Stochastic Pursuit-evasion Research Articles

On-line solution of a stochastic pursuit-evasion game

In this paper, the concepts of prior-commitment and delayed-commitment strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are applied to a detailed example of a pursuit-evasion game. Quasilinearization is used to solve the nonlinear two-point boundary-value problem of the prior-commitment game. A closed form solution is obtained for the delayed-commitment strategies. Comparison of the payoff functionals confirms the relationships discussed in Ref. 1.

On the solution of a general stochastic linear pursuit-evasion game

In this paper we have considered the existence and uniqueness of a random solution of a stochastic linear pursuit-evasion game described by a linear stochastic differential equation of the form We give only one transition equation where x( t;ω) can be thought of as the distance between the pursuer and evader, Thus, by a simple transformation, a pursuit-evasion game becomes a contest to bring a point in n-dimenaional space into an e-ball about the origin. The pursuer tries to minimize the time required, while the evader tries to maximize the time. The above transition equation is the most general formalization of a stochastic linear differential equation in the sense that all the functions involved are stochastic. Furthermore, the random function x(t;ω) appears on the right-hand side of the equation. Physically this means that the object(s) being controlled have energy of their own. Integrating the state equation with respect to time l and using some concepts of admissibility theory introduced by Tsokos in...

Formal solutions for a class of stochastic linear persuit-evasion games with perfect information

The aim of this paper is to give a brief review of a class of pursuit-evasion games which are governed by linear stochastic differential equations, and utilizing Roxin and Tsokos's definition of a stochastic differential game obtain formal solutions to the stochastic differential pursuit-evasion games of the form with pay-off given by The formal solutions are obtained by discretizing the game and applying the work of Ho et al.

Formal solutions for a class of stochastic pursuit-evasion games

A class of differential pursuit-evasion games is examined in which the dynamics are linear and perturbed by additive white Gaussian noise, the performance index is quadratic, and both players receive measurements perturbed independently by additive white Gaussian noise. Linear minimax solutions are characterized in terms of a set of implicit integro-differential equations. A game of this type also possesses a "certainty-coincidence" property, meaning that its minimax behavior coincides with that of the corresponding deterministic game in the event that all noise values are zero. This property is used to decompose the minimax strategies into sums of a certainty-equivalent term and error terms.

Formal solutions for a class of stochastic pursuit-evasion games

Formal solutions for a class of stochastic pursuit-evasion games

Fractional Brownian Motions, Fractional Noises and Applications

Fractional Brownian Motions, Fractional Noises and Applications

On a class of linear stochastic differential games

The solution for a class of stochastic pursuit-evasion differential games between two linear dynamic systems is given. This class includes the classical interception game in Euclidean space. The performance index which is optimized is quadratic, and one of the two players has imperfect (noisy) knowledge of the states of the two systems. The certainty-equivalence principle' or, equivalently, the technique of separating the estimator and the controller which characterizes the standard stochastic control problem is shown to be applicable to this class of differential games.