Learning-based Optimal Control for Linear Systems with Model Uncertainties

The problem of optimal control with unknown dynamics is important and challenging. Most existing learning-based methods usually do not utilize the prior knowledge of the model and choose to learn the system model from scratch, leading to high identification costs and unbounded identification time. In practice, prior knowledge of the model may be available. Therefore, in this paper, we investigate the Linear Quadratic Gaussian ( LQG) control problem for an unknown system but with prior knowledge of model uncertainties. We develop an effective learning procedure to identify the optimal controller parameters, leading to the least possible cost. Specifically, we analyze the performance of the optimal observer under unknown system dynamics and reveal the relationship between the regression error and the observer performance. We propose a learning procedure to design the optimal controller incorporating prior knowledge of the system. Simulations are conducted to illustrate the effectiveness of our controller design.