Path Tracking of Autonomous Vehicles with Model Predictive Control (MPC) Optimized with Particle Swarm Optimization (PSO)

For continuously changing road conditions and vehicle operating states, the exactitude of vehicle path tracking has not been secured by model predictive control based on linear lateral stiffness. An amended square root cubature Kalman filter method based on the minimization of a new covariance of interest is proposed to calculate the tire lateral deflection force in real time. The ratio of the estimated tire force to the linear tire force was used as a ratio to adjust the lateral deflection stiffness, and an adaptive model predictive controller was built based on the vehicle path-tracking error model to correct the tire lateral deflection stiffness. Finally, an analysis based on the joint CarSim and Simulink simulation platform shows that compared to a conventional model predictive control (MPC) controller, a trajectory-following controller built based on this method can effectively reduce the lateral distance error and heading error of an autonomous vehicle. Especially under low adhesion conditions, the conventional MPC controllers will demonstrate large instability during trajectory tracking due to the deviation of the linear tire force calculation results, whereas the adaptive model predictive control (AMPC) controllers can correct the side deflection stiffness by estimating the tire force and still achieve stable and effective tracking of the target trajectory. This suggests that the proposed algorithm can improve the effectiveness of trajectory tracking control for autonomous vehicles, which is an important reference value for the optimization of autonomous vehicle control systems.

The efficiency of a SAGD operation depends on developing a uniform steam chamber and maintaining an optimal subcool along the length of the well pair. Heterogeneity in reservoir properties may lead to suboptimal subcool levels. Recently, Model Predictive Control (MPC) based on the real-time production, temperature, and pressure data along with other well and surface constraint information has been proposed for a real-time feedback control of SAGD well pairs. Reservoir dynamics in MPC is represented using either linear step response model or one-dimensional ordinary differential equation. However, such simplified models are insufficient in MPC since SAGD is more complex and highly nonlinear process. Therefore, MPC framework that represents nonlinear behaviour of SAGD over an extended control period is required to achieve optimized subcool and steam conformance. In this research, two novel workflows are proposed to handle nonlinear reservoir dynamics in MPC. First approach known as Adaptive MPC includes recursive estimations at each control interval based on system identification theory. This allows evolution of the coefficients of a fixed model structure such that the updated system identification model in MPC controller reflects current reservoir dynamics adequately. Another approach, Gain-Scheduled MPC, decomposes the subcool control problem in a parallel manner and uses a bank of multiple controllers rather than only one controller. This ensures effective control of the nonlinear reservoir system even in adverse control situations by employing aggressive variations in input parameters. Suggested workflows are implemented using history-matched numerical model of a reservoir located in northern Alberta. Steam injection rates and liquid production rate are considered as input variables in MPC, constrained to available surface facilities. Well-pair is divided into multiple sections and subcool of each section is considered as an output variable. Optimum set-point for subcool is considered as 20°C. Results are compared with actual field data (in which no control algorithm is used) and analyzed based on two criteria: 1) Do all subcools track optimum set-point while maintaining stability in input variables and 2) Does net present value (NPV) of oil improve in case of Adaptive and Gain-Scheduled MPC? In general, we conclude that both Adaptive and Gain-Scheduled MPC provide superior tracking of subcool set-point and hence better steam conformance due to adequate representation of reservoir dynamics by recursive estimation of coefficients and multiple controllers. In addition, results indicate stability in input parameters and improvement in economic performance. NPV is improved by 23.69% and 10.36% in case of Adaptive and Gain-Scheduled MPC, respectively. Under current economic scenario, proposed workflows can improve the NPV of a SAGD reservoir by optimizing the well operational parameters while considering constraints of surface facilities and minimizing environmental footprints.

In this paper, a nonlinear model predictive control (NMPC) scheme for path tracking of autonomous vehicles using discrete previewed points in the inertial coordinate is presented. The control objective is to improve the tracking accuracy under small lateral acceleration in the scenario of low speed and narrow space. The path tracking problem is formulated as a nonlinear model predictive control model, in which the vertical distance between the vehicle position and the tangent of previewed point is adopted to evaluate the tracking error. The discrete previewed points are generated from the path points independently, which does not rely on the approximate path functions. The iterative initial values of the optimization model are appropriately selected by combining with the Stanley method to accelerate optimization computations. A simulation comparison between the proposed NMPC controller and a linear model predictive control (LMPC) controller is conducted through Carsim-Matlab/Simulink co-simulations. Simulation results show that the proposed controller exhibits better tracking accuracy than the LMPC controller under small lateral acceleration, especially when the path curvature is large and continuously changing.

<div class="section abstract"><div class="htmlview paragraph">Vehicles equipped with articulated steering systems have advantages such as low energy consumption, simple structure, and excellent maneuverability. However, due to the specific characteristics of the system, these vehicles often face challenges in terms of lateral stability. Addressing this issue, this paper leverages the precise and independently controllable wheel torques of a hub motor-driven vehicle. First, an equivalent double-slider model is selected as the dynamic control model, and the control object is rationalized. Subsequently, based on the model predictive control method and considering control accuracy and robustness, a weight-variable adaptive model predictive control approach is proposed. This method addresses the optimization challenges of multiple systems, constraints, and objectives, achieving adaptive control of stability, maneuverability, tire slip ratio, and articulation angle along with individual wheel torques during the entire steering process of the vehicle. Finally, the effectiveness of the controller is validated through hardware-in-the-loop testing, and the data indicates that the proposed adaptive model predictive controller significantly enhances the vehicle’s handling stability.</div></div>

Among various control methods, model predictive control (MPC) becomes one of the major control strategies and has many successful applications. This paper presents an automatic tuning method of MPC using particle swarm optimization (PSO). One of the challenges in MPC is how control parameters can be turned for various target plants and usage of PSO for automatic tuning is one of the solutions. The tuning problem of MPC is formulated as an optimization problem and PSO is applied as the optimization techniques. PSO is one of meta-heuristic methods which are known to search a global optimum at a relatively high ratio and with no use of a gradient. The numerical results for simple examples show the effectiveness of the proposed PSO-based automatic tuning method.

Model predictive control (MPC) is used in the CO2 removal process in the Subang field to improve its control performance. MPC is used to maintain the CO2 concentration at the sweet gas output by controlling the feed gas pressure (PIC-1101), makeup water flow rate (FIC-1102), and amine flow rate (FIC-1103). The empirical model applied to MPC to represent the process model is the auto-regressive exogenous (ARX) model. The ARX model is compared with the first order plus dead time (FOPDT) model based on the root mean square error (RMSE) between the model and the actual process, then MPC parameters are tuned which include sampling time (T), prediction horizon (P) and control horizon (M) to control for the three variables. Improved control performance is measured based on the integral square error (ISE). The results show that the ARX model is the best model for the CO2 removal process with an RMSE value of 35%-91% smaller than the FOPDT model. The optimal control parameters Prediction Horizon (P), Control Horizon (M) and Sampling Time (T) in the CO2 removal process are 75, 25 and 1 on PIC-1101, 25, 10 and 1 on FIC-1102, and 30, 25 and 1 on FIC-1103. The MPC-ARX (MPC using ARX model) can improve the control performance of 33% in the servo control and 6-56% on the regulatory control. However, not all of them showed an increase in control performance improvement from previous studies even though they had used the best model (ARX). This is due to the MPC parameter setting that is not yet appropriate, so it needs to be retuning.

Intelligent state estimation for fault tolerant integrated frequent RTO and adaptive nonlinear MPC

This paper presents the implementation of an autonomous electric vehicle (EV) project in the National Taiwan University of Science and Technology (NTUST) campus in Taiwan. The aim of this work was to integrate two important practices of realizing an autonomous vehicle in a campus environment, including vehicle positioning and path tracking. Such a project is helpful to the students to learn and practice key technologies of autonomous vehicles conveniently. Therefore, a laboratory-made EV was equipped with real-time kinematic GPS (RTK-GPS) to provide centimeter position accuracy. Furthermore, the model predictive control (MPC) was proposed to perform the path tracking capability. Nevertheless, the RTK-GPS exhibited some robust positioning concerns in practical application, such as a low update rate, signal obstruction, signal drift, and network instability. To solve this problem, a multisensory fusion approach using an unscented Kalman filter (UKF) was utilized to improve the vehicle positioning performance by further considering an inertial measurement unit (IMU) and wheel odometry. On the other hand, the model predictive control (MPC) is usually used to control autonomous EVs. However, the determination of MPC parameters is a challenging task. Hence, reinforcement learning (RL) was utilized to generalize the pre-trained datum value for the determination of MPC parameters in practice. To evaluate the performance of the RL-based MPC, software simulations using MATLAB and a laboratory-made, full-scale electric vehicle were arranged for experiments and validation. In a 199.27 m campus loop path, the estimated travel distance error was 0.82% in terms of UKF. The MPC parameters generated by RL also achieved a better tracking performance with 0.227 m RMSE in path tracking experiments, and they also achieved a better tracking performance when compared to that of human-tuned MPC parameters.

<div class="section abstract"><div class="htmlview paragraph">Conventional cruise control systems in automotive applications are usually designed to maintain the constant speed of the vehicle based on the desired set-point. It has been shown that fuel economy while in cruise control can be improved using advanced control methods namely adopting the Model Predictive Control (MPC) technology utilizing the road grade preview information and allowance of the vehicle speed variation. This paper is focused on the extension of the Adaptive Nonlinear Model Predictive Controller (ANLMPC) reported earlier by application to the trailer tow use-case. As the connected trailer changes the aerodynamic drag and the overall vehicle mass, it may lead to the undesired downshifts for the conventional cruise controller introducing the fuel economy losses. In this work, the ANLMPC concept is extended to avoid downshifts by translating the downshift conditions to the constraints of the underlying optimization problem to be solved. To deal with significant noise factors, e.g., overall vehicle mass, change of aerodynamic drag, actual weather conditions, fuel type, the on-line adaptation of the parameters is performed by the constrained Recursive Least Squares (RLS) method. The issue of the lack of the excitation due to the limited changes in torque and engine speed in cruise is solved by the directional forgetting and dead-zone approach together with limits on the parameters. The implementation details of ANLMPC are given describing a technique leading the significant reduction of the RAM memory. The ANLMPC has been validated in real world driving conditions running in production PCM module of a Sport Utility Vehicle (SUV) towing a trailer with 1600 kg of load, showing 6.3-8.8% fuel economy improvement compared to production cruise controller with the same time of arrival.</div></div>

<div class="section abstract"><div class="htmlview paragraph">To meet the traffic control demands of highway merging areas and address the accuracy error of traffic flow prediction models, a cooperative control strategy based on adaptive prediction horizon Model Predictive Control (MPC) has been proposed for variable speed limits (VSL) and dynamic hard shoulder running (HSR). Firstly, the METANET model was improved based on the characteristics of merging areas and the impact of cooperative control strategy. Secondly, to mitigate the negative impact of the METANET prediction errors on control effectiveness, a fuzzy rule-based adaptive prediction horizon controller is designed. Thirdly, a cooperative control strategy for VSL and dynamic HSR is formulated under the MPC framework, aiming to optimize Total Time Spent(TTS)and Total Travel Distance (TTD), using genetic algorithms equipped with sliding time windows for resolution. Finally, using actual traffic flow data from Changtai Highway, simulation experiments are conducted, involving four scenarios: HSR-VSL control, VSL-only control, HSR-only control, and no control. In the cooperative control scenario, both adaptive and fixed prediction horizon approaches are considered. Results show that the proposed HSR-VSL control strategy with fixed prediction horizon reduces the total travel time and mainline density by 20.02% and 10.78% respectively, outperforming single strategies (only HSR or VSL). Compared to a fixed prediction horizon, the VSL-HSR with adaptive prediction horizon delivers even better results, reducing total travel time and mainline density by 24.53% and 12.94% respectively, proving the effectiveness of the cooperative control strategy and the adaptive prediction horizon controller.</div></div>

This paper presents a novel motion control strategy based on model predictive control (MPC) for distributed drive electric vehicles (DDEVs), aiming to simultaneously control the longitudinal and lateral motion while considering efficiency and the driving feeling. Initially, we analyze the vehicle's dynamic model, considering the vehicle body and in-wheel motors, to establish the foundation for model predictive control. Subsequently, we propose a model predictive direct motion control (MPDMC) approach that utilizes a single CPU to directly follow the driver's commands by generating voltage references with a minimum cost function. The cost function of MPDMC is constructed, incorporating factors such as the longitudinal velocity, yaw rate, lateral displacement, and efficiency. We extensively analyze the weighting parameters of the cost function and introduce an optimization algorithm based on particle swarm optimization (PSO). This algorithm takes into account the aforementioned factors as well as the driving feeling, which is evaluated using a trained long short-term memory (LSTM) neural network. The LSTM network labels the response under different weighting parameters in various working conditions, i.e., "Nor", "Eco", and "Spt". Finally, we evaluate the performance of the optimized MPDMC through simulations conducted using MATLAB and CarSim software. Four typical scenarios are considered, and the results demonstrate that the optimized MPDMC outperforms the baseline methods, achieving the best performance.

This work introduces an adaptive model predictive control (MPC) scheme for nonlinear processes. It is well-known that the conventional MPC uses linear model to represent local dynamics of a nonlinear process and resulting optimization problem is convex. However, the model mismatch between linear model and nonlinear process may significantly degrade the performance of MPC and thereby the closed-loop stability may not be guaranteed. To address this issue, the model used in MPC should be accurate enough for different operating conditions. The contribution of this paper is the development of a steady state constrained autoregressive with exogenous terms model (SSARX) that is still linear and adaptive to the variation of operating conditions. This new model then can be integrated with a linear MPC to achieve a trade-off between computational complexity and model accuracy. The proposed controller is applied in a continuous fermentation process and compared to an MPC with unconstrained ARX model (non-adaptive). The simulation shows that the MPC with ARX model leads to an offset during setpoint tracking while the MPC with SSARX model is offset free.

In the hot strip rolling process, inter-stand speed coordination directly affects product quality and production stability. Traditional linear speed compensation strategies perform poorly under extreme conditions such as strip tension and strip piling, making it difficult to maintain stable loop control. This study proposes a speed compensation strategy that integrates Particle Swarm Optimization (PSO) with Model Predictive Control (MPC). Based on the mechanism of hot rolling, a nonlinear state-space model is constructed, in which the compensation parameter is treated as an optimization variable to formulate a rolling optimization problem. PSO is employed to globally solve the nonlinear MPC problem, yielding an optimal compensation sequence that adapts to disturbance variations. The proposed algorithm can adaptively adjust the speed compensation parameter under typical strip piling and strip tension conditions, thereby achieving stable loop regulation and maintaining the looper angle within the desired range. This effectively addresses the speed coordination problem under abnormal conditions in hot strip rolling, improving the control performance. The experimental results verify the effectiveness of the proposed method.

An optimal control technique is proposed to address the problem of path tracking of an autonomous ground vehicle. This technique utilizes a Fractional Order Proportional Integral Derivative (FOPID) controller to control a non-holonomic autonomous ground vehicle to track the behaviour of the predefined reference path. Two FOPID controllers are designed to control the vehicle's inputs. These inputs represent the torques that are used in order to manipulate the implemented model of the vehicle to obtain the actual path. The implemented model of the non-holonomic autonomous ground vehicle takes into consideration both of the kinematic and dynamic models. In additional, a Particle Swarm Optimization (PSO) algorithm is used to optimize the FOPID controllers' parameters. These optimal tuned parameters of FOPID controllers minimize the cost function used in the algorithm. The effectiveness and validation of the proposed method have been verified through different patterns of reference paths using MATLABSIMULINK software package. The newly obtained results of FOPID controller show the advantage and the performance of the technique in terms of minimizing path tracking error and the complement of the path following.

This paper investigates the problem of path tracking for autonomous vehicles with parameter uncertainties and constraints. The dynamical model for the autonomous driving system is presented using fuzzy modeling techniques. Through online calculation, the robust positively invariant (RPI) set is determined, then an robust fuzzy model predictive controller is obtained. The system performance of the controller is computed by solving a series of constraints in terms of linear matrix inequalities. Finally, Carsim/Matlab co-simulation platform demonstrates the performance of the mentioned methodology.