Model Predictive Controller Weight Tuning and Real-Time Learning-Based Weight Selection

Abstract

A variety of control systems with specific goals are designed and utilized in every vehicle system. Optimal performance of each of these control systems is essential to keep the vehicle in a safe and desirable driving condition. A model predictive controller (MPC) is a type of control system that employs an internal model of the system being controlled to predict its future behavior and determine the optimal control actions to achieve desired outcomes. The controller works by continuously updating its predictions based on the current state of the system and using an optimization algorithm to calculate the best control actions while satisfying any constraints on the system.

In each MPC controller, there is an objective function with a set of weights. These weights can directly affect the response of the system. The appropriate selection of weights results in the generation of an effective control action, which reduces tracking errors to a minimum. In the conventional MPC controllers, the focus is solely on optimizing the control actions, and weight values remain fixed or scheduled for different ranges of system operations. Therefore, the effects of real-time selection of optimum weights in the controller performance are overlooked.

This research aims to improve the performance of MPC control systems by developing a weight tuning and real-time weight selection scheme that considers the dynamic system's state. The proposed approach is applied to the vehicle stability control under a variety of environmental and/or driving conditions. The weight tuning is performed by using the prediction model of the vehicle and the Bayesian optimization (BO) technique. The weight selection is carried out in real-time by learning the adjusted weights through Gaussian process regression (GPR). These are two main modules developed to be used for selecting and tuning the weights of an MPC controller. Hence, in addition to optimizing control actions through the MPC controller's optimization problem, the weights of the MPC controller are also assessed and adjusted to achieve the highest level of optimality in the vehicle control system.

Furthermore, an authentication process is proposed to evaluate the tuned weights after being selected in the tests. This way, unnecessary increases or decreases in the weights stored in the weight selection dataset can be avoided. To further enhance the model predictions, a blending-based multiple model approach is utilized. In this approach, instead of considering a fixed prediction model with invariant parameters, a combination of finite number of models with different parameters are considered. Based on the prediction error of each model, a weighted sum of matrices of these models are utilized both in the MPC controller and weight tuning modules.

To verify the proposed methodology, MATLAB/Simulink and CarSim co-simulations as well as experimental tests are carried out. Comparing the vehicle responses with and without the proposed weight tuning and real-time weight selection approach strongly corroborates the proposed technique in enhancing the controller performance. The capability of the proposed multiple model technique in improving the weight tuning has been demonstrated in the simulations and experimental results.