Explicit Model Predictive Control Research Articles

Revisiting reachability-driven explicit MPC for embedded control

The real-time implementation of the explicit MPC suffers from the evaluation of the, potentially large, lookup table. The paper revisits the original approach and presents an efficient reachability-sets-driven-based explicit MPC method addressing this issue by splitting the look-up table into the set of the “relevant” subsets. Simultaneously, effective binary encoding is introduced to minimize the runtimes and the memory footprint. Further acceleration is achieved by introducing the “smart” order of the considered critical regions. Then, the significant real-time complexity reduction is ensured by online pruning and traversing the sorted lookup table associated with the optimal control law evaluation. Technically, the number of critical regions to be explored is reduced and the order is redefined to accelerate the point location problem and minimize the computational effort. While the optimality of the control law is still preserved, the cost that we need to pay for the accelerated point location problem lies in an additional offline computation effort and a minor increase in memory requirements of the underlying controller. The benefits of the proposed method are demonstrated using an extensive case study. The complexity reduction strategy was investigated on two fast-dynamic benchmark systems and the computational burden was analyzed by implementing the designed controllers on an embedded hardware.

RBS and ABS Coordinated Control Strategy Based on Explicit Model Predictive Control.

During the braking process of electric vehicles, both the regenerative braking system (RBS) and anti-lock braking system (ABS) modulate the hydraulic braking force, leading to control conflict that impacts the effectiveness and real-time capability of coordinated control. Aiming to enhance the coordinated control effectiveness of RBS and ABS within the electro-hydraulic composite braking system, this paper proposes a coordinated control strategy based on explicit model predictive control (eMPC-CCS). Initially, a comprehensive braking control framework is established, combining offline adaptive control law generation, online optimized control law application, and state compensation to effectively coordinate braking force through the electro-hydraulic system. During offline processing, eMPC generates a real-time-oriented state feedback control law based on real-world micro trip segments, improving the adaptiveness of the braking strategy across different driving conditions. In the online implementation, the developed three-dimensional eMPC control laws, corresponding to current driving conditions, are invoked, thereby enhancing the potential for real-time braking strategy implementation. Moreover, the state error compensator is integrated into eMPC-CCS, yielding a state gain matrix that optimizes the vehicle braking status and ensures robustness across diverse braking conditions. Lastly, simulation evaluation and hardware-in-the-loop (HIL) testing manifest that the proposed eMPC-CCS effectively coordinates the regenerative and hydraulic braking systems, outperforming other CCSs in terms of braking energy recovery and real-time capability.

Explicit flatness-based MPC design for indoor nano-quadcopter position tracking

Due to the nonlinearities and operational constraints of quadcopters, Model Predictive Control (MPC) encounters the requirement of high computational power. This problem may prove impractical, especially for hardware-limited setups. By removing the need for online solvers, Explicit MPC (ExMPC) stands out as a strong candidate. Yet, the formulation was usually hindered by the system's nonlinearity and dimensionality. In this paper, we propose an ExMPC solution for quadcopter position stabilisation. With the former issue, the system is exactly linearised into a concatenation of three double integrators. For the latter, with a suitable characterisation of the new convoluted constraints, the stabilising ExMPC can be computed for each double integrator separately. The controller is validated via simulations and experiments on a nanodrone platform. The proposed scheme provides similar performance and theoretical guarantees to the up-to-date nonlinear MPC solutions but with notably less computational effort, allowing scalability in a centralised manner.

A Multi-Source Braking Force Control Method for Electric Vehicles Considering Energy Economy

Advancements in electric vehicle technology have promoted the development trend of smart and low-carbon environmental protection. The design and optimization of electric vehicle braking systems faces multiple challenges, including the reasonable allocation and control of braking torque to improve energy economy and braking performance. In this paper, a multi-source braking force system and its control strategy are proposed with the aim of enhancing braking strength, safety, and energy economy during the braking process. Firstly, an ENMPC (explicit nonlinear model predictive control)-based braking force control strategy is proposed to replace the traditional ABS strategy in order to improve braking strength and safety while providing a foundation for the participation of the drive motor in ABS (anti-lock braking system) regulation. Secondly, a grey wolf algorithm is used to rationally allocate mechanical and electrical braking forces, with power consumption as the fitness function, to obtain the optimal allocation method and provide potential for EMB (electro–mechanical brake) optimization. Finally, simulation tests verify that the proposed method can improve braking strength, safety, and energy economy for different road conditions, and compared to other methods, it shows good performance.

Explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models. While ML models can capture nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. To address this issue, in this work, we propose an explicit ML-MPC framework for nonlinear processes using multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain a piecewise linear affine function that approximates the behaviors of ML models. Then, multi-parametric quadratic programming (mpQP) problems are formulated to generate the solution map for states in discretized state–space. Furthermore, to accelerate the implementation of explicit ML-MPC, a neighbor-first search algorithm is developed. Finally, an example of a chemical reactor is used to demonstrate the effectiveness of the explicit ML-MPC.

Demand response of an Electric Vehicle charging station using a robust-explicit model predictive control considering uncertainties to minimize carbon intensity

This paper presents a novel approach to address uncertainties and enable demand response in Electric Vehicle (EV) charging station optimization. A two-stage optimization strategy is proposed, integrating Robust Optimization and explicit Model Predictive Control (eMPC). The first stage involves day-ahead planning using Robust Optimization technique to limit the hourly power consumption of EVs, considering worst-case scenarios caused by uncertainties in EV consumption and CO2 emissions. The objective is to minimize environmental impact by reducing CO2 emissions. An Explicit Model Predictive Control strategy is developed in the second stage for real-time operation. The explicit solution, calculated offline, models uncertainties such as the initial state of charge of the battery energy storage, photovoltaic power production, and EV power consumption. During real-time operation, the explicit solution is accessed using measured data from the charging station, refining the schedule derived from the first stage. The proposed solution is implemented and evaluated at an EV charging station in Trieste, Italy. The results demonstrate a significant 69% reduction in CO2 emissions compared to a deterministic approach while maintaining a real-time computation time of less than 0.1 s.

Composing MPC With LQR and Neural Network for Amortized Efficiency and Stable Control

Model predictive control (MPC) is a powerful control method that handles dynamical systems with constraints. However, solving MPC iteratively in real time, i.e., implicit MPC, remains a computational challenge. To address this, common solutions include explicit MPC and function approximation. Both methods, whenever applicable, may improve the computational efficiency of the implicit MPC by several orders of magnitude. Nevertheless, explicit MPC often requires expensive pre-computation and does not easily apply to higher-dimensional problems. Meanwhile, function approximation, although scales better with dimension, still requires pre-training on a large dataset and generally cannot guarantee to find an accurate surrogate policy, the failure of which often leads to closed-loop instability. To address these issues, we propose a triple-mode hybrid control scheme, named Memory-Augmented MPC, by combining a linear quadratic regulator, a neural network, and an MPC. From its standard form, we derive two variants of such hybrid control scheme: one customized for chaotic systems and the other for slow systems. The proposed scheme does not require pre-computation and is capable of improving the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">amortized</i> running time of the composed MPC with a well-trained neural network. In addition, the scheme maintains closed-loop stability with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">any</i> neural networks of proper input and output dimensions, alleviating the need for certifying optimality of the neural network in safety-critical applications. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article was motivated by the need to reduce the amortized cost of MPC in repetitive industrial robotic applications, where long-term operational cost is important and safety is critical. Examples of such applications include factory robotic arm manipulation and fixed-route quadcopter payload transport. Unlike explicit MPC or function approximation, our approach does not require any pre-computation or pre-training. Rather, it attains task proficiency over time by learning a surrogate neural network on the spot and by gradually replacing the costly MPC with the more efficient surrogate model so long as safety permits. Consequently, the proposed scheme incurs a learning cost during the initial phase of the deployment but usually becomes more adept on the task afterwards, leading to amortized efficiency.

Networked explicit hybrid predictive control of an industrial benchmark process

Hybrid systems have acquired deep attention in research as many systems in industries and laboratories manifest hybrid dynamic behaviors. Optimal control design for hybrid systems exhibits challenges for controlling the interacting continuous and discrete dynamics. A double-tank hybrid system (DTHS) is proposed in this paper with a mixed-integer actuation mechanism. The proposed DTHS aims to control the liquid level of the two tanks simultaneously by a networked hybrid predictive controller. Hybrid frameworks are provided to investigate the system through reachability analysis. An explicit hybrid model predictive control (EHMPC) has been developed to control the levels of the DTHS. Hardware-In-the-Loop (HIL) simulation is performed for assessing the performance of the EHMPC with a hardware real-time networked controller. The networked real-time controller is constructed and implemented using the Node.js frameworks. The simulation and realtime results are presented and discussed to evaluate the hybrid controller performance.

Robust EMPC-Based Frequency-Adaptive Grid Voltage Sensorless Control for an LCL-Filtered Grid-Connected Inverter

A robust explicit model predictive control (EMPC)-based frequency-adaptive grid voltage sensorless control is developed for a grid-connected inverter (GCI) via a linear matrix inequality (LMI) approach under the model parametric uncertainties as well as distorted and imbalanced grid voltages. In order to ensure the quality of grid currents injected into the utility grid even when the system model parameters vary, the proposed control scheme is accomplished by an enhanced prediction model rather than the conventional prediction model obtained by fixed parameters. Furthermore, an LMI-based observer is integrated with the disturbance observer to improve the reference tracking performance and to reject disturbances. The proposed observer is employed for the grid frequency-adaptive control without the need for grid voltage sensors. The proposed current controller and observer employ the LMI scheme to maintain a stable and robust operation of the GCI. The discrete-time frequency response and pole-zero map analyses are utilized to examine the system performance including the stability and robustness against parametric uncertainties. Comprehensive simulation and experimental tests as well as theoretical analyses clearly validate the robustness of the proposed control scheme under various harsh test conditions with non-ideal and unexpected grid and system parametric uncertainties.

Explicit model predictive control of magnetorheological suspension for all-terrain vehicles with road preview

The integration of magnetorheological (MR) semi-active suspension systems in all-terrain vehicles (ATV) has garnered significant attention due to their ability to enhance damping performance and off-road capabilities. However, traditional control strategies result in poor control accuracy and limited vibration reduction effects when facing complex road excitations and impact disturbances. With technological advancements, enhanced vehicle environmental perception and road sensing capabilities have made it possible to implement model predictive control (MPC) for vehicle suspensions. Nevertheless, traditional MPC is limited in vehicle suspension applications due to its high computational complexity. To address these issues, this study introduces an explicit model predictive control based on road preview (EMPC-P). Firstly, road data obtained through a non-contact measurement method enables the system to perceive road excitation information in advance. Subsequently, a 7 Degree-of-Freedom (7-DOF) suspension model incorporating road excitations is constructed. By adhering to system constraints and employing a multiparameter optimization method, the control problem based on rolling optimization is transformed into an explicit polyhedral system. The offline precomputation of control state relations enhances the computational efficiency of the control system. Through this approach, the designed EMPC allows the vehicle suspension system to make optimal control decisions quickly and accurately in response to complex driving conditions, thus improving the damping effect of the system. Through a combined approach of simulation and experimental validation, the designed EMPC-P controller is compared with the Skyhook controller under preview and non-preview states, respectively. Empirical testing confirms that the EMPC-P exhibits superior damping effects, significantly improving vehicle ride comfort and handling stability.

Multiple-model adaptive explicit predictive control for nonlinear MIMO system

This work is to develop a blending-based multiple model adaptive explicit predictive control scheme for nonlinear MIMO systems that can handle parametric uncertainties. Here, for each identification model, an explicit nonlinear model predictive control (ENMPC) law is computed in advance for the corresponding model. The generated control inputs from the set of ENMPC controllers are being blended online using a weighting vector that is continuously updated by the proposed adaptive identification schemes. The proposed control scheme is used to govern the tracking of a highly nonlinear helicopter model known as the twin rotor MIMO system (TRMS). Here, an extended Kalman filter (EKF) is used to estimate the unavailable states of the TRMS. Finally, simulation and experimental results are presented to prove that the proposed controller gives better performance than some reported works in the literature. The effectiveness of the proposed controller is demonstrated by experimental studies of the TRMS model.

Critical Review of Optimal Control Methods for Li‐Ion Batteries in Electric Vehicles

AbstractBattery management systems are important for the safe and efficient operation of electric vehicles. Although high hardware performance and effective configurations of batteries have been realized, a management algorithm is required for ensuring optimal system performance. This review focuses on optimal controllers for charging, thermal control, and cell balancing of electric vehicles. A potential approach for practical applications is the direct optimal control method, particularly model predictive control (MPC). The objective function, prediction model types, and manipulated variables are summarized, along with the computational performance. Typical nonlinear MPC, linear MPC, explicit MPC, and hierarchical MPC are the main formulations for the optimal control of EVs. The AI‐based approach learns the optimal control law as a function from the optimal control result data. Although few studies have applied the reinforcement approach to battery systems, additional safety considerations for constraints must be considered for real applications. Cell variations, aging factors, and uncertainty considerations have been analyzed for improving the controller design. Addressing the computational issue with a reliable optimizer is critical to the implementation of an optimal controller for EVs.

Explicit hybrid MPC for the lateral stabilization of electric vehicle system

This paper presents a hybrid Model Predictive Control (hMPC) approach to improve Electric Vehicle (EV) stability when cornering or in high-risk driving conditions. By using approximations of tire force characteristics, the EV system proposed in this study is considered as a Piecewise Affine (PWA) system which is a class of Hybrid Dynamical Systems (HDSs). First, a hybrid modeling of the studied system is developed within the PWA framework. Then, the synthesis of an explicit hybrid MPC law, based on the integration of the Active Front-wheel Steering control method (AFS) and Direct Yaw moment Control method (DYC), can be established. The purpose of the PWA-MPC is to force the yaw rate and sideslip angle of the EV system to follow the given references to guarantee lateral stability. The calculation of the control laws of this proposed approach is performed offline using multiparametric programming. Finally, this paper investigates the effectiveness of the designed controller by performing a set of simulations to analyze the efficiency and robustness of the proposed approach. A comparative study is addressed in this work to demonstrate the efficiency of the proposed hybrid MPC controller compared to the conventional MPC approach which considers the linear model of the system. Another simulations are carried out to assess the robustness of the proposed control, important disturbances and uncertainties were incorporated such as the change of the additional mass, the change of terrain and the high velocity. The simulation results show that the PWA EV system model with the designed controller is able to ensure lateral stability by keeping the sideslip angle and yaw rate tracking the ideal values.

A Two-Degree-of-Freedom Explicit Model Predictive Non-Cascaded Direct Speed Control for SPMSM Drives

A Two-Degree-of-Freedom Explicit Model Predictive Non-Cascaded Direct Speed Control for SPMSM Drives

Stability Analysis and Controller Synthesis Using Single-Hidden-Layer ReLU Neural Networks

This paper presents algorithms to solve analysis and controller synthesis problems for dynamical systems modeled as a recurrent single-hidden-layer rectified linear unit neural network (ReLU NN), or equivalently, a piecewise affine dynamical system. Such models are interesting since they may arise through the use of modern machine learning methods for system identification, or as closed-loop solutions in certain classes of model predictive control (MPC) problems. A key idea in the proposed approach is to use piecewise affine Lyapunov functions parametrized as ReLU neural networks, and similarly parametrized controllers. This compatible representation between the Lyapunov function and the dynamics simplifies the automation of analysis of and controller synthesis for learned models. Our method of verifying a candidate Lyapunov function is faster than methods based on mixed integer programming. We ‘learn’ controllers and Lyapunov functions using both weight updates and network architecture search, without gradients. We demonstrate the proposed algorithm on examples involving learned models, explicit MPC controllers, and constrained controller synthesis.

Fuel-efficient predictive cruise control using the explicit MPC method for commercial vehicles

Fuel-efficient predictive cruise control using the explicit MPC method for commercial vehicles

Ride comfort oriented integrated design of preview active suspension control and longitudinal velocity planning

Aiming for further improvement in ride comfort, a novel integrated system combining preview active suspension control with longitudinal velocity planning based on road height information is proposed. From the suspension control side, the presented semi-EMPC (Explicit Model Predictive Control)-based controller, which is augmented with preview road information, can make up for the shortcomings of traditional implicit MPC and explicit MPC, and achieve a balance between computational burden and memory usage, thus enhancing the practicality of implementing preview suspension in real-world applications. Adopting dynamic programming and quadratic programming algorithms, a longitudinal velocity planning method based on preview information is provided to overcome the vibration that cannot be effectively suppressed by single suspension control, thus expanding the dimension of ride comfort improvement from the original vertical dimension alone to both longitudinal and vertical dimensions. Throughout the design process, the transformation of pavement information among spatial, time, and frequency domains has been regarded as a bridge to combine two systems, thus handling the complex coupling between above two highly interdependent systems. Experiments in the Quanser active suspension plant have been conducted to verify the superiority of semi-EMPC with preview. The integrated approach is simulated in Carsim and shows a significant improvement over single suspension control.

Closed-loop optimisation of neural networks for the design of feedback policies under uncertainty

Solving model predictive control (MPC) problems online can be computationally intractable, especially when considering uncertainty and nonlinear systems. One approach to avoid this is to train a neural network on a data-set of solutions of MPC problems (potentially nonlinear) offline, and to evaluate the trained control policy online. However, due to the separation of these optimisation problems the neural network controller must be carefully verified to ensure adequate closed loop performance. In this paper we propose a method to train a neural network in closed loop for control systems, in continuous or discrete time, while allowing for flexible consideration of parametric uncertainty. This method does not require off-line solutions of the NMPC problem, and instead directly optimises the desired closed loop performance. We prove that our method can approximate the optimal closed-loop control policy to arbitrary tolerance and in numerical examples demonstrate its performance compared to explicit MPC, imitation learning and nominal MPC.

Explicit model predictive control design for artificial respiratory ventilation system

Explicit model predictive control design for artificial respiratory ventilation system

Lattice piecewise affine approximation of explicit nonlinear model predictive control with application to trajectory tracking of mobile robot

AbstractTo promote the widespread use of mobile robots in diverse fields, the performance of trajectory tracking must be ensured. To address the constraints and nonlinear features associated with mobile robot systems, nonlinear model predictive control (MPC) is applied to realize trajectory tracking of mobile robots. Specifically, to alleviate the online computational complexity of nonlinear MPC, this paper devises a lattice piecewise affine (PWA) approximation method that can approximate both the nonlinear system and control law of explicit nonlinear MPC. The kinematic model of the mobile robot is successively linearized along the trajectory to obtain a linear time‐varying description of the system, which is then expressed using a lattice PWA model. Subsequently, the nonlinear MPC problem can be transformed into a series of linear MPC problems. Furthermore, to reduce the complexity of online calculation of multiple linear MPC problems, the optimal solution of the linear MPCs is approximated by using the lattice PWA models. That is, for different sampling states, the optimal control inputs are obtained offline, and lattice PWA approximations are constructed for the state control pairs. Simulations are performed to evaluate the performance of the method in comparison with the state‐of‐the‐art methods, and the results show that the method has a higher online computing speed and can decrease the offline computing time without significantly increasing the tracking error.