Broadcast Feedback for Stochastic Cellular Actuator Systems Consisting of Nonuniform Actuator Units

In this paper, the concept of broadcast feedback for stochastic cellular control systems is expanded to a system with nonuniform cellular length and nonuniform transition probability. The cellular control architecture was originally inspired by skeletal muscles comprising a vast number of tiny functional units, called sarcomeres. The output of the actuator system is an aggregate effect of numerous cellular units, each taking a bistable ON-OFF state. A central controller broadcasts the error between the aggregate output and a reference input. Rather than dictating the individual units to take specific states, the central controller merely broadcasts the overall error signal to all the cellular units uniformly. In turn each cellular unit makes a stochastic decision with a state transition probability, which is modulated in relation to the broadcasted error. Stability conditions of the broadcast feedback system are obtained by using a stochastic Lyapunov function. It is demonstrated that, even in the presence of the distribution of the cell length and/or the distribution of the transition probability generated in each cell, the aggregate output of the cellular units can track a given trajectory stably and robustly.