Matrix Inequalities Based Robust Model Predictive Control for Vehicle Considering Model Uncertainties, External Disturbances, and Time-Varying Delay

In this paper, we design a robust model predictive control (MPC) controller for vehicle subjected to bounded model uncertainties, norm-bounded external disturbances and bounded time-varying delay. A Lyapunov-Razumikhin function (LRF) is adopted to ensure that the vehicle system state enters in a robust positively invariant (RPI) set under the control law. A quadratic cost function is selected as the stage cost function, which yields the upper bound of the infinite horizon cost function. A Lyapunov-Krasovskii function (LKF) candidate related to time-varying delay is designed to obtain the upper bound of the infinite horizon cost function and minimize it at each step by using matrix inequalities technology. Then the robust MPC state feedback control law is obtained at each step. Simulation results show that the proposed vehicle dynamic controller can steer vehicle states into a very small region near the reference tracking signal even in the presence of external disturbances, model uncertainties and time-varying delay. The source code can be downloaded on https://github.com/wenjunliu999.

[1]  Milan Simic,et al.  Receding horizon lateral vehicle control for pure pursuit path tracking , 2018 .

[2]  Defeng He,et al.  Delayed Feedback MPC Algorithms of Vehicle Platoons Subject to Constraints on Measurement Range and Driving Behaviors , 2018 .

[3]  Hamid Reza Karimi,et al.  Synchronization of Network Systems via Aperiodic Sampled-Data Control With Constant Delay and Application to Unmanned Ground Vehicles , 2020, IEEE Transactions on Industrial Electronics.

[4]  Ilya V. Kolmanovsky,et al.  Lyapunov Methods for Time-Invariant Delay Difference Inclusions , 2012, SIAM J. Control. Optim..

[5]  G. Feng,et al.  Robust model predictive control of discrete-time uncertain linear systems with persistent disturbances , 2013, 2013 IEEE International Conference on Cyber Technology in Automation, Control and Intelligent Systems.

[6]  Zhong-Ping Jiang,et al.  Input-to-state stability for discrete-time nonlinear systems , 1999 .

[7]  Meng Joo Er,et al.  Fast and Accurate Trajectory Tracking Control of an Autonomous Surface Vehicle With Unmodeled Dynamics and Disturbances , 2016, IEEE Transactions on Intelligent Vehicles.

[8]  Arthur G. Richards,et al.  Robust constrained model predictive control , 2005 .

[9]  A. Teel.  Connections between Razumikhin-type theorems and the ISS nonlinear small gain theorem , 1998, IEEE Trans. Autom. Control..

[10]  Mohammad Haeri,et al.  Integrated guidance and control of elastic flight vehicle based on robust MPC , 2015 .

[11]  Yifan Tang,et al.  Preview Path Tracking Control With Delay Compensation for Autonomous Vehicles , 2021, IEEE Transactions on Intelligent Transportation Systems.

[12]  Huajin Tang,et al.  Event-Based Neuromorphic Vision for Autonomous Driving: A Paradigm Shift for Bio-Inspired Visual Sensing and Perception , 2020, IEEE Signal Processing Magazine.

[13]  Andrew R. Teel,et al.  Input-to-state stability analysis for interconnected difference equations with delay , 2012, Math. Control. Signals Syst..

[14]  Youyi Wang,et al.  Fuzzy Model Predictive Control of Discrete-Time Systems with Time-Varying Delay and Disturbances , 2018, IEEE Transactions on Fuzzy Systems.

[15]  Amir Khajepour,et al.  A study on actuator delay compensation using predictive control technique with experimental verification , 2019 .

[16]  Xin Zhang,et al.  A Model Predictive Controller With Switched Tracking Error for Autonomous Vehicle Path Tracking , 2019, IEEE Access.

[17]  M. Kothare,et al.  Robust constrained model predictive control using linear matrix inequalities , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[18]  Andreas Hansen,et al.  A Computationally Efficient Predictive Controller for Lane Keeping of Semi-Autonomous Vehicles , 2014 .

[19]  Mohammed Chadli,et al.  Constrained model predictive control for time-varying delay systems: Application to an active car suspension , 2016 .

[20]  PooGyeon Park,et al.  Constrained MPC algorithm for uncertain time-varying systems with state-delay , 2005, IEEE Trans. Autom. Control..

[21]  Xu Wang,et al.  Robust Model Predictive Control for Path Tracking of a Tracked Vehicle with a Steerable Trailer in the Presence of Slip , 2016 .

[22]  G. Duan,et al.  LMIs in Control Systems: Analysis, Design and Applications , 2013 .

[23]  Ping Wang,et al.  An MPC-based manoeuvre stability controller for full drive-by-wire vehicles , 2019 .

[24]  Nasser L. Azad,et al.  Adaptive Tube-Based Nonlinear MPC for Economic Autonomous Cruise Control of Plug-In Hybrid Electric Vehicles , 2018, IEEE Transactions on Vehicular Technology.

[25]  David Q. Mayne,et al.  Constrained model predictive control: Stability and optimality , 2000, Autom..

[26]  Gang Feng,et al.  Robust Model Predictive Control for Discrete-Time Takagi–Sugeno Fuzzy Systems With Structured Uncertainties and Persistent Disturbances , 2014, IEEE Transactions on Fuzzy Systems.

[27]  Shuo Cheng,et al.  Robust LMI-Based H-Infinite Controller Integrating AFS and DYC of Autonomous Vehicles With Parametric Uncertainties , 2021, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[28]  Kunsoo Huh,et al.  Active Front Steering for Driver’s Steering Comfort and Vehicle Driving Stability , 2019, International Journal of Automotive Technology.

[29]  Zhiheng Li,et al.  Comprehensive Predictive Control Method for Automated Vehicles With Delays , 2019, IEEE Access.

[30]  Jiaxing Yu,et al.  Robust Model Predictive Control for Path Tracking of Autonomous Vehicle , 2019, SAE technical paper series.

[31]  Rajesh Rajamani,et al.  Vehicle dynamics and control , 2005 .

[32]  Yingbai Hu,et al.  Mobile Robot Learning from Human Demonstrations with Nonlinear Model Predictive Control , 2019, 2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[33]  Zheng Chen,et al.  A Novel Lane Change Decision-Making Model of Autonomous Vehicle Based on Support Vector Machine , 2019, IEEE Access.