Best Response Strategies for Asymmetric Sensing in Linear-Quadratic Differential Games

TL;DR

This paper studies a two-player linear-quadratic differential game with asymmetric sensing constraints, deriving optimal sensing and control strategies for the disadvantaged player and demonstrating their effectiveness through simulations.

Contribution

It introduces an optimal sensor policy for the player with sensing limitations and analyzes its impact on the game, a novel approach in asymmetric differential games.

Findings

The disadvantaged player can approach its security level by relaxing sensing constraints.

Optimal sensor policies can be stationary and randomized.

Simulations confirm the effectiveness of the proposed strategies.

Abstract

In this paper, we revisit the two-player continuous-time infinite-horizon linear quadratic differential game problem, where one of the players can sample the state of the system only intermittently due to a sensing constraint while the other player can do so continuously. Under these asymmetric sensing limitations between the players, we analyze the optimal sensing and control strategies for the player at a disadvantage while the other player continues to play its security strategy. We derive an optimal sensor policy within the class of stationary randomized policies. Finally, using simulations, we show that the expected cost accrued by the first player approaches its security level as its sensing limitation is relaxed.