Data Driven Linear Quadratic Gaussian Control Design

Abstract

The implementation of the Linear Quadratic Gaussian (LQG) scheme is often considered problematic as it requires a dynamic model of the system as a whole. The challenges come from state variables without a physical representation and the interference factors that affect the reading process. This paper presents and assesses a combination of methods to adapt the LQG scheme to a discrete-time linear system. The method KalmanNet constructed by the Long-Short Term Memory architecture (LSTM) is employed to replace the role of Kalman Filter (KF). The Value Iteration (VI) algorithm supersedes the role of the Linear Quadratic Regulator (LQR) controller in solving quadratic regulation issues. The assessment of the proposed algorithm on a cart-pole system and batch distillation column with a disturbance factor in uncorrelated Gaussian white noise is carried out in a simulated way under a discrete-time linear system. The result indicates that the solving of regulation problems through the conventional LQG method is not conclusive as the output response oscillation is still in progress. The combination of the KalmanNet and VI algorithm, as aforementioned, provides better results as it proves to solve the regulation problem as well as to compel the system output to converge.

Keywords

• Optimal control
• LQG
• LSTM
• state estimation
• reinforcement learning