model-predictive control (MPC) for a building’s energy system is a challenging task due to high computational and modeling costs. In this study, an MPC controller based on EnergyPlus and MATLAB is developed, and its performance is evaluated through a case study in terms of energy savings, optimality of solutions, and computational time. The MPC determines the optimal setpoint trajectories of supply air temperature and chilled water temperature in a simulated office building. A comparison between MPC and rule-based control (RBC) strategies for three test days showed that the MPC achieved 49.7% daily peak load reduction and 17.6% building energy savings, which were doubled compared to RBC. The MPC optimization problem was solved multiple times using the Ant Colony Optimization (ACO) algorithm with different starting points. Results showed that ACO consistently delivered high-quality optimized control sequences, yielding less than a 1% difference in energy savings between the worst and best solutions across all three test days. Moreover, the computational time for solving the MPC problem and obtaining nearly optimal control sequences for a three-hour prediction horizon was observed to be around 22 min. Notably, reasonably good solutions were attained within 15 min by the ACO algorithm.

Model predictive control of heating in a low energy single-family house

This paper presents a control scheme that uses a Model Predictive Control (MPC) approach to manage the heating system of a low-energy single-family house. The house is equipped with an air-to-water Heat Pump (HP) and individually controlled hydronic underfloor heating circuits for each of its 11 heating zones. The MPC scheme is designed to maintain individual room comfort levels in each zone, while incorporating weather forecasts and following a heating reference to allow for load shifting for periods with low energy prices and high Photovoltaic (PV) production calculated by an upper level in a hierarchical control scheme. The focus of the design has been the model structure that allows for fast solutions to the MPC optimisation problem, while still capturing the high complexity, non-linear dynamics of the building. The controller is tested on a high-fidelity simulation model of the house, achieving disturbance rejection and system stabilisation. The rapid solving time makes repeated experiments and longer simulations feasible.

Parameter identification and model prediction path following control of underactuated AUV: Methodology and experimental verification

This paper explores the integrated optimal control scheme from the identification of underactuated autonomous underwater vehicle (AUV) system dynamics model parameters to the application of Model Predictive Control (MPC) technology in underactuated AUV motion control, and presents the simulation and field test results. First, the AUV kinematics and dynamics models are introduced to represent the horizontal plane motion characteristics. Based on Computational Fluid Dynamics (CFD) numerical simulation and overset mesh technology, AUV plane motion is simulated to determine the unknown hydrodynamic coefficients in the model, and the accuracy of the mathematical model is validated by comparing the maneuverability simulation and field test results. After that, an adaptive line-of-sight (ALOS) guiding algorithm with exponentially variable forward distance is utilized in the guidance layer to reconcile the rapidity and stability of tracking. The path following problem is formulated as an MPC optimization problem that takes into account multiple realistic constraints and then converted into a standard convex quadratic programming structure, permitting for online real-time optimization. Simulation and field test results indicate that the control algorithm proposed in this paper provides a more effective control strategy than the traditional LOS+PID controller in tracking effect and robustness.

PDE‐constrained model predictive control of open‐channel systems

AbstractA PDE‐constrained model predictive control (MPC) algorithm for open‐channel systems based on the Saint‐Vevant(S‐V) equations is investigated in this paper. The S‐V equations, which precisely model the dynamics of open‐channel systems, are quasi‐linear hyperbolic partial differential equations (PDEs) without analytical solutions. Directly applying the S‐V equations to an MPC controller design becomes sophisticated. In this work, the calculus of variation is used to obtain the adjoint equations and the adjoint analysis method is utilized to deduce the gradients of the MPC optimization problem. Particularly, the physical constraints involving both the state and control variables are also considered. A gradient‐based optimization algorithm in combination with the numerical computation of Preissmann implicit scheme is proposed to solve the constrained MPC optimization problem. The control performances of the developed PDE‐constrained MPC algorithm with respect to the controlled water levels and gate openings are compared with those of the MPC controller designed for the linearized model. All the simulation tests are carried out on an aqueduct reach in Yehe Irrigation District in Hebei Province, China. The results show that the proposed PDE‐constrained MPC algorithm is a promising method in dealing with the constraints in terms of hyperbolic PDEs, control variables and state variables simultaneously.

A novel bi-level temporally-distributed MPC approach: An application to green urban mobility

Model predictive control (MPC) has been widely used for traffic management, such as for minimizing the total time spent or the total emissions of vehicles. When long-term green urban mobility is considered including e.g. a constraint on the total yearly emissions, the optimization horizon of the MPC problem is significantly larger than the control sampling time, and thus the number of the variables that should be optimized per control time step becomes very large. For systems with dynamics that involve nonlinear, non-convex, and non-smooth functions, including urban traffic networks, this results in optimization problems that are computationally intractable in real time. In this paper, we propose a novel bi-level temporal distribution of such complex MPC optimization problems, and we develop two mathematically linked short-term and long-term MPC formulations with small and large control sampling times that will be solved together instead of the original complex optimization problem. The resulting bi-level control architecture is used to solve the two MPC formulations online for real-time control of urban traffic networks with the objective of long-term green mobility. In order to assess the performance of the bi-level control architecture, we perform a case study where a rough version of the model of the urban traffic flow, S-model, is used by the long-term MPC level to estimate the states of the urban traffic networks, and a detailed version of the model is used by the short-term MPC level. The results of the simulations prove the effectiveness (with respect to the objective of control, as well as computational efficiency) of the proposed bi-level MPC approach, compared to state-of-the-art control approaches.

Standoff Tracking Using DNN-Based MPC With Implementation on FPGA

This work studies the standoff tracking problem to drive an unmanned aerial vehicle (UAV) to slide on a desired circle over a moving target at a constant height. We propose a novel Lyapunov guidance vector (LGV) field with tunable convergence rates for the UAV’s trajectory planning and a deep neural network (DNN)-based model predictive control (MPC) scheme to track the reference trajectory. Then, we show how to collect samples for training the DNN offline and design an integral module (IM) to refine the tracking performance of our DNN-based MPC. Moreover, the hardware-in-the-loop (HIL) simulation with a field-programmable gate array (FPGA) at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$200$</tex-math> </inline-formula> MHz demonstrates that our method is a valid alternative to embedded implementations of MPC for addressing complex systems and applications which is impossible for directly solving the MPC optimization problems.

Data-Driven FMPC Based Dynamic Coordination Control Strategy for Power-Split Hybrid Electric Bus

Since no engine clutch exists in the power-split system of the hybrid electric bus, the torque variations of the power sources (i.e., the engine, motor, and generator) are easy to cause system shock during mode switching. To yield a better control effect, the model predictive control (MPC) based dynamic coordination control strategy (DCCS) is considered as an effective solution to guarantee the drivability and reliability of the system. However, the existing MPC-based DCCS still have the challenge of model accuracy and computational complexity. Therefore, to solve the problem, a data-driven Fast-MPC(FMPC) based DCCS is proposed for a power-split hybrid electric bus in this paper. Firstly, to ensure the accuracy of the engine dynamic model, a piecewise data fitting method is proposed by analyzing the historical data of the engine. Then, considering the high dimension of the control model (based on the dynamics model of the power-split system), a fast solving method for the quadratic optimization problem of MPC is proposed with respect to the proper assumption and simplification. Finally, to verify the effectiveness of the proposed control strategy, offline simulation and hardware-in-the-loop (HIL) simulation experiments are carried out. Simulation results show that good driving comfort and real-time performance have been achieved. This research is expected to promote the application of MPC in the DCCS and further improve the dynamic performance of the power-split system.

Event‐triggered model predictive control of switched systems with denial‐of‐service attacks

AbstractObserver‐based model predictive control (MPC) for the discrete‐time switched systems suffered by event‐triggered mechanism and denial‐of‐service (DoS) attacks is discussed in this paper. We assume that the switch is slow enough and the attacker's energy is limited. To save network resources, an event‐triggered mechanism is designed based on dwell time and triggered error. Under the coupled influence of attack and trigger, a complex mismatch of system mode and controller mode occurs, which brings difficulties to the transformation of MPC optimization problem. To address this problem, a new performance index coefficient is designed by using the increasing/decreasing law of Lyapunov function. On this basis, the transformation of the optimization problem is realized. Then, the controller gain and observer gain for the attack‐free case are designed to guarantee the exponential convergence of the closed‐loop system. In the presence of attacks, we obtain the upper bound of attack duty cycle, below which the exponential convergence of the system can still be archived. An example is illustrated at last to verify the validity of the main results.

An Explicit Dual Control Approach for Constrained Reference Tracking of Uncertain Linear Systems

A finite horizon optimal tracking problem is considered for linear dynamical systems subject to parametric uncertainties in the state-space matrices and exogenous disturbances. A suboptimal solution is proposed using a model predictive control (MPC) based explicit dual control approach which enables active uncertainty learning. A novel algorithm for the design of robustly invariant online terminal sets and terminal controllers is presented. Set membership identification is used to update the parameter uncertainty online. A predicted worst-case cost is used in the MPC optimization problem to model the dual effect of the control input. The cost-to-go is estimated using contractivity of the proposed terminal set and the remaining time horizon, so that the optimizer can estimate future benefits of exploration. The proposed dual control algorithm ensures robust constraint satisfaction and recursive feasibility, and navigates the exploration-exploitation trade-off using a robust performance metric.

Grey-box model and neural network disturbance predictor identification for economic MPC in building energy systems

This paper presents a novel model identification procedure to treat the occupancy induced unmeasured heat disturbance in the building model identification step for a model predictive control (MPC) implementation. First, we present a grey-box identification framework to estimate a dynamic building model that systematically accounts for the large unmeasured disturbance in the training data. Then, we discuss an approach to compute the confidence intervals (CIs) on the parameters estimated in the building model. Next, we develop a framework to identify a neural network (NN) using historical operational data to give the feedforward predictions of the heat disturbance in the MPC optimization problem. Further, we discuss the application of the composite building model and the NN disturbance predictor for energy cost optimization using an economic MPC formulation. We present case studies using a simple two time scale based building model, and demonstrate the effectiveness of the proposed grey-box model and the NN disturbance predictor identification procedures. We perform closed-loop simulations to highlight that additional energy cost savings of up to 4–5% are provided by including the feedforward NN disturbance predictions in the MPC controller. Finally, we also demonstrate the suitability of the proposed two-step model identification procedure to estimate accurate and reliable models using an industrial data set collected from a real office building.

Modeling and Efficient Passenger-Oriented Control for Urban Rail Transit Networks

Real-time timetable scheduling is an effective way to improve passenger satisfaction and to reduce operational costs in urban rail transit networks. In this paper, a novel passenger-oriented network model is developed for real-time timetable scheduling that can model time-dependent passenger origin-destination demands with consideration of a balanced trade-off between model accuracy and computation speed. Then, a model predictive control (MPC) approach is proposed for the timetable scheduling problem based on the developed model. The resulting MPC optimization problem is a nonlinear non-convex problem. In this context, the online computational complexity becomes the main issue for the real-time feasibility of MPC. To reduce the online computational complexity, the MPC optimization problem is therefore reformulated into a mixed-integer linear programming (MILP) problem. The resulting MILP problem is exactly equivalent to the original MPC optimization problem and can be solved very efficiently by existing MILP solvers, so that we can obtain the solution very fast and realize real-time timetable scheduling. Numerical experiments based on a part of Beijing subway network show the effectiveness and efficiency of the developed model and the MILP-based MPC method.

Distributed Economic MPC for Dynamically Coupled Linear Systems: A Lyapunov-Based Approach

This article develops a distributed economic model predictive control (EMPC) method which is applied in a group of interconnected linear subsystems subject to unknown bounded disturbances. Multiple subsystems are coupled through the dynamics, and the control objective is to optimize some general performance criteria of the whole system which may take economic considerations into account. First, a two operation modes EMPC optimization problem is formulated, which incorporates the constraints derived from the Lyapunov technique. In the first mode, each subsystem focuses on the optimization of the economic performance while maintaining the state in a certain region. In the second mode, the system states are steered to a neighborhood of a steady state by making use of the Lyapunov-based constraints. Furthermore, a consensus alternating direction method of multipliers (ADMM) is adopted to solve the model predictive control optimization problems with a coupled predicted model constraint in a distributed way. By introducing consensus constraints, the resulting local optimization problem does not depend on real-time optimal solutions from neighboring subsystems and allows subsystems to solve it in parallel. Moreover, the closed-loop system is ensured to be input-to-state stable (ISS) with respect to the disturbances. To demonstrate the effectiveness of the algorithm, we conduct numerical simulations on a thermal power interconnected system.

Distributed Model Predictive Control for Heterogeneous Vehicle Platoon With Inter-Vehicular Spacing Constraints

This paper proposes a distributed control scheme for a platoon of heterogeneous vehicles based on the mechanism of model predictive control (MPC). The platoon composes of a group of vehicles interacting with each other via inter-vehicular spacing constraints, to avoid collision and reduce communication latency, and aims to make multiple vehicles driving on the same lane safely with a close range and the same velocity. Each vehicle is subject to both state constraints and input constraints, communicates only with neighboring vehicles, and may not know a priori desired setpoint. We divide the computation of control inputs into several local optimization problems based on each vehicle’s local information. To compute the control input of each vehicle based on local information, a distributed computing method must be adopted and thus the coupled constraint is required to be decoupled. This is achieved by introducing the reference state trajectories from neighboring vehicles for each vehicle and by employing the interactive structure of computing local problems of vehicles with odd indices and even indices. It is shown that the feasibility of MPC optimization problems is achieved at all time steps based on tailored terminal inequality constraints, and the asymptotic stability of each vehicle to the desired trajectory is guaranteed even under a single iteration between vehicles at each time. Finally, a comparison simulation is conducted to demonstrate the effectiveness of the proposed distributed MPC method for heterogeneous vehicle control with respect to normal and extreme scenarios.

Distributed model predictive control for reconfigurable systems based on Lyapunov analysis

This paper focuses on Distributed Model Predictive Control (DMPC) for systems composed of many interacting subsystems, in the case that process topology changes, e.g., the isolation of a part of subsystems due to system maintenance, or processing change due to production change. The reconfiguration of the process may cause the Model Predictive Control (MPC) optimization problem infeasible for the updated system. The proposed DMPC is based on Lyapunov techniques. After discussing the reasons causing infeasibility of the reconfigured system (violation of constraints), a transition optimization problem of each subsystem-based MPC is designed for the case that the topology change cannot be conducted immediately, which focuses on steering the states that will remain in the updated system into the region that makes the updated system feasible. Besides, to enlarge the attraction region of each subsystem-based MPC, an auxiliary variable is added to the optimization problem as a decision variable. The auxiliary variable is a steady state and the MPC lets the state track this auxiliary variable. The distance between the auxiliary variable and the set-point is also minimized in each subsystem-based optimization problem. The Lyapunov constraints which consider the auxiliary variable are designed to guarantee that the state converges to a small region around the set-point. The stability analysis and an application to a chemical process example are presented to show the effectiveness of the proposed method.

Grammatical-Evolution-based parameterized Model Predictive Control for urban traffic networks

While Model Predictive Control (MPC) is a promising approach for network-wide control of urban traffic, the computational complexity of the, often nonlinear, online optimization procedure is too high for real-time implementations. In order to make MPC computationally efficient, this paper introduces a parameterized MPC (PMPC) approach for urban traffic networks that uses Grammatical Evolution to construct continuous parameterized control laws using an effective simulation-based training framework. Furthermore, a projection-based method is proposed to remove the nonlinear constraints that are imposed on the parameters of the parameterized control laws and to guarantee the feasibility of the solution of the MPC optimization problem. The performance and computational efficiency of the constructed parameterized control laws are compared to those of a conventional MPC controller in an extensive simulation-based case study. The results show that the parameterized control laws, which are automatically constructed using Grammatical Evolution, decrease the computational complexity of the online optimization problem by more than 80% with a decrease in performance by less than 10%.