Inverse Stochastic Optimal Control for Linear-Quadratic Tracking

This paper focuses on the Inverse Stochastic Optimal Control (ISOC) problem for linear-quadratic Gaussian (LQG) tracking control, which defines and solves the problem of identifying the weight matrices in the LQG cost function using input and output trajectory data in the presence of unknown process and observation noises. The proposed method first estimates the covariance matrices of the process and observation noises, which are then used as prior knowledge to identify the weight matrix. As a result, the paper solves the noise covariance matrices and the weight matrix in two sequential steps (rather than iteratively), leading to higher computational efficiency. The first step uses an EM algorithm with guaranteed convergence, and the second step is a convex optimization problem. Simulation results show that the proposed method significantly outperforms methods that cannot compensate for noise in terms of parameter estimation accuracy when unknown levels of process noise are present.