Camille-Alain Rabbath

A nonautonomous version of continuous-time fictitious play is considered to achieve global asymptotic stability of a unique Nash equilibrium of a game. The proposed approach to prove global asymptotic stability consists of combining successively in time a continuous-time static fictitious play characterized by a time-varying rate of convergence with a continuous-time proportional derivative fictitious play, which has been recently proposed. Convergence to the basin of attraction of the empirical frequency of the proportional derivative fictitious play, if it exists, is obtained by means of contraction tools, reminiscent of the small-gain theorem, provided a set of inequalities involving the parameter of the continuous-time dynamics is satisfied. Furthermore, a discrete-time fictitious play is derived from its continuous-time counterpart. Convergence with probability one to the unique Nash equilibrium is shown. The approach is illustrated with a modified version of the Shapley game for which the proposed scheme is shown to be convergent to the unique equilibrium with the additional flexibility of selecting the rate of convergence

The design of a target assignment strategy is proposed in the context of a small group of vehicles engaged against a large set of static targets. The targets are assumed distributed randomly along a prescribed route. The strategy relies on the minimization of a quadratic cost that is an indicator of the total energy consumed by the group. The proposed target assignment strategy is designed for groups of two and three pursuer vehicles, leading to sequences of 2 times 2 and 3 times 3 confrontations, respectively. The cost function is based on the quantification of the neighboring space of each vehicle. Such modelling involves potential conflicts, which are solved by the introduction of a simple stochastic process whose function is to achieve a certain amount of unpredictability from the perspective of the enemy targets. Measurements of relative distances and line-of-sight (LOS) angles between neighboring vehicles are required. Noisy measurements may lead to inconsistent utility matrices in the confrontations. Thus, a probabilistic test is included in the target assignment strategy to activate communications between two neighbors whenever a confidence threshold is violated. Numerical examples show that the proposed scheme compares advantageously to a strategy that randomizes each action and to a law that minimizes the cost of confrontation without accounting for past moves