SIAM Journal on Computing
The mixing rate of Markov chains, an isoperimetric inequality, and computing the volume
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Abstraction and control for Groups of robots
IEEE Transactions on Robotics
A compositional framework for programming stochastically interacting robots
International Journal of Robotics Research
Broadcast stochastic receding horizon control of multi-agent systems
Automatica (Journal of IFAC)
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This paper formulates a self-organization algorithm to address the problem of global behavior supervision in engineered swarms of arbitrarily large population sizes. The swarms considered in this paper are assumed to be homogeneous collections of independent identical finite-state agents, each of which is modeled by an irreducible finite Markov chain. The proposed algorithm computes the necessary perturbations in the local agents' behavior, which guarantees convergence to the desired observed state of the swarm. The ergodicity property of the swarm, which is induced as a result of the irreducibility of the agent models, implies that while the local behavior of the agents converges to the desired behavior only in the time average, the overall swarm behavior converges to the specification and stays there at all times. A simulation example illustrates the underlying concept.