Offline Robust Model Predictive Control for Autonomous Vehicle Steering Systems Using LMI-Based Optimization

Abstract

The well-known offline robust model predictive control (RMPC) effectively addresses uncertain parameters for autonomous vehicle systems. However, it requires memory to save the variable and more computation time to search the lookup table to find the best values of the weighting matrices. To address these issues, this article introduces a new offline RMPC approach for enhancing the steering control of autonomous vehicles (AVs) using linear matrix inequality (LMI) optimization that can eliminate storing variables and lookup tables. In order to effectively handle the potential uncertainties associated with the vehicle system parameters, such as total vehicle mass, front and rear cornering stiffness, and varying vehicle speeds by confining them within a defined polytope. By utilizing the polytopic uncertainty method, the offline RMPC is designed to handle a wide range of parameter variations within the defined polytope. Specifically, by defining the upper bound of the cost function as a quadratic form, an offline RMPC method is directly designed, resulting in a significant reduction in the computation burden. Moreover, optimal control is designed by solving an optimization problem based on LMI, allowing the use of efficient convex optimization algorithms. Input and output constraints are enforced to guarantee the safe operation of the AV system in complex and dynamic environments. Finally, the simulation results are presented and compared with the existing studies to demonstrate the effectiveness of our approach. Additionally, co-simulation based on Matlab and Simulink and CarSim software were also conducted to further verify the proposed method. The results show that all state variables satisfy the enforced constraints, and both the path-tracking trajectory performance and execution time are better than those of recent research.