Learning-Based Data-Enable Predictive Control for Trajectory Tracking of Unknown Systems

This paper addresses the problem of tracking a reference trajectory with high-accuracy for a controlled object with unknown system dynamics, subject to input and output constraints. To this end, we propose a novel learning-based data-enabled predictive control (DeePC) trajectory tracking algorithm, which consists of two main parts: Off-line training of a Gaussian process regression (GPR) model and online high-accuracy tracking control by using the probabilistic information obtained from the GPR model. To train the GPR model, we develop a method capable of predicting the output of an unknown system subjected to perturbations and obtaining probabilistic information about the distribution of predicted output. This enables us to utilize the uncertain nature of the predicted output to improve the accuracy of the tracking control. To track the reference trajectory for unknown systems, we extend the DeePC algorithm by leveraging the trained GPR model and behavioral theory. We transform the expected cost function and chance constraints into a more calculable form using the probabilistic information of the predicted output, which allows us to formulate the computationally efficient data-driven predictive control optimization problem. To demonstrate the high-accuracy in trajectory tracking performance of our proposed algorithm, we perform a comparison simulation with the DeePC method. Finally, to demonstrate the effectiveness of our proposed algorithm in practical applications, we present a case study on the eight-shaped trajectory tracking control of a mobile robot. This case study highlights the ability of our proposed algorithm to achieve high-accuracy trajectory tracking in a real-world scenario, while satisfying input and output constraints.