Preview Control Theory Research Articles

Robust Preview Path Tracking Control of Autonomous Vehicles Under Time-Varying System Delays and Saturation

Realistic uncertainties and disturbances cannot be ignored when striving towards high-performance autonomous driving. Meanwhile, advanced vehicular sensing technology enables more and more self-driving techniques to come out. Against this backdrop, this paper aims to holistically address the system uncertainties and disturbances in the path tracking control of autonomous vehicles (AVs) by the preview control theory to achieve superior control performance. First, unmeasureable multi-uncertainties and the external disturbance are considered simultaneously into the robust gain-scheduling framework with variable longitudinal velocity. Then, by the equivalent delay approach, ineluctable time-varying system delays are effectively handled. Next, the physical constraints of the steering system and direct yaw moment control (DYC) system are considered for practical implementation through robust set invariance theory. The parallel distributed compensation (PDC) technique and auxiliary feedback matrices approach are introduced for reducing design conservatism. After that, by incorporating the road curvature into the augmented system state, the path tracking preview control problem can be solved without online optimization. Thereafter, the closed-loop system stability and guaranteed performance have been proved through the Lyapunov- Krasovski approach. The proposed controller design is finally reformulated as the optimization problem based on linear matrix inequalities (LMIs) via specific convexification techniques. Finally, to verify the validity of the proposed controller, Software in Loop (SIL) tests with Carsim full-vehicle model under different dynamic conditions have been implemented.

Research on Trajectory Tracking of Sliding Mode Control Based on Adaptive Preview Time

The preview model is one of the common methods used in trajectory tracking. The traditional fixed preview time is not adaptable to most speeds and road conditions, which not only reduces the tracking accuracy but also reduces the vehicle stability. Therefore, a controller can be designed to determine the adaptive preview time based on an optimization function of the lateral deviation, the road boundary, and the road boundary of the whole vehicle motion response characteristics. Traditional optimal preview control theory predicts the next state of the vehicle by the assumption of constant transverse pendulum angular velocity. In this paper, an expectation-based approach is used to find the ideal steering wheel turning angle based on the adaptive preview time, and a single-point preview model is established. Based on the two-degree-of-freedom dynamics model, a sliding mode controller is designed for control, and the low-pass filters are designed to suppress jitter in the sliding mode controller. Simulation results with different preview times, different speeds and different road adhesion coefficients prove that the controller has a good control effect and has good effectiveness and adaptability to speed and adhesion coefficient.

Modeling adaptive preview time of driver model for intelligent vehicles based on deep learning

In order to improve the adaptability and tracking performance of intelligent vehicles under complex driving conditions, and simulate the manipulation characteristics of the real driver in the driver–vehicle–road closed-loop system, a kind of adaptive preview time model for intelligent vehicle driver model is proposed. This article builds the intelligent vehicle driver model based on optimal preview control theory and the basic preview time is identified to minimize path error under various conditions based on particle swarm optimization. Then, the ideal compensation preview time is constructed in various conditions and the appropriate factors affecting compensation preview time are filtered out according to correlation analysis. Moreover, the architecture and training procedure of deep network is specified for compensation preview time prediction. Finally, the adaptive preview time is modeled by combining the basic preview time with the compensation preview time and the validity of adaptive preview time model is verified by the driver–vehicle–road closed-loop system under normal and aggressive driving conditions. The results show that the proposed adaptive preview time model can help intelligent vehicles better adapt complex driving conditions and effectively improve the path-following performance.

Design of an optimal preview controller for linear discrete-time periodic systems

In this paper, the preview tracking control problem for linear discrete-time periodic systems is considered. First, to overcome the difficulty arising from periodicity of the system, the linear discrete-time periodic system is transformed into an ordinary time-invariant system by lifting method. Secondly, the difference between a system state and its steady-state value is used to derive an augmented system instead of the usual difference between system states. Then, the preview controller for the augmented system is proposed by the preview control theory, which solves the preview tracking control problem for the periodic systems. Moreover, an integrator is introduced to ensure that the output can track the reference signal without static error. Finally, the obtained results are illustrated by the simulation examples.

Modeling human-like longitudinal driver model for intelligent vehicles based on reinforcement learning

The driver model is the decision-making and control center of intelligent vehicle. In order to improve the adaptability of intelligent vehicles under complex driving conditions, and simulate the manipulation characteristics of the skilled driver under the driver-vehicle-road closed-loop system, a kind of human-like longitudinal driver model for intelligent vehicles based on reinforcement learning is proposed. This paper builds the lateral driver model for intelligent vehicles based on optimal preview control theory. Then, the control correction link of longitudinal driver model is established to calculate the throttle opening or brake pedal travel for the desired longitudinal acceleration. Moreover, the reinforcement learning agents for longitudinal driver model is parallel trained by comprehensive evaluation index and skilled driver data. Lastly, training performance and scenarios verification between the simulation experiment and the real car test are performed to verify the effectiveness of the reinforcement learning based longitudinal driver model. The results show that the proposed human-like longitudinal driver model based on reinforcement learning can help intelligent vehicles effectively imitate the speed control behavior of the skilled driver in various path-following scenarios.

Research on intelligent vehicle trajectory tracking based on model predictive control

Intelligent vehicle trajectory tracking lateral control is the key technology to realize intelligent driving. Aiming at the problems that the existing control methods have a small effective control area and poor control effect under cornering conditions or small road adhesion coefficients, a model predictive control (MPC) algorithm is proposed for trajectory tracking control. Based on the two-degree-of-freedom vehicle model, a state space equation is established and discretized to obtain a predictive model that meets the conditions. Then, the corresponding objective function is designed based on the ideal yaw angular velocity under the optimal preview control theory, and the input-output constraints and side-slip angle constraints are designed according to the control and state quantities. The controller model is established in MATLAB / Simulink, and the road model is built in CarSim for joint simulation. Compared with CarSim’s own algorithm, the changes in side acceleration and steering wheel angle are smoother and less oscillating. The maximum lateral deviation and lateral acceleration are also smaller, and the lateral stability of the car is improved. It has better adaptability on pavement with lower adhesion coefficient, and can also maintain control stability. The real vehicle test results are consistent with the simulation results, with a maximum lateral error of 0.44m and a maximum heading angle deviation of 1.43 °. Therefore, the trajectory tracking control algorithm based on model predictive control designed in this paper has significantly improved control accuracy and stability, and can maintain control stability even when the road surface adhesion coefficient is low.

Preview Path Tracking Control With Delay Compensation for Autonomous Vehicles

Delay and lag deteriorate path tracking accuracy and system stability. If not properly compensated, they can cause instability or limit the driving speed of autonomous vehicles. This paper presents a preview steering control design considering both communication delay and steering lag to achieve accurate, smooth, and computationally efficient path tracking for highly automated vehicles. Two strategies are adopted for the delay: forward state predictor and delay augmentation. The steering lag is approximated by a first-order lag system. The path tracking problem with delay and lag is solved by the preview control theory. The resulted controller is in an analytical form and is computationally efficient for online implementation. We also analyze the system stability and closed-loop responses in both the time and frequency domain. The control is implemented on an automated vehicle platform and tested inside Mcity and on open roads. Experimental results showed lower tracking errors and significantly improved stability margin compared to the controls ignoring delay and lag.

Optimal Tracking Control for Discrete-time Systems with Time-delay Based on the Preview Control Method

Abstract In this paper, the optimal tracking control problem for discrete-time with state and input delays is studied based on the preview control method. First, a transformation is introduced. Thus, the system is transformed into a non-delayed system and the tracking problem of the time-delay system is transformed into the regulation problem of a non-delayed system via processing of the reference signal. Then, by applying the preview control theory, an augmented system for the non-delayed system is derived, and a controller with preview function is designed, assuming that the reference signal is previewable. Finally, the optimal control law of the augmented error system and the optimal control law of the original system are obtained by letting the preview length of the reference signal go to zero.

The preview control of a class of linear systems and its application in the fault-tolerant control theory

ABSTRACTIn the fault-tolerant control theory based on model following control, the desired signal of the control system is the output of a reference system. This paper is concerned with the design of the preview controller for a class of fault systems. A composite vector is introduced by including error vector, fault system state vector and reference system state vector. Then, we derived an augmented system from the known system equation, in which the reference input has equal status with the desired signal in the traditional preview control theory. Therefore, we can use the known theory to design the preview controller for the augmented system, then the preview controller of the original fault system can be obtained by the integration method. This paper strictly discusses the connection between stabilisation and detectability of the augmented system and the corresponding characteristics of the original system. Finally, by applying this theory to a real steam generator water level control system, it is found that the actions of the reference input preview and the fault signal preview can effectively eliminate the effect of the fault signal on the water level of the steam generator. The simulation shows the effectiveness of the controller designed.

A Method for Bipedal Robot Locomotion Control along an Arbitrary Trajectory

This paper presents an algorithm for stable bipedal walking control along an arbitrary curve. The algorithm starts with a foot planner, which takes a parametrically defined desired path as an input and calculates feet positions and orientations at each step. Zero moment point (ZMP) concept is used for robot stability control. The dynamics of the robot is modeled as a running cart on a table. Given the reference ZMP trajectory, ZMP tracking servo controller based on preview control theory is used to calculate robot’s center of mass (CoM) trajectory. The preview controller is made of three terms: the integral error of ZMP, the state feedback proportional to a current state vector and the preview action which takes into account future values of the desired ZMP position. We propose robot’s state estimator based on linear Kalman filter with measured CoM acceleration and position as system inputs. Swing foot trajectories are calculated using trigonometric functions, since they are simple and can provide zero velocities at contact moments. We put some additional constraints on a system by assuming that there is no forward-backward inclination of the robot trunk and swing foot is always parallel to the ground. To avoid kinematic limits in hip and ankle roll joints we calculate a minimal angle to rotate robot trunk in frontal plane. After position and orientation of robot trunk and swing foot are found we apply inverse kinematics solution for robot legs to get robot joint angles. Finally, joint angles are sent to robot actuators. Software package based on ROS operating system was developed for AR601 robot. Verification tests were executed with robot model in Gazebo simulator. The robot successfully completed series of experiments confirming modelling results.

Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

Design of an Optimal Preview Controller for Dual-Rate Linear Discrete-Time Systems

Abstract A dual-rate preview control strategy for a type of discrete-time system is proposed based on the theory of multirate control. First, by using the discrete lifting technique, the general dual-rate discrete-time system is converted into a single-rate augmented system. On this basis, the augmented error system is constructed by introducing a first-order difference operator and the previewable reference signal. Then the tracking problem is transformed into a regulator problem of the augmented error system. The optimal preview control law of the augmented error system is obtained by using standard linear quadratic optimal preview control theory, and then the optimal preview controller of the original system is derived. In addition, the necessary and sufficient conditions for the controller are given. Finally, simulation results show the effectiveness of the proposed method.

Design of Preview Controller for Linear Continuous-time Systems with Input Delay

This paper makes it possible to design a preview controller for linear continuous-time systems with input delay, which expands the preview control theory. An augmented error system is established. And a variable substitution is used to transform the delay preview control system into a delay-free one whose preview controller uses the future value of the augmented state vector. The future value of the augmented state vector is estimated by the information of the current state vector, the control input on the past time window, and the reference signal on the future time window. Under the assumption of zero initial conditions, a simplified controller with both delay compensation and preview compensation is obtained for the original system. In addition, a preview controller with full-order observer is offered. Finally, simulation results are presented to illustrate the effectiveness and robustness of the controller.

Preview tracking control for a class of discrete-time Lipschitz non-linear time-delay systems

AbstractThe design of a preview tracking controller for a class of discrete-time Lipschitz non-linear time-delay systems is considered in this paper. First, based on preview control theory, we introduce a difference operator and deduce an augmented error system which contains previewable information on the reference signal. The original tracking problem is thus transformed into a regulation problem. Second, we design a memory state feedback controller for the augmented error system. Applying Lyapunov’s second method, the sufficient condition for stability of the closed-loop system is derived in the form of linear matrix inequality (LMI), and the preview controller is obtained accordingly. Finally, to show the superiority of the controller proposed, two numerical examples are presented.

Cooperative optimal preview tracking for linear descriptor multi-agent systems

In this paper, a cooperative optimal preview tracking problem is considered for continuous-time descriptor multi-agent systems with a directed topology containing a spanning tree. By the acyclic assumption and state augmentation technique, it is shown that the cooperative tracking problem is equivalent to local optimal regulation problems of a set of low-dimensional descriptor augmented subsystems. To design distributed optimal preview controllers, restricted system equivalent (r.s.e.) and preview control theory are first exploited to obtain optimal preview controllers for reduced-order normal subsystems. Then, by using the invertibility of restricted equivalent relations, a constructive method for designing distributed controller is presented which also yields an explicit admissible solution for the generalized algebraic Riccati equation. Sufficient conditions for achieving global cooperative preview tracking are proposed proving that the distributed controllers are able to stabilize the descriptor augmented subsystems asymptotically. Finally, the validity of the theoretical results is illustrated via numerical simulation.

Braking Control in Railway Vehicles: A Distributed Preview Approach

The braking control problem for railway vehicles is considered. Communication flow from the front coaches to the rear ones is introduced, and a novel distributed braking control algorithm is proposed that, based on preview control theory, allows one to reduce the stopping distance. The effectiveness of the designed algorithm is corroborated by simulation comparisons to other standard approaches.

Cooperative global optimal preview tracking control of linear multi-agent systems: an internal model approach

ABSTRACTThis paper investigates the cooperative global optimal preview tracking problem of linear multi-agent systems under the assumption that the output of a leader is a previewable periodic signal and the topology graph contains a directed spanning tree. First, a type of distributed internal model is introduced, and the cooperative preview tracking problem is converted to a global optimal regulation problem of an augmented system. Second, an optimal controller, which can guarantee the asymptotic stability of the augmented system, is obtained by means of the standard linear quadratic optimal preview control theory. Third, on the basis of proving the existence conditions of the controller, sufficient conditions are given for the original problem to be solvable, meanwhile a cooperative global optimal controller with error integral and preview compensation is derived. Finally, the validity of theoretical results is demonstrated by a numerical simulation.

Parameter‐dependent preview control with robust tracking performance

The problem of static output feedback preview tracking control is proposed for a class of polytopic uncertain discrete-time systems by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) technique. First, the error system method of preview control theory is adopted and the difference operator is introduced, and then an augmented error system including previewed information is constructed, which transforms a tracking problem into a regulation problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the derived augmented error system while considering the output feedback. Sufficient conditions for designing a robust static feedback preview controller are given in terms of solutions to a set of LMIs. Based on the criterion, a static output feedback controller with preview action is designed such that the output can asymptotically track the reference signal. Finally, the numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the study.

Adaptive preview control for piecewise discrete-time systems using multiple models

In this paper, the problem of multi-model adaptive preview control is proposed for discrete-time systems with unknown piecewise constant coefficients. Following preview control theory, corresponding augmented error systems for piecewise discrete-time systems are constructed. By making use of the Heine–Borel covering theorem, a finite set of fixed augmented systems covering the range of the unknown parameters is established, and associated fixed preview controllers are derived. Based on the core idea of multi-model adaptive control, switching law of the controllers is designed, and eventually, an adaptive preview controller is obtained. The exponential asymptotic stability of closed-loop systems with large uncertainties is discussed in detail. Finally, simulation results are given to demonstrate the effectiveness of the theoretical results.

The Application of Predictor Feedback in Designing a Preview Controller for Discrete-Time Systems with Input Delay

This paper presents a method for designing a type one servomechanism for a discrete-time linear system with input delay subject to a previewable desired output and a nonmeasurable constant disturbance. The tracking problem of a delay system is transformed into a regulation problem of a delay-free system via constructing an augmented error system and a variable substitution. A controller is obtained with delay compensation and preview compensation based on preview control theory and the predictor method. When the state vector is not directly measurable, a full-dimensional observer is offered. The effectiveness of the design method is demonstrated by numerical simulations.