Guaranteed Strategies for Nonlinear Multi-Player Pursuit-Evasion Games

Abstract

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, comparison principle, and differential inequalities.

Collision avoidance and trajectory tracking control based on approximations of the maximum function

“…These problems are known to be extremely difficult even in the case of static optimization as pointed out in [11]. Our approach to address this issue is based on convergent approximations of the minimum and the maximum function as introduced in [9]. The basic idea is to represent multiple objectives (in this paper trajectory tracking and collision avoidance) with corresponding objective functions first, and then use these functions as arguments for the overall goal function.…”

“…In this paper we present a distributed Model Predictive Control (MPC) formulation based on convergent approximations of the maximum function [9] and elements of avoidance control (avoidance functions, [1], [10]). The proposed formulation allows each vehicle to achieve collision avoidance (minimal allowed separation with neighbors) and…”

Singular surfaces in multi-agent connectivity maintenance games

“…The inherent hardness in obtaining an analytical solution to the associated Hamilton-Jacobi-Isaacs equation has led to the development of numerical techniques for the computation of the value function. Recent efforts in this direction to compute an approximation of the reachable sets have been provided by Mitchell and Tomlin [17], Stipanović, Hwang and Tomlin [22], and Stipanović, Sriram and Tomlin [24]. Solutions for particular multi-player games were presented by Pashkov and Terekhov [19], Levchenkov and Pashkov [12], Hagedorn and Breakwell [9], Breakwell and Hagedorn [7], Sriram et al [21], and recently, by Fuchs et al [8].…”

Spatial approaches to broadband jamming in heterogeneous mobile networks: a game-theoretic approach

“…The inherent hardness in obtaining an analytical solution to the underlying Hamilton-Jacobi-Isaacs equation has led to the development of numerical techniques for the computation of the value function. Recent efforts in this direction to compute an approximation of the reachable sets have been provided by Mitchell and Tomlin (2003) and Stipanović et al (2004Stipanović et al ( , 2008. In this paper, we obtain the optimal strategies of players in teams involved in a multi-player zero-sum differential game with a specific focus on the jamming problem.…”