Stable control of distributed hysteretic systems using cellular broadcast stochastic feedback

Abstract

This work develops a provably stable broadcast feedback approach to regulating the aggregate output of a collection of stochastically behaving cellular units with pronounced hysteresis. Similar to skeletal muscle, comprised of a number of muscle fibers, the cellular units are independent and each contributes to an aggregate system output. The control architecture consists of a central controller that only observes the aggregate system output and cell-level controllers that manage cell state on the hysteresis loop. The central controller stochastically recruits cells to reduce expected squared error. Stability analysis based on supermartingale theory guarantees that the control framework is stable.