Approximate solution of singularly perturbed nonlinear pursuit-evasion games

Pursuit- Evasion Games

Two players, Red and Blue, each independently choose a vertex of a connected graph G. Red must then pay Blue an amount equal to the distance between the vertices chosen. In this note, w e investigate the value v(G) of this pursuit-evasion game for various classes of graphs G, as well as those optimal mixed strategies for achieving v(G). It is shown that some rather counterintuitive behavior can...

Singularly Perturbed Piecewise Deterministic Games

In this paper we consider a class of hybrid stochastic games with the piecewise openloop information structure. These games are indexed over a parameter ε which represents the time scale ratio between the stochastic (jump process) and the deterministic (differential state equation) parts of the dynamical system. We study the limit behavior of Nash equilibrium solutions to the hybrid stochastic ...

Guaranteed Strategies for nonlinear Multi-Player Pursuit-Evasion Games

In this paper, we provide a methodology to design strategies for either guaranteed capture or guaranteed evasion in the case of pursuit-evasion games with multiple players which are represented by nonlinear dynamic models. This methodology is based on the continuously differentiable upper and lower approximations of the minimum and maximum function of an arbitrary number of arguments, compariso...

How Pursuit-evasion Games help

Stochastic Stability of Singularly Perturbed Nonlinear Systems

The stability of a nonlinear stochastic dynamic system with singular perturbations is considered. Based on the notion of stochastic input-to-state stability and using time scale decomposition, a result of the total stability type is obtained, i.e. if the fast subsystem and the slow subsystem are both input-to-state stable with respect to disturbances, then this property continues to hold for th...