Linear Quadratic Tracking Control of Car-in-the-Loop Test Bench Using Model Learned via Bayesian Optimization

In this paper, we introduce a control method for the linear quadratic tracking (LQT) problem with zero steady-state error. This is achieved by augmenting the original system with an additional state representing the integrated error between the reference and actual outputs. One of the main contributions of this paper is the integration of a linear quadratic integral component into a general LQT framework. In this framework, the reference trajectories are generated using a linear exogenous system. During a simulative implementation for the specific real-world system of a car-in-the-loop (CiL) test bench, we assumed that the ‘real’ system was completely known. Therefore, for model-based control, we could have a perfect model identical to the ‘real’ system. It became clear that for CiL, stable solutions cannot be achieved with a controller designed with a perfect model of the ‘real’ system. On the contrary, we show that a model trained via Bayesian optimization (BO) can facilitate a much larger set of stable controllers. It exhibited an improved control performance for CiL. To the best of the authors’ knowledge, this discovery is the first in the LQT-related literature, which is a further distinctive feature of this work.