Bang-Bang Evasion: Its Stochastic Optimality and a Terminal-Set-Based Implementation

TL;DR

This paper extends the concept of bang-bang evasion to stochastic scenarios with imperfect information, proving optimality and proposing a terminal-set-based implementation that outperforms traditional strategies in simulations.

Contribution

It proves the existence of optimal bang-bang evasion strategies in stochastic settings and introduces a novel terminal-set-based control method.

Findings

TSE strategy outperforms traditional stochastic evasion methods in simulations.

Optimal evasion strategies always include at least one bang-bang policy.

The problem's finite-dimensional structure enables practical implementation.

Abstract

We address the problem of optimal evasion in a planar endgame engagement, where a target with bounded lateral acceleration seeks to avoid interception by a missile guided by a linear feedback law. Contrary to existing approaches, that assume perfect information or use heuristic maneuver models in stochastic settings, we formulate the problem in an inherently stochastic framework involving imperfect information and bounded controls. Complying with the generalized separation theorem, the control law factors in the posterior distribution of the state. Extending the well-known optimality of bang-bang evasion maneuvers in deterministic settings to the realm of realistic, stochastic evasion scenarios, we firstly prove that an optimal evasion strategy always exists, and that the set of optimal solutions includes at least one bang-bang policy, rendering the resulting optimal control problem finite-dimensional. Leveraging this structure, we secondly propose the closed-loop terminal-set-based evasion (TSE) strategy, and demonstrate its effectiveness in simulation against a proportional navigation pursuer. Monte Carlo simulations show that the TSE strategy outperforms traditional stochastic evasion strategies based on random telegraph, Singer, and weaving models.