From open-loop representations to closed-loop feedback implementations in differential games: A numerical case study
This work addresses the challenge of synthesizing feedback strategies for differential games, which is typically limited to open-loop solutions, but the approach is demonstrated only on a specific game and is incremental in nature.
The paper proposes a numerical scheme to compute feedback strategies for a surveillance-evasion differential game by training neural networks on open-loop solution data, demonstrating effectiveness through simulations. It also analyzes the impact of sample-and-hold versus continuous-time feedback on player performance.
Solutions to pursuit-evasion and surveillance-evasion differential games are typically computed and expressed using open-loop representations, with the synthesis of feedback strategies significantly less common. We propose a numerical scheme for obtaining feedback strategies for the recently introduced prying-pedestrian surveillance-evasion differential game. The scheme involves computing feedback strategies as input-output maps approximated via neural networks trained using data obtained from open-loop representations of solutions. Simulations show the effectiveness of neural networks trained with an appropriate learning-loss function. Since optimal feedback strategies are discontinuous, as a second contribution, the potential loss/gain of individual players is subsequently studied for players using sample-and-hold feedback compared to continuous-time feedback.