Inverse linear quadratic dynamic games using partial state observations

As an extension of the inverse optimal control, the inverse linear quadratic (LQ) two-player dynamic game is studied in this paper. The considered inverse problem is to infer the cost function of one player using partial state observations as well as the control inputs of the other player. An identification framework is designed by firstly decoupling the causal and anticausal parts of the associated Hamilton–Jacobi–Bellman (HJB) equation and then identifying the coefficient matrices in the cost function. The twofold features of the presented method include: (i) the data-driven identification approach provides an easy-to-implement solution which avoids the direct optimization of a non-convex inverse problem as well as complicated algebraic manipulations on Riccati equations; (ii) the identification framework does not rely on the initial states or terminal costates, which enables its implementation using only segments of data trajectories. The effectiveness of the proposed method is demonstrated by simulation examples.