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BY DYNAMIC MODELING
WITH APPLICATION TO SOCIAL AND TECHNICAL SYSTEMS
Mihaela Ulieru and Subramanian Ramakris
The University of Calgary, Alberta
CANADA
Multi-agent systems constitute an important area in Distributed Artificial Intelligence. Despite the considerable advances in this area, a rigorous mathematical description of agent systems and their interaction is yet to be formulated. Apart from the obvious advantages of having a mathematical framework, the characteristics of agent systems and their interaction, do seem to offer abundant scope for a mathematical approach. The task is highly nontrivial, considering the complexity of agent interactions and the various considerations involved therein. In this paper an attempt is made to approach multi-agent systems from the point of view of dynamical system theory.
Agents can be understood as autonomous problem solvers, in general heterogeneous in nature, who interact with other agents in a given setting towards generating effective solutions. Thus interactions and evolution in time are prime features of an agent. Once a meaningful framework is established for these interactions and evolution, it is then natural to view the agents (in isolation and in a group) as dynamical systems. By formulating a control-theoretic model of multi-agent systems, this paper introduces concepts like stability and robustness and examines interesting phenomena such as bifurcations and chaos in the context of MAS behavior. We assume that uncertainty in the overall behavior of the multi-agent system is a consequence of the fact that the dynamical behavior of the agent is, at least in part, unknown or that it may depend on a stochastic phenomenon. An interesting analogy can be drawn between the goals of an agent system and the attractor basins of a dynamical system. In this context there exists a treatment of precisely these qualitative aspects with respect to the stochastic system described earlier.
The exact definitions of the functions, the random processes involved and the interpretation of the 'noises' in the context of multi-agent systems development will be presented in the paper as a tool for their behavioral analysis. A proposal to model the amount of learning by a mathematically sound entropy function is suggested. Also, the implication of this idea to the fundamental stochastic model is made clear. The suggestions converge to the idea that the dynamics of the stochastic model of agent systems, while retaining the Markovian character, should be driven by the total entropy function that is composed of the content of information as well as the extent of learning at any given instant in time. Application to social and technical systems will be discussed.
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