|Control and communication issues are traditionally
decoupled in discussions of decision and control problems because this
simplifies the analysis and generally works well for classical models.
This fundamental assumption deserves re-examination as control applications
spread into areas where lack of time on a network shared by sensors, actuators
and the controller is as important as lack of computational power. Such
areas include the coordinated control of robots, formations of aerial vehicles,
micro-actuator arrays and other settings where many systems must share
the attention of a decision-maker. This thesis proposes a model that
captures the essential characteristics of control systems with limited
communication. Under our model, controller-plant communication occurs
at discrete times and the controller must choose which actuators/sensors
to update/read at a particular time. These constraints lead to the need
for a theory of sampled-data systems where communication and control are
intrinsically coupled. In this work we formulate such a theory
linking dynamical systems, combinatorics and linear algebra. This theory
allows us to revisit classical tracking and stabilization problems, this
time with the communication and control aspects interweaved. In the
process, we are lead to a quantitative definition for ``attention'' (in
the context of control systems with limited communication) that is both
rigorous and intuitive.
The effectiveness of the theory is evaluated using simulations and experiments. We present a limited communication control system consisting of a two-fingered dexterous robot with tactile sensing and vision capabilities. Application of our theory leads to improved trajectory tracking in manipulation tasks, especially when the controller is challenged to perform near or above its Nyquist rate.