Model Predictive Control Design Research Articles

A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees

ABSTRACT This paper presents a learning- and scenario-based model predictive control (MPC) design approach for systems modelled in the linear parameter-varying (LPV) framework. Using input-output data collected from the system, a state-space LPV model with uncertainty quantification is first learned through the variational Bayesian inference Neural Network (BNN) approach. The learned probabilistic model is assumed to contain the true dynamics of the system with a high probability and is used to generate scenarios that ensure safety for a scenario-based MPC. Moreover, to guarantee stability and enhance the performance of the closed-loop system, a parameter-dependent terminal cost and controller, as well as a terminal robust positive invariant set are designed. Numerical examples will be used to demonstrate that the proposed control design approach can ensure safety and achieve desired control performance.

Correction to “Enhancing topological information of the Lyapunov‐based distributed model predictive control design for large‐scale nonlinear systems”

Correction to “Enhancing topological information of the Lyapunov‐based distributed model predictive control design for large‐scale nonlinear systems”

Hierarchical Predictive Control of an Unmanned Aerial Vehicle Integrated Power, Propulsion, and Thermal Management System

Increasing electrification of air vehicles presents challenges to the energy management of their coupled electric power, propulsion, and thermal systems. Notably, the complexity and multi-timescale nature of this class of systems make it difficult to design control algorithms that can simultaneously optimize dynamics across each energy domain. The unique contribution of this work is the design and experimental validation of a hierarchical model predictive controller that coordinates the electro-mechano-thermal dynamics of an unmanned aerial vehicle (UAV) integrated power, propulsion, and thermal management system. To support this contribution, a novel UAV energy system testbed is introduced. A graph-based framework is used to model the multi-domain dynamics of the UAV. To estimate the states of the experimental platform, a decentralized observer is described. When compared to a baseline approach, the hierarchical control strategy results in a higher performing and more reliable closed-loop system while decreasing fuel utilization by approximately 16%.

A Fast Model Predictive Control Framework for Multi-Float and Multi-Mode-Motion Wave Energy Converters

Recently, multi-float and multi-mode-motion wave energy converters (M-WECs) have been developed to improve energy conversion capability. Although model predictive control (MPC) can be very effective to solve the constrained energy maximization control problem of point absorber WECs, the increased complexity of the M-WEC hydrodynamics can bring significant challenges due to computational demand. This brief proposes a novel computational-efficient fast MPC (FMPC) design method for the M-WECs requiring complex linear hydrodynamic models. The controller design objective is to maximize the energy conversion with some available wave forecasting information and to satisfy state and control input constraints to ensure safe operation. The main advantage of the proposed FMPC is the reduced computational burden with a negligible impact on performance. A demonstrative numerical simulation based on a 1:50 laboratory-scale M-WEC design, M4, for which linear hydrodynamics has been verified experimentally, is presented to verify the efficacy of the proposed control method in terms of both computational load and energy output.

Thermal comfort-conscious eco-climate control for electric vehicles using model predictive control

In the heating, ventilation, and air-conditioning (HVAC) system of electric vehicles (EVs), an electric heater is often used for a reheating process that warms up the chilled evaporator outlet air for thermal comfort before it is supplied to the cabin. The usage of the electric heater can significantly reduce the driving range of an EV. Therefore, optimal control of the HVAC system with consideration of the reheating process becomes essential for an increased driving range. In addition, considering the primary role of cabin climate control, it is desirable to intelligently consider the passengers’ thermal comfort in climate control design. In this paper, thermal comfort-conscious eco-climate control (TCC-ECC) based on model predictive control (MPC) is proposed to enhance the energy efficiency of the HVAC operation while ensuring passengers’ thermal comfort. The MPC design uses a reduced-order HVAC system model based on an ideal vapor-compression cycle. For the integration of thermal comfort into the MPC, a new approach is proposed to obtain an approximate solution of a predictive mean vote (PMV)-based thermal comfort model, which aims to balance computational efficiency and prediction accuracy. With the proposed TCC-ECC, a parametric study is conducted to analyze the impact of weighting factors on energy consumption and thermal comfort under two different thermal load conditions. Then, the performance of the tuned TCC-ECC is evaluated in comparison with a rule-based (RB) controller and the baseline eco-climate control (ECC) without considering thermal comfort. In the performance evaluation, the proposed TCC-ECC demonstrates that with the inclusion of thermal comfort it performs better in terms of energy efficiency and thermal comfort than manually adjusting a target cabin temperature depending on the environmental thermal load. The energy consumption of the proposed TCC-ECC is 22.5% and 35.24% less than that of the RB controller at an ambient temperature of 24 °C and 35 °C, respectively, and 14.5% and 18.5% less than the baseline ECC at the same conditions, respectively.

Model Predictive Controller Design Based on Residual Model Trained by Gaussian Process for Robots

Model mismatch is inevitable in robot control due to the presence of unknown dynamics and unknown perturbations. Traditional model predictive control algorithms are usually based on constant value assumptions and are not able to overcome the degradation of controller performance due to model mismatch. In this paper, a model predictive control (MPC) algorithm based on Gaussian process regression (GPR) is proposed. Firstly, the kinematic equations of the mobile robot are established by the mechanistic analysis method; similarly, the dynamics of the mobile robot system are modeled using the second-class Lagrangian equations. Secondly, the problem of stability and reliability degradation due to model mismatch during the operation of mobile robot is considered. This paper uses a MPC algorithm with a main model plus residual model to solve the MPC closed-loop control strategy. The state at each moment is decomposed into a predicted state based on the first-principles model and a residual state. The residual state is learned by GPR in real-time and used to compensate for deviations between the real process model and the predicted model. The proposed method requires fewer data samples, enhancing the technique’s practicality. Finally, the simulation results show that the proposed algorithm is more stable and achieves the desired tracking faster. Compared with the MPC algorithm, the arrival time of the system is reduced by 28% and the speed error is controlled within 0.07.

Dynamic risk-based process design and operational optimization via multi-parametric programming

We present a dynamic risk-based process design and multi-parametric model predictive control optimization approach for real-time process safety management in chemical process systems. A dynamic risk indicator is used to monitor process safety performance considering fault probability and severity, as an explicit function of safety–critical process variables deviation from nominal operating conditions. Process design-aware risk-based multi-parametric model predictive control strategies are then derived which offer the advantages to: (i) integrate safety–critical variable bounds as path constraints, (ii) control risk based on multivariate process dynamics under disturbances, and (iii) provide model-based risk propagation trend forecast. A dynamic optimization problem is then formulated, the solution of which can yield optimal risk control actions, process design values, and/or real-time operating set points. The potential and effectiveness of the proposed approach to systematically account for interactions and trade-offs of multiple decision layers toward improving process safety and efficiency are showcased in a real-world example, the safety–critical control of a continuous stirred tank reactor at T2 Laboratories.

Koopman Model Predictive Control of an Integrated Thermal Management System for Electric Vehicles

AbstractThis paper is concerned with energy efficient operation of an integral thermal management system (ITMS) for electric vehicles using a nonlinear model predictive control (MPC). Driven by a heat pump (HP), this ITMS can handle battery thermal management (BTM) while serving the need for cabin cooling or heating need. The objectives of the ITMS MPC control strategy include minimization of power consumption and achieving temperature setpoint regulation for the battery and cabin space based on predictive information of traction power and cabin thermal load. The control design is facilitated by a gray-box modeling framework, in which the nonlinear dynamics of HP subsystem are characterized with a data-driven Koopman subspace model, while the BTM subsystem dynamic is a bilinear physics-based model. The computational efficiency of the proposed MPC framework is improved with two aspects of convexification for the underlying receding-horizon constrained optimization problem: the Koopman-operator lifting and the McCormick envelopes implemented for handling the bilinear dynamics. The proposed control method is evaluated with simulation study, by developing a Modelica-Python cosimulation platform via the functional mockup interface (FMI), where the electric vehicle (EV)-ITMS plant is modeled in Modelica with Dymola and the MPC design is implemented in Python. By benchmarking against a recurrent-neural-networks (RNN) model based nonlinear MPC, the simulation results validate the effectiveness and improved computational efficiency of the proposed method.

Analytical Design of Optimal Model Predictive Control and Its Application in Small-Scale Helicopters

A new method for controlling the position and speed of a small-scale helicopter based on optimal model predictive control is presented in this paper. In the proposed method, the homotopy perturbation technique is used to analytically solve the optimization problem and, as a result, to find the control signal. To assess the proposed method, a small-scale helicopter system is modeled and controlled using the proposed method. The proposed method has been investigated under different conditions and its results have been compared with the conventional predictive control method. The simulation results show that the proposed technique is highly proficient in the face of various uncertainties and disturbances, and can quickly return the helicopter to its path.

Encrypted model predictive control design for security to cyberattacks

AbstractIn recent years, cyber‐security of networked control systems has become crucial, as these systems are vulnerable to targeted cyberattacks that compromise the stability, integrity, and safety of these systems. In this work, secure and private communication links are established between sensor–controller and controller–actuator elements using semi‐homomorphic encryption to ensure cyber‐security in model predictive control (MPC) of nonlinear systems. Specifically, Paillier cryptosystem is implemented for encryption‐decryption operations in the communication links. Cryptosystems, in general, work on a subset of integers. As a direct consequence of this nature of encryption algorithms, quantization errors arise in the closed‐loop MPC of nonlinear systems. Thus, the closed‐loop encrypted MPC is designed with a certain degree of robustness to the quantization errors. Furthermore, the trade‐off between the accuracy of the encrypted MPC and the computational cost is discussed. Finally, two chemical process examples are employed to demonstrate the implementation of the proposed encrypted MPC design.

Centralized controller design for voltage estimation error constrained in islanded DC-microgrids: Kalman Filtering Method

The traditional model predictive control (MPC) design strategy heavily depends on the discritization of the non-linear model of DC/DC power converters to approximate the direct current (DC) microgrid system model. The system model does not includes the whole information of the physical implementation of the system. Assumptions have been made to add the model and sensor uncertainties in the system model to form a model with fully physical information that enables its solution through the linear kalman filtering method ( LKFM ). Due to the unbounded of the DC bus voltage estimation error, the instability of the LKFM during transient response increases exponentially. To standardize the MPC model and ensure bounded the DC bus voltage estimation error, a centralized controller design for DC bus voltage estimation error constrained is proposed in this paper. The proposed system model is constructed from DC/DC power converters and then translated into a deterministic model. Through measurements and time updates, the LKFM has been employed to estimate the DC bus voltage. The linear quadratic regulator is used for stabilizing the DC bus voltage estimation and current sharing error between DC/DC power converters. During a transient response, an integral action is utilized to close the loop and eliminate an error in DC bus voltage. A feedback control rule of the DC bus voltage estimation and a Riccati equation have been used to develop the proposed controller. Finally, the proposed approach was validated using Simulink, the Hardware-in-the-loop laboratory, and compared with conventional control approaches. Moreover, the LKFM's stability was examined using exponential stability criteria.

Nonlinear tight formation control of multiple UAVs based on model predictive control

A tight formation of unmanned aerial vehicles (UAVs) has many advantages, such as fuel saving and deceiving enemy radar during battlefield entry. As a result, research on UAVs in close formation has received much attention, and the controller design for formation holding has become a popular research topic in the control field. However, there are many unknown disturbances in tight formation, and the tail aircraft is disturbed by the wake. This paper establishes a mathematical model of wake vortices for tail aircraft that considers uncertainty and strong interference. Two UAVs are simulated by Computational Fluid Dynamics software, followed by the design of a semiphysical simulation model predictive control (MPC) scheme that suppresses uncertainty and interference sufficiently to enable the tail aircraft to accurately track the lead aircraft and maintain a stable, tight formation. The tight formation controller is verified by numerical simulation and semiphysical simulation. The results show that the designed controller has an excellent control effect in the case of disturbance caused by the wake vortex.

Offline Computation of the Explicit Robust Model Predictive Control Law Based on Deep Neural Networks

A significant challenge in robust model predictive control (MPC) is the online computational complexity. This paper proposes a learning-based approach to accelerate online calculations by combining recent advances in deep learning with robust MPC. The use of soft constraint variables addresses feasibility issues in the robust MPC design, while the employment of a symmetrical structure deep neural network (DNN) approximates the robust MPC control law. The symmetry of the network structure facilitates the training process. The use of soft constraints expands the feasible region and also increases the complexity of the training data, making the network difficult to train. To overcome this issue, a dataset construction method is employed. The performance of the proposed method is demonstrated through simulated examples, and the proposed algorithm can be applied to control systems in various fields such as aerospace, three-dimensional printing, optical imaging, and chemical production.

Physics-informed machine learning for MPC: Application to a batch crystallization process

This work presents a framework for developing physics-informed recurrent neural network (PIRNN) models and PIRNN-based predictive control schemes for batch crystallization processes. The population balance model of the aspirin crystallization process is first developed to describe the formation of crystals through nucleation and growth. Then, the PIRNN modeling scheme is introduced to integrate observational data and mechanistic models for the development of machine learning models. Additionally, the physical constraints on process states are embedded in the machine learning models to prevent physically unreasonable predictions. Subsequently, the PIRNN model that captures the dynamic behavior of the batch crystallization process is utilized in the design of model predictive controller that optimizes the operation of the crystallizer. Through open-loop and closed-loop simulations, it is demonstrated that the PIRNN models using less training data achieve prediction accuracy and closed-loop performance comparable to the purely data-driven model.

Computationally Efficient Stability-Based Nonlinear Model Predictive Control Design for Quadrotor Aerial Vehicles

This article presents the design of a stability-guaranteed nonlinear model predictive controller for quadrotor-type microaerial vehicles to operate robustly on fast trajectories. The basic controller structure operates without having to use terminal conditions in the optimization problem. As a result, the controller is computationally less demanding and provides more stable closed-loop performance than traditional nonlinear predictive control schemes. This article presents a detailed stability analysis without terminal costs or terminal constraints and proves the asymptotic stability and necessary conditions for the recursive feasibility of the system. This article derives the growth-bound sequence that enables obtaining the shortest possible prediction horizon for stability. The proposed analysis provides the necessary conditions to implement the controller while using the shortest stabilizing prediction horizon compared to major traditional predictive control schemes reported in the literature. This particular feature enables the proposed controller to perform fast optimization and, hence, the capability to implement fast trajectories using feedback regularization. In order to demonstrate the validity of this new proposed control scheme, first, several MATLAB simulations are conducted to demonstrate the improved performance of the controller especially when the quadrotor vehicle follows fast trajectories. Real-time lab experiments are also conducted to validate the performance of the proposed scheme for point stabilization (hovering) and trajectory tracking problems. The results show that the proposed scheme can stabilize the system with a relatively short prediction horizon, a fast convergence rate, and a small tracking error.

A Model Predictive Control of Electronic Limited Slip Differential and Differential Braking for Improving Vehicle Yaw Stability

This article presents a model predictive control design for improving the yaw stability of a rear-wheel-drive vehicle equipped with an electronic limited slip differential (ELSD) and differential braking capability. It first develops a model for an ELSD system for predicting its torque distribution dynamics, then uses the model in designing an intelligent ELSD control that prevents unwanted oversteering yaw moments through direct control of the ELSD clutch pressure. Since differential braking degrades the vehicle’s longitudinal motion and driver comfort, two control actuations are prioritized: 1) ELSD clutch pressure and 2) differential braking. An appropriate stability limit is defined for the vehicle yaw rate, and two control objectives: 1) enforcing the yaw rate stability limit and 2) tracking the desired yaw rate are defined and prioritized. The actuation priorities and the objective priorities are combined within a model predictive control structure with particular soft constraints such that the low priority actuation is activated when the high priority objective demands it. Additionally, optimum corner braking forces are calculated by geometrically analyzing tire force vectors. The performance of the proposed controller, implemented in a Cadillac CTS vehicle, is experimentally evaluated for a variety of driving maneuvers.

Isolating Trajectory Tracking From Motion Control: A Model Predictive Control and Robust Control Framework for Unmanned Ground Vehicles

This letter studies the trajectory tracking and motion control problems of unmanned ground vehicles (UGVs). A model predictive control and robust control (MPC-RC) framework for UGVs is proposed to improve tracking accuracy, yaw stability and robustness in a modular fashion without introducing complexity into controller. The trajectory tracking problem and three-dimensional phase trajectory planning with high stability of a vehicle motion can be performed in the model predictive control design simultaneously. Also, combining the advantages of linear matrix inequality, sliding mode control, and back-stepping control law, three robust motion controllers can track the generated three-dimensional phase trajectory steadily so that the UGV motion stability is guaranteed. The robust performance is guaranteed through considering model uncertainties and terra-aerodynamic disturbances in robust controllers. Sufficient conditions for closed-loop stability under the diverse robust factors are provided by the Lyapunov method analytically, which ensures the series system's feasibility. The results of simulations on MATLAB-Carsim platform demonstrate that the proposed controller can significantly enhance tracking accuracy, motion stability, and robustness compared to the existing methods, which guarantees the feasibility and capability of driving in a nonlinear extreme scenario.

Least Square Support Vector Machines Laguerre Hammerstein Model Identification and Non-linear Model Predictive Controller Design for pH Neutralization Process

The ability to describe the nonlinear process dynamics is an essential feature of the Hammerstein model that paved more research and application studies in system identification and control. Using the Hammerstein model, this study shows an alternative approach to identify and control the highly nonlinear pH neutralization process. This Hammerstein model called Laguerre Least Square Support Vector Machines (LLSSVM) models the static nonlinearity with LSSVM and the linear part with Laguerre filter. The identified LLSSVM Hammerstein model performance evaluation with Mean Squared Error (MSE) and Variance Accounted For (VAF) is better than the Linear Laguerre model. We apply the identified LLSSVM Hammerstein model to implement a Nonlinear Model Predictive Controller (NMPC) to control the pH neutralization process. Then evaluated NMPC performance in terms of Integral Squared Error (ISE), Integral Absolute Error (IAE), and Total Variation (TV) and Control Effort (CE) parameters to verify its effectiveness in set-point tracking and disturbance rejection problems. The comparison of the NMPC with the Linear Laguerre Model-based Predictive Controller (LMPC) shows better performance of the NMPC than the LMPC. Results show that the LLSSVM Hammerstein model replicates the pH neutralization process well than the Linear Laguerre model. Also, the identified LLSSVM Hammerstein model provides an efficient NMPC than the LMPC for the pH neutralization process.

Design of a robust model predictive control for nonlinear switched systems: A low‐conservative and recursive feasibility strategy

AbstractThis article proposes a robust H∞ based model predictive control scheme for Lipschitz nonlinear switched systems with persistent dwell time. In the developed method, the constraints corresponding to the recursive feasibility are included and the recursive feasibility is guaranteed. In this scheme, the existence of unstabilizable sub‐systems and exogenous disturbances are included which makes it possible to avoid considering an ideal and simplistic assumption about switched systems. By simultaneously designing the controller and the switching signal and using multiple Lyapunov functions, the unacceptable conservatism in methods involving common Lyapunov functions and arbitrary switching signals is avoided. In the proposed solution, a time‐varying prediction horizon is used for finite horizon cost functions, which in turn will be effective in reducing conservatism. In the suggested design strategy, the non‐convex control scheme is formulated as an optimization problem in the framework of linear matrix inequality. Finally, a numerical example is developed and the performance of the proposed scheme is evaluated.

Trajectory Tracking Model Predictive Controller Design for Autonomous Vehicles with Updating Constrains of Tire Characteristics

In this paper, we address the problem of trajectory tracking control of autonomous vehicles by considering the nonlinear characteristics of tires. By considering the influence of the tires’ dynamics on steering stability, the proposed predictive controller can track the desired trajectory and desired velocity in the presence of road curvature while minimizing the lateral tracking deviation. First of all, a hierarchical control structure is adopted, in which the upper-level controller is used to calculate the desired acceleration and the desired front-wheel angle to maintain the control target, and the lower-level controller realized the command through the corresponding component devices. Moreover, a force estimator is designed based on the radial basis function (RBF) neural network to estimate the lateral force of the tires, which is incorporated into the boundary conditions of the vehicle envelope constraint to improve the adaptability of the controller to the vehicle performance. Finally, the proposed controller is tested by co-simulation of CarSim (a simulation software specifically for vehicle dynamics)/Simulink (a modular diagram environment for multidomain simulation as well as model-based design) and hardware-in-loop simulation system. The co-simulation and experimental results demonstrate the controller safely driving at the vehicle’s handling limits and effectively reduce the slip phenomenon of the vehicle.