Time-varying Model Predictive Control Research Articles

A practical trajectory tracking control of autonomous vehicles using linear time-varying MPC method

With the rapid development and implementation of autonomous vehicles (AVs), the simultaneous and accurate trajectory tracking problem for such AVs has become a popular research topic. This paper proposes a comprehensive linear time-varying model predictive controller (LTV-MPC) design for a type of AV, aiming to achieve good trajectory tracking in a practical driving scenario. First, a two-degree-of-freedom kinematic model of an AV is established. Next, an error model of the AV’s trajectory tracking system is constructed using linear time-varying theory. A successive linearization is introduced to linearize the nonlinear tracking error model, and a quadratic programming optimization problem is then formulated. Thus, the control sequence for this AV is incorporated into the predictive control framework, and the desired controller can be solved with a relatively higher computational efficiency and lower computational cost. Finally, the effectiveness and performance of the proposed controller are validated via a comparison of simulations conducted using MATLAB software and experiments conducted using a self-established test platform. The results demonstrate that the proposed LTV-MPC method can track the prescribed reference road trajectories with high precision and stability for an AV under various driving conditions.

Prediction of Motion Simulator Signals Using Time-Series Neural Networks

A motion cueing algorithm (MCA) is employed to transform the linear and angular motion signals generated from a motion simulator without violating the physical and dynamical boundaries of the motion platform. In this respect, the accurate prediction of the motion scenarios is essential to enhance the efficiency of the MCA using prepositioning or time-varying reference model predictive control. While a recent approach that utilizes a feedforward neural network (NN) to forecast the motion scenarios is useful, the feedforward NN model has only forward dynamics relating to the signals without any feedback loop. In this article, a time-delay feedforward NN, a recurrent NN, and a nonlinear autoregressive (NAR) models with three different training procedures, i.e., Levenberg–Marquardt, Bayesian regularization, and scaled conjugate gradient, are exploited to predict the motion scenarios. As the NAR model employs the historical signals as the inputs, it can predict the motion scenarios with higher accuracy rates. Based on the series of empirical evaluations, NAR trained with Levenberg–Marquardt is able to outperform the other two counterparts in producing more accurate predictions of the motion signals. The NAR method has a lower computational load as compared with that of the recurrent NN, facilitating its real-time application. In addition to the MCA, the NAR method can be employed in other areas, including autonomous vehicles and motion sickness studies. It can also be easily implemented for air, sea, and/or land vehicle simulators for training purposes in virtual reality environments.

An Enhanced Predictive Cruise Control System Design With Data-Driven Traffic Prediction

The predictive cruise control (PCC) is a promising method to optimize energy consumption of vehicles, especially the heavy-duty vehicles (HDV). Due to the limited sensing range and computational capabilities available on-board, the conventional PCC system can only obtain a sub-optimal speed trajectory based on a shorter prediction horizon. The recently emerging information and communication technologies such as vehicular communication, cloud computing, and Internet of Things provide huge potentials to improve the traditional PCC system. In this paper, we propose a general framework for the enhanced cloud-based PCC system which integrates a data-driven traffic predictive model and the instantaneous control algorithms. Specifically, we introduce a novel multi-view CNN deep learning algorithm to predict traffic situation based on the historical and real-time traffic data collected from fields, and the time-varying adaptive model predictive control (MPC) to calculate the instantaneous optimal speed profile with the aim of minimizing energy consumption. We verified our approach via simulations in which the impact of various traffic condition on the PCC-enabled HDV has been fully evaluated.

Full-scale field test of a\xa0model predictive control system for a\xa03\u202fMW wind turbine

Model predictive control (MPC) is a strong candidate for modern wind turbine control. While the design of model predictive wind turbine controllers in simulations has been extensively investigated in academic studies, the application of these controllers to real wind turbines reveals open research challenges. In this work, we focus on the validation of a linear time-variant MPC system for a 3 MW wind turbine in a full-scale field test. First, the study proves the MPC’s capability to control the real wind turbine in the partial load region. Compared to the turbine’s baseline PID controller, the MPC system offers similar results for the electrical power output and for the occurring mechanical loads. Second, the study validates a previously proposed, simulation-based rapid control prototyping process for a systematic MPC development. The systematic development process allows to completely design and parameterize the MPC system in a simulative environment independent of the real wind turbine. Through the rapid control prototyping process, the MPC commissioning in the wind turbine’s programmable logic controller can be realized within a few hours without any modifications required in the field. Thus, this study establishes the proof of concept for a linear time-variant MPC system for a 3 MW wind turbine in a full-scale field test and bridges the gap between the control design and field testing of MPC systems for wind turbines in the multi-megawatt range.

Weight-scheduling for linear time-variant model predictive wind turbine control toward field testing

Modern multi-megawatt wind turbines require powerful control algorithms which consider several control objectives at the same time and respect process constraints. Model predictive control (MPC) is a promising control method and has been a research topic for years. So far, very few studies evaluated MPC algorithms in field tests. This work aims to prepare a real-time MPC system for a full-scale field test in a 3 MW wind turbine. To this end, we introduce a weight-scheduling scheme for a linear time-variant MPC in order to ensure control operation over the entire operating range from the partial to the full load range. We use a rapid control prototyping process, in particular with comprehensive software-in-the-loop (SiL) tests, in order to design and validate the MPC system for the field test.In this contribution, we present the implementation of the linear time-variant MPC with weight-scheduling to be tested in the field test. With the weight-scheduling for the optimization problem inside the MPC, we achieved good performance over the entire operating range of the wind turbine. In the SiL tests, the proposed MPC algorithm achieved loads, comparable to the baseline controller of the wind turbine and improved the reference tracking of the power output and the rotational speed. The proposed linear time-variant MPC with weight-scheduling is fully validated in the presented software-in-the-loop tests and is ready for full-scale field test in the 3 MW wind turbine. We present the experimental field test results of the introduced MPC system in a separated contribution.

Design of a Linear Time-Varying Model Predictive Control Energy Regulator for Grid-Tied VSCs

This article presents an energy regulator based on a Model Predictive Control (MPC) algorithm for a Voltage Source Converter (VSC). The MPC is formulated to optimise the converter performance according to the weights defined in an objective function that trades off additional features, such as current harmonic distortion, reactive power tracking and DC bus voltage oscillation. Differently from most approaches found in the research literature, the MPC proposed here considers the coupling dynamics between the AC and DC sides of the VSC. This study is focused on the example case of a single-phase VSC, which presents a nonlinear relationship between its AC and DC sides and a sustained double-line frequency power disturbance in its DC bus. To reduce the burden of the MPC, the controller is formulated to benefit from the slow energy dynamics of the system. Thus, the cascaded structure typically used in the control of VSCs is kept and the MPC is set as an energy regulator at a reduced sampling frequency while the current control relies on a fast inner controller. The computational burden of the algorithm is further reduced by using a linear time-varying approximation. The controller is presented in detail and experimental validation showing the performance of the algorithm is provided.

New Integrated Vehicle Stability Control of Active Front Steering and Electronic Stability Control Considering Tire Force Reserve Capability

To address the problem of the mutual interference and control distribution in the integrated stability control of active front steering (AFS) and electronic stability control (ESC), this study proposes a new integrated stability controller of AFS and ESC based on holistic control framework. A distribution rule of longitudinal and lateral tire force based on equal reserve capacity of tire force is designed to distribute the control right of steering and braking. A UniTire model with combined slip condition is also designed for the integrated control of steering and braking. Model predictive control (MPC) is adopted to address the constrained multi-objective control problem. To reduce the complexity of the system and improve the real-time performance of the system, a linear time-varying MPC controller is designed by linearizing the nonlinear system, and then the constrained MPC control problem is transformed into a quadratic programming problem for solving. Finally, the proposed method is validated on the basis of Matlab/Simulink and CarSim co-simulation platform. Results show that the proposed method has obvious effects on solving the mutual interference and control right distribution of steering and braking and improving vehicle stability.

Performance improvement of an air-to-water heat pump through linear time-varying MPC with adaptive COP predictor

Air-to-water heat pumps are one of the most common and energy efficient heating systems for buildings, particularly floor-heating plants. One way to further improve their effectiveness is to control the heat pump exploiting the dependence of its coefficient of performance (COP) on the external temperature and temperature of the return water from the load. In particular, it is possible to exploit the heat pump when its efficiency is higher, so optimizing its performance in a predictive manner, anticipating the impact of external conditions. For the case of an air-to-water heat pump, the optimization problem is nonlinear due to the load dependence of the heat pump COP and variable supply water flow rate. This may pose implementation problems. If we address a standard control hardware, simplified optimal control formulations are more effective. In this paper, we specifically address this issue, and a reduced-order, linear, but adaptive time-varying predictive model of the heat pump COP is designed. Our solution takes into account the variation of the heat pump efficiency based on the external temperature and the load profile, which are changing within the control horizon. The proposed COP model is then used within a linear time-varying model predictive controller formulation which provides a prediction of the heat pump dynamical behavior based on the load dependence of the heat pump COP, while tackling the nonlinearities of the system imposed by the variable water flow rate in the hot water tank and also by the load dependence of the heat pump COP. The proposed approach has been implemented and in detail tested on a reference model based on a real case study from the Denmark Technical University, Risø Campus, SYSLAB. An intensive simulation analysis and complements the testing, showing the accuracy and the potential of the method, also in the perspective of practical implementation.

Time-Varying Tube-Based Output Feedback MPC for Constrained Linear Systems with Intermittently Delayed Data

Abstract This paper proposes a time-varying tube-based output feedback model predictive control (MPC) design for constrained linear systems in the presence of intermittently delayed observations, where the delayed/missing data patterns for each period satisfy a finite-length language. The design consists of a dynamic state estimator whose estimation errors satisfy equalized recovery (a weaker form of invariance with time-varying finite bounds), as well as an output feedback control law that extends existing tube-based output feedback MPC approaches to allow time-varying tubes for tightening the original state and input constraints. The resulting time-varying tube-based output feedback MPC design is robust to time-varying disturbances and errors, including when the observations are intermittently delayed. Further, we provide sufficient conditions for recursive feasibility and robust exponential stability of the proposed design. Simulation results demonstrate that the proposed approach is able to robustly stabilize and control a constrained linear system despite disturbances, noise and missing/delayed data.

Relative navigation control of articulated vehicle based on LTV-MPC

The automation of the articulated vehicle is an important trend of the intelligent transportation system in the mining industry. And the relative navigation is a key technology to automatic vehicles. One of the challenges in the relative navigation of the articulated vehicle is that the system constraints may cause the actuator saturation and other problems. In order to solve these problems, this paper presents a relative navigation control method based on linear time varying model predictive control (LTV-MPC). This control method can explicitly take the system constraints into account. The performance of the controller is verified by simulation and experiment. The results show that the articulated vehicle with the LTV-MPC controller can track the target heading direction, the steady-state error is less than 0.3 rad. The relative navigation controller based on LTV-MPC can be used to improve the automatic driving performance of the articulated vehicle.

MPC Based Vehicular Trajectory Planning in Structured Environment

In this paper, the hierarchical architecture of trajectory planning and control is set up for safe driving with multiple participants without collision, where both levels utilize a time-varying model predictive control methodology. Firstly, a high-level planner formulates an optimal control problem to obtain an optimal trajectory while satisfying different constraints. In particular, due to obstacles’ occupation, several partition functions are generated as linear collision constraints through an optimization process in order to convexify the collision-free region into sub-regions. Secondly, the low-level controller receives the desired trajectory from the high-level planner, and then computes an appropriate steering angle to execute the planned maneuver. Both levels are formulated within the model predictive control(MPC) methodology. The strength of this framework is that it combines different constraints in each optimal control problem. Including a high-level planner ensures the feasibility of safe trajectory planning and the use of a low-level controller ensures tracking stability for safe driving, even under various collision constraints and model mismatch between system plant and predictive process model. Finally, several simulations verified the proposed framework, which was used to compute an optimal, safe trajectory over a set of static or moving obstacles and stabilize the vehicle around it.

Fault-Tolerant Control for Intelligent Electrified Vehicles Against Front Wheel Steering Angle Sensor Faults During Trajectory Tracking

Steer-by-Wire (SBW) systems are an integral and essential component of intelligent electrified vehicles and are critical to ensure safe vehicle operations. In this paper, a fault-tolerant control method for SBW is proposed to mitigate the adverse influence of front wheel steering angle sensor faults based on the Kalman filtering technique. First, a linearized vehicle model is derived based on tire characteristics and is further combined with a steering actuator model to provide the modelling foundation for estimating the front wheel steering angle. Considering multi-source noises and their significant influence on the front wheel steering angle sensor, the Butterworth filter is employed to filter out the high-frequency noises. The front wheel steering angle estimation is realized by incorporating the measurements of the yaw rate and lateral acceleration of vehicle and the current of steering motor. In particular, a dynamic threshold mechanism is adopted to activate the fault diagnosis and fault-tolerant compensation based on the residual theory. Finally, a linear time-varying model predictive controller is presented to execute the trajectory tracking task for an intelligent electrified vehicle. The effectiveness of the proposed scheme is verified under the single lane change and double lane change maneuvers during the trajectory tracking.

Trajectory planning and tracking control of unmanned ground vehicle leading by motion virtual leader on expressway

Formation driving can effectively solve the problem of driving efficiency and safety of unmanned ground vehicles (UGVs) on expressways. This study introduces a trajectory planning and tracking control method from initial position to its motion virtual leader in formation driving. In order to reduce the disturbance to the surrounding UGVs, trajectory planning is divided into two stages: steady speed tracking stage and parameter value matching stage. A tracking controller combined with a trajectory planner is designed to track the reference trajectory accurately. To ensure calculation speed and accuracy, a nonlinear model-predictive control model is used in the trajectory planner, and the tracking controller is based on the linear time-varying model-predictive control (LTV MPC) model. Simulations are carried out with Carsim and MATLAB/Simulink, and the simulation results and comparative analysis show that the planned trajectory is feasible and can effectively avoid static and moving obstacles. Compared with the Stanley controller, the LTV MPC controller has the advantages of faster convergence speed, better stability and accurately tracking.

On the Distributed Path Planning of Multiple Autonomous Vehicles Under Uncertainty Based on Model-Predictive Control and Convex Optimization

In this article, a fully distributed control structure named distributed linear time-varying model predictive controller is proposed for motion control of multiple vehicles in dynamic environments with uncertainty resources based on local communication and local controllers. Efficient operation of this structure in such real-world conditions needs reasoning about the future and the uncertainties over environmental objects; therefore, future evolution of vehicles and environmental objects is accounted as a planning strategy. A general planning framework is proposed, which integrates estimation, prediction, and planning. Simulation results for different dynamic scenarios demonstrate the benefit and applicability of this approach.

Energy Management of the Power-Split Hybrid Electric City Bus Based on the Stochastic Model Predictive Control

The energy management strategy of hybrid electric vehicles is of significant importance to improve the fuel economy. In this regard, two energy management strategies are designed for power-split hybrid electric city bus (HECB), which are based on the linear time-varying stochastic model predictive control (LTV-SMPC) and stochastic model predictive control based on Pontriagin’s minimum principle (PMP-SMPC). In the present study, the Markov chain and long short-term memory (LSTM) forecast demand torque and velocity respectively are applied to establish a combination forecast model. Then several processes, including linear approximation, processing simplified control model, the proposed nonlinear vehicle model is converted into a linear time-varying model. Meanwhile, the energy management problem in a linear quadratic programming problem is solved. Considering linearization error and limitations of the quadratic optimization, Pontriagin’s minimum principle (PMP) is applied to optimize the nonlinear model predictive control. Based on the reference theory, the range of coordinated variables is derived, and the optimal coordination variable is searched by dichotomy to realize the rolling optimization of the model predictive control (MPC). Finally, the effectiveness of the proposed energy management strategy is verified by simulating several case studies. Obtained results show that compared with the rule-based (RB) control strategy, the fuel economy of LTV-SMPC and PMP-SMPC increases by 8.79% and 14.42%, respectively. Meanwhile, it is concluded that the two strategies have real-time computing potential.

Modeling, Simulation, and Vision-/MPC-Based Control of a PowerCube Serial Robot

A model predictive control (MPC) scheme for a Schunk PowerCube robot is derived in a structured step-by-step procedure. Neweul-M2 provides the necessary nonlinear model in symbolical and numerical form. To handle the heavy online computational burden concerning the derived nonlinear model, a linear time-varying MPC scheme is developed based on linearizing the nonlinear system concerning the desired trajectory and the a priori known corresponding feed-forward controller. Camera-based systems allow sensing of the robot on the one hand and monitoring the environments on the other hand. Therefore, a vision-based MPC is realized to show the effects of vision-based control feedback on control performance. A semi-automatic trajectory planning is used to perform two meaningful experimental studies in which the advantages and restrictions of the proposed (vision-based) linear time-varying MPC scheme are pointed out. Everything is implemented on a slim, low-cost control system with a standard laptop PC.

Modeling, simulation, and vision-/MPC-based control of a PowerCube serial robot

A model predictive control (MPC) scheme for a Schunk PowerCube robot is derived in a structured step-by-step procedure. Neweul-M2 provides the necessary nonlinear model in symbolical and numerical form. To handle the heavy online computational burden concerning the derived nonlinear model, a linear time-varying MPC scheme is developed based on linearizing the nonlinear system concerning the desired trajectory and the a priori known corresponding feed-forward controller. Camera-based systems allow sensing of the robot on the one hand and monitoring the environments on the other hand. Therefore, a vision-based MPC is realized to show the effects of vision-based control feedback on control performance. A semi-automatic trajectory planning is used to perform two meaningful experimental studies in which the advantages and restrictions of the proposed (vision-based) linear time-varying MPC scheme are pointed out. Everything is implemented on a slim, low-cost control system with a standard laptop PC.

Human-Like Obstacle Avoidance Trajectory Planning and Tracking Model for Autonomous Vehicles That Considers the River's Operation Characteristics.

Developing a human-like autonomous driving system has gained increasing amounts of attention from both technology companies and academic institutions, as it can improve the interpretability and acceptance of the autonomous system. Planning a safe and human-like obstacle avoidance trajectory is one of the critical issues for the development of autonomous vehicles (AVs). However, when designing automatic obstacle avoidance systems, few studies have focused on the obstacle avoidance characteristics of human drivers. This paper aims to develop an obstacle avoidance trajectory planning and trajectory tracking model for AVs that is consistent with the characteristics of human drivers’ obstacle avoidance trajectory. Therefore, a modified artificial potential field (APF) model was established by adding a road boundary repulsive potential field and ameliorating the obstacle repulsive potential field based on the traditional APF model. The model predictive control (MPC) algorithm was combined with the APF model to make the planning model satisfy the kinematic constraints of the vehicle. In addition, a human driver’s obstacle avoidance experiment was implemented based on a six-degree-of-freedom driving simulator equipped with multiple sensors to obtain the drivers’ operation characteristics and provide a basis for parameter confirmation of the planning model. Then, a linear time-varying MPC algorithm was employed to construct the trajectory tracking model. Finally, a co-simulation model based on CarSim/Simulink was established for off-line simulation testing, and the results indicated that the proposed trajectory planning controller and the trajectory tracking controller were more human-like under the premise of ensuring the safety and comfort of the obstacle avoidance operation, providing a foundation for the development of AVs.

Fault-Tolerant Model Predictive Control Algorithm for Path Tracking of Autonomous Vehicle.

The fault detection and isolation are very important for the driving safety of autonomous vehicles. At present, scholars have conducted extensive research on model-based fault detection and isolation algorithms in vehicle systems, but few of them have been applied for path tracking control. This paper determines the conditions for model establishment of a single-track 3-DOF vehicle dynamics model and then performs Taylor expansion for modeling linearization. On the basis of that, a novel fault-tolerant model predictive control algorithm (FTMPC) is proposed for robust path tracking control of autonomous vehicle. First, the linear time-varying model predictive control algorithm for lateral motion control of vehicle is designed by constructing the objective function and considering the front wheel declination and dynamic constraint of tire cornering. Then, the motion state information obtained by multi-sensory perception systems of vision, GPS, and LIDAR is fused by using an improved weighted fusion algorithm based on the output error variance. A novel fault signal detection algorithm based on Kalman filtering and Chi-square detector is also designed in our work. The output of the fault signal detector is a fault detection matrix. Finally, the fault signals are isolated by multiplication of signal matrix, fault detection matrix, and weight matrix in the process of data fusion. The effectiveness of the proposed method is validated with simulation experiment of lane changing path tracking control. The comparative analysis of simulation results shows that the proposed method can achieve the expected fault-tolerant performance and much better path tracking control performance in case of sensor failure.

Decision Making, Planning, and Control Strategies for Intelligent Vehicles

The intelligent vehicle will play a crucial and essential role in the development of the future intelligent transportation system, which is developing toward the connected driving environment, ultimate driving safety, and comforts, as well as green efficiency. While the decision making, planning, and control are extremely vital components of the intelligent vehicle, these modules act as a bridge, connecting the subsystem of the environmental perception and the bottom-level control execution of the vehicle as well. This short book covers various strategies of designing the decision making, trajectory planning, and tracking control, as well as share driving, of the human-automation to adapt to different levels of the automated driving system. More specifically, we introduce an end-to-end decision-making module based on the deep Q-learning, and improved path-planning methods based on artificial potentials and elastic bands which are designed for obstacle avoidance. Then, the optimal method based on the convex optimization and the natural cubic spline is presented. As for the speed planning, planning methods based on the multi-object optimization and high-order polynomials, and a method with convex optimization and natural cubic splines, are proposed for the non-vehicle-following scenario (e.g., free driving, lane change, obstacle avoidance), while the planning method based on vehicle-following kinematics and the model predictive control (MPC) is adopted for the car-following scenario. We introduce two robust tracking methods for the trajectory following. The first one, based on nonlinear vehicle longitudinal or path-preview dynamic systems, utilizes the adaptive sliding mode control (SMC) law which can compensate for uncertainties to follow the speed or path profiles. The second one is based on the five-degrees-of-freedom nonlinear vehicle dynamical system that utilizes the linearized time-varying MPC to track the speed and path profile simultaneously. Toward human-automation cooperative driving systems, we introduce two control strategies to address the control authority and conflict management problems between the human driver and the automated driving systems. Driving safety field and game theory are utilized to propose a game-based strategy, which is used to deal with path conflicts during obstacle avoidance. Driver's driving intention, situation assessment, and performance index are employed for the development of the fuzzy-based strategy. Multiple case studies and demos are included in each chapter to show the effectiveness of the proposed approach. We sincerely hope the contents of this short book provide certain theoretical guidance and technical supports for the development of intelligent vehicle technology.