Stability of sequence-based anytime control with Markovian processor availability

We study an anytime algorithm to calculate the control input for nonlinear processes when the processing resources available are time-varying. The basic idea is to calculate the control input for as many time steps into the future as allowed by the available processing resources at every time step so as to compensate for those future time steps when the processor is not available to calculate any control input. We consider the case when the processor availability, and hence the number of control inputs calculated at any time step, is described by a Markov chain. Using a stochastic Lyapunov function based approach, we derive sufficient conditions for stability of the closed loop system.