Partial Observability Analysis of an Adversarial Swarm Model

Abstract

This paper introduces a new concept of partial observability for nonlinear systems. This new approach enables a quantitative analysis on the observability of an individual state variable and unknown parameters of a nonlinear dynamics even when the system is not observable in the traditional sense. The paper develops theoretical properties of partial observability and its computational algorithms. These results are applied and validated on a nonstandard estimation problem of detecting the internal cooperating strategy of a particular adversarial swarm model. Partial observability analysis on the parameters that define the cooperating strategy reveals interesting findings. For example, some parameters are observable even when the swarm is at a steady state that is not observable in traditional sense. It is also shown that observability of the internal cooperating strategy depends on both the swarm trajectory and the time window of the measurement. Motivated by these findings, a variational method of estimation based on the dynamic optimization of a cost function is proposed. Simulation results show that the proposed estimation method outperforms Kalman filters. The results in this paper provide useful tools for applications involving adversarial swarms, including defense against swarm attacks and herding of biological swarms.