We present an algorithm for controlling and scheduling multiple linear
time-invariant processes on a shared bandwidth limited communication network
using adaptive sampling intervals. The controller is centralized and computes
at every sampling instant not only the new control command for a process, but
also decides the time interval to wait until taking the next sample. The
approach relies on model predictive control ideas, where the cost function
penalizes the state and control effort as well as the time interval until the
next sample is taken. The latter is introduced in order to generate an adaptive
sampling scheme for the overall system such that the sampling time increases as
the norm of the system state goes to zero. The paper presents a method for
synthesizing such a predictive controller and gives explicit sufficient
conditions for when it is stabilizing. Further explicit conditions are given
which guarantee conflict free transmissions on the network. It is shown that
the optimization problem may be solved off-line and that the controller can be
implemented as a lookup table of state feedback gains. Simulation studies which
compare the proposed algorithm to periodic sampling illustrate potential
performance gains.Comment: Accepted for publication in IEEE Transactions on Control Systems
Technolog