Stochastic Recruitment Control of Large Ensemble Systems With Limited Feedback

Abstract

A new approach to controlling the ensemble behavior of many identical agents is presented in this paper, inspired by motor recruitment in skeletal muscles. A group of finite state agents responds randomly to broadcast commands, each producing a state-dependent output that is measured in aggregate. Despite the lack of feedback signal and initial state information, this control architecture allows a single central controller to direct the aggregate output of the ensemble toward a desired value. First, the system is modeled as an ensemble of statistically independent, identically distributed, binary-state Markov processes with state transition probabilities designated by a central controller. Second, steady-state behavior, convergence rate, and variance of the aggregate output, i.e., the total number of recruited agents, are analyzed, and design trade-offs in terms of accuracy, convergence speed, and the number of spurious transitions are made. Third, a limited feedback signal, only detecting if the output has reached a goal, is added to the system, and the recruitment controller is designed as a stochastic shortest path problem. Optimal convergence rate and associated transition probabilities are obtained. Finally, the theoretical results are verified and demonstrated with both numerical simulation and control of an artificial muscle actuator made up of 60 binary shape memory alloy motor units.