Lyapunov Functions in Differential Games

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

“…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…”

“…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.…”

“…Instead, Lyapunov-based methods were developed for nonlinear identification, nonlinear controllers, and nonlinear Model Reference Adaptive Control (MRAC)-the implementation of which was described compendiously as the Product State Space Technique (PSST) 1-8 -in a body of robotics research that has more recently enjoyed a revival. [9][10][11][12][13] This provided the genesis of a medical platform technology 14,15 demonstrated here in an AP context.…”

Differential games, continuous Lyapunov functions, and stabilisation of non‐linear dynamical systems

“…Two-player differential games involving linear dynamical systems and quadratic cost functions over the infinite time horizon are discussed in [14]. In addition, differential games on the infinite horizon for non-linear systems have been explored in [15,16], without accounting for any form of stability of the closed-loop system.…”

The study of dynamic processes in the hydraulic system of the roll clamp of a two-cone unwinder rolls pipe-welding unit 159-529

“…Математична модель довгої гідромагістралі як системи з розподіленими параметрами, для несталого руху реальної пружної рідини, описується диференційними рівняннями в приватних похідних [2,12]: 29…”