A differential game in three dimensions: The aerial dogfight scenario

A Computational Proof of Concept of a Machine-Intelligent Artificial Pancreas Using Lyapunov Stability and Differential Game Theory

“…17,32 This also means that an additional layer of machine-intelligent computation can be introduced to operate within a feasible time, as is done here.…”

“…11,14,16,17,40 Equation 4 shows the essential criterion for steering a trajectory to a target set despite uncertainty. The Lyapunovbased Game against Nature (L-GaN) goes further, assuming all such (bounded) uncertainty || ( ) || w t w ≤ + is being manipulated intelligently by a hostile player ("Nature") to thwart these control efforts.…”

“…The solution to handling these dynamic uncertainties was to overlay the so-called Game against Nature as an additional layer of machine-intelligent decision making on top of the Lyapunov formulation. 11,14,16,17,40 Equation 4 shows the essential criterion for steering a trajectory to a target set despite uncertainty. The Lyapunovbased Game against Nature (L-GaN) goes further, assuming all such (bounded) uncertainty || ( ) || w t w ≤ + is being manipulated intelligently by a hostile player ("Nature") to thwart these control efforts.…”

“…This was done using differential game theory, inspired by earlier nonbiological works. 16,17 One or more Lyapunov functions were to be used to describe controller objectives in terms of steering solution trajectories to a target set sandwiched between nested contours of a Lyapunov function. Uncertainties or uncontrolled elements were to be ascribed to a hostile player ("Nature"), who would endeavor to prevent those trajectories from colliding with or being captured by the target.…”

Optimal guidance strategy for the defense of a non‐manoeuvrable target in 3‐dimensions

“…They took into account physical aircraft limits such as structural and stall limits [4]. Greenwood designed a realistic differential game in 3‐dimensions by modelling fighter aircraft [5]. Greenwood used dynamics of two fighter aircraft in space and even considered firing envelopes as part of this barrier analysis.…”