Micro-Macro Links for Self-Organizing Collective Systems: From Local State Transition Rules to Global Transition Probabilities and Back
نویسندگان
چکیده
The design of self-organizing, collective systems is challenging. The major challenge is understanding the complex, non-linear relation between the microscopic level (individual agent) and the macroscopic level (collective behavior). An option to get an understanding of these systems is to derive micro-macro links that define a direct (mathematical) connection between the two levels. Models can help in gaining novel, general insights about collective systems and can also help during the design process of a particular system (Hamann and Wörn, 2008). In the following, we present a modeling technique that has high potential for general applicability in the domain of self-organizing collective systems. Natural and artificial collective systems typically rely on simple agents. The controllers of simple agents (e.g., reactive control) are easily modeled with finite state automata. The transitions between states depend on the agent’s internal state s and its perceptions {p0, . . . , pn}. These perceptions could represent anything from detected objects, walls, neighboring agents and their communicated internal states, etc. We denote the probability of a transition from sj to si as P (si|sj , p0, . . . , pm) where we assume the Markov property. We assume ergodicity and that perceptions pi can be modeled by probabilities depending on the agent’s state averaged over time and ensembles. This definition allows the notation of a master equation (van Kampen, 1981) df dt = ∑ T (s|s′)f(s′, t)− T (s′|s)f(s, t). (1)
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