A Game Theoretic Approach to Resilient Space System Design

Abstract

There is a growing need for space missions that maintain performance in uncooperative or even adversarial environments. Space system designers must account for resilience to non-cooperative interactions in the design process while trading resilience and performance against cost. Prior academic work has considered resilience for system design, especially in the context of environmental factors; however, current literature does not include a space system design methodology that explicitly models non-cooperative, interactive threats to produce a more resilient design. To address this gap, a novel game-theoretic methodology is proposed to capture the interactive nature of non-cooperative systems at the strategic design level. The result is a two-player strategic design game in which the system under design and the threat system are both modeled as rational actors, and design options for the system architecture and threat system architecture are strategic choices for each actor. Performance, resilience, and cost metrics are calculated by an operational-level simulation of system-threat interactions. Tradespace and sensitivity analyses based on the results are used to evaluate the cost premium of adding resilience to the system and to demonstrate the strategic design choices that provide the most cost-effective means of increasing resilience to the modeled threats. The resulting methodology is presented through three case studies demonstrating the applicability of the methodology across multiple space mission applications.

The first case study evaluates a low earth orbit (LEO) Satellite Communications (SATCOM) system design. The results show that perfect resilience (no drop in performance) to the modeled ground based jamming threat requires a 224\% cost increase and that additional satellites are a more cost effective means of increasing resilience than fewer, more capable satellites. The second case study focuses on a Global Navigation Satellite System (GNSS) and adds more fidelity to the physical model and the design choices available to both the threat and the system. A medium earth orbit (MEO) constellation that maximizes resilience to the modeled jamming and kinetic threats consists of 56 satellites in 7 planes, while in LEO this requires 819 satellites in 21 planes. For a LEO GNSS constellation to be more cost effective than a MEO GNSS constellation with the same level of resilience, the LEO system's first unit cost must be $\leq 1/10$ the MEO system's first unit cost. Cost based sensitivity analyses demonstrate how results are influenced by cost model estimates and show how program managers can use this methodology to guide program decisions as cost estimates improve over time. The third case study looks at a non-cooperative GEO mission through an abstracted two player game environment called GEO Patrol. This case study adds fidelity to the operational interactions by requiring complex decision making. Reinforcement learning is used with over 7 million games of self play to train a 2 hidden layer neural network to generate actions. Human-in-the-loop experiments verify the simulation results and improve understanding of the underlying system dynamics. Over 20 volunteers played 53 games representing 3 distinct scenarios. The average difference between the volunteer and simulation results is 5.1\%, verifying the simulation. The three case studies demonstrate how the methodology can be applied across disparate space missions with varying levels of model fidelity. Systems designers can apply the methodology to produce both quantitative and qualitative recommendations to ensure the final system is resilient by design.