  Optimal sensor scheduling with applications to networked estimation and
control systems is considered. We model sensor measurement and transmission
instances using jumps between states of a continuous-time Markov chain. We
introduce a cost function for this Markov chain as the summation of terms
depending on the average sampling frequencies of the subsystems and the effort
needed for changing the parameters of the underlying Markov chain. By
minimizing this cost function through extending Brockett's recent approach to
optimal control of Markov chains, we extract an optimal scheduling policy to
fairly allocate the network resources among the control loops. We study the
statistical properties of this scheduling policy in order to compute upper
bounds for the closed-loop performance of the networked system, where several
decoupled scalar subsystems are connected to their corresponding estimator or
controller through a shared communication medium. We generalize the estimation
results to observable subsystems of arbitrary order. Finally, we illustrate the
developed results numerically on a networked system composed of several
decoupled water tanks.
