Non-Zero-Sum LQG Pursuit-Evasion Games for UUVs Under Nested Asymmetric Information

A pursuit-evasion problem for unmanned underwater vehicles (UUVs) under a nested asymmetric information structure is investigated in this paper within a finite-horizon non-zero-sum linear quadratic Gaussian (LQG) framework. In the considered scenario, the pursuer has access to more complete state information than the evader, which makes the derivation of Nash equilibrium strategies more challenging than in the conventional symmetric-information setting. To formulate the problem, the nonlinear UUV dynamics are linearized and discretized, and the interaction between the pursuer and the evader is modeled as a discrete-time stochastic dynamic game with distinct information filtrations. Based on the stochastic maximum principle, the necessary and sufficient conditions for the existence of a Nash equilibrium are established in the form of forward-backward stochastic difference equations (FBSDEs). To address the structural coupling caused by the nested information pattern, an orthogonal decomposition method is proposed, through which the coupled equations can be decoupled and explicit affine-feedback equilibrium strategies can be derived. Numerical simulations based on the REMUS 100 UUV model are provided to demonstrate the effectiveness of the proposed method.