Using Physical Stigmergy in Decentralized Optimization under Multiple Non-separable Constraints: Formal Methods and an Intelligent Lighting Example

In this paper, a distributed asynchronous algorithm for intelligent lighting is presented that minimizes collective power use while meeting multiple user lighting constraints simultaneously and requires very little communication among agents participating in the distributed computation. Consequently, the approach is arbitrarily scalable, adapts to exogenous disturbances, and is robust to failures of individual agents. This algorithm is an example of a decentralized primal-space algorithm for constrained non-linear optimization that achieves coordination between agents using stigmergic memory cues present in the physical system as opposed to explicit communication and synchronization. Not only does this work make of stigmergy, a property first used to describe decentralized decision making in eusocial insects, but details of the algorithm are inspired by classic social foraging theory and more recent results in eusocial-insect macronutrient regulation. This theoretical analysis in this paper guarantees that the decentralized stigmergically coupled system converges to within a finite neighborhood of the optimal resource allocation. These results are validated using a hardware implementation of the algorithm in a small-scale intelligent lighting scenario. There are other real-time distributed resource allocation applications that are amenable to these methods, like distributed power generation, in general, this paper means to provide proof of concept that physical variables in cyberphysical systems can be leveraged to reduce the communication burden of algorithms.