NDLI: Replicator dynamics under perturbations and time delays

Content Provider	Springer Nature Link
Author	Obando, Germán Poveda, Jorge I. Quija, Nicar
Copyright Year	2016
Abstract	Along with the appearance of new optimization and control problems, novel paradigms emerge. A large number of them are based on behavioral ecology, where population dynamics play an important role. One of the most known models of population dynamics is the replicator equation, whose applications in optimization and control have increased in recent years. This fact motivates the study of the replicator dynamics’ properties that are related to the implementation of this method for solving optimization and control problems. This paper addresses implementation issues of the replicator equation in engineering problems. We show by means of the Lyapunov theory that the replicator dynamics model is robust under perturbations that make the state to leave the simplex (among other reasons, this phenomenon can emerge due to numerical errors of the solver employed to obtain the replicator dynamic’s response). A refinement of these results is obtained by introducing a novel robust dynamical system inspired by the replicator equation that allows to control and optimize plants under arbitrary initial conditions on the positive orthant. Finally, we characterize stability bounds of the replicator dynamics model in problems that involve N strategies that are subject to time delays. We illustrate our results via simulations.
Starting Page	1
Ending Page	32
Page Count	32
File Format	PDF
ISSN	09324194
Journal	Mathematics of Control, Signals, and Systems
Volume Number	28
Issue Number	3
e-ISSN	1435568X
Language	English
Publisher	Springer London
Publisher Date	2016-07-11
Publisher Place	London
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Replicator dynamics Evolutionary game theory Singular perturbation Time-delay systems Systems Theory, Control Control, Robotics, Mechatronics Communications Engineering, Networks
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Applied Mathematics Signal Processing Control and Systems Engineering

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