### Abstract

In a networked control system (NCS), sensors, actuators and controllers are spatially
distributed and interconnected via a shared communication medium, i.e. control loops
are closed through a real-time network. NCSs enable the integration of an increasing
number of complex control systems implemented on distributed control units. The
presence of the network inevitably introduces new challenges for the control engineering
community that lie in the intersection of control and communication theory.
We first review several recent results on modeling, control and communication scheduling
of NCSs with particular attention to those technique aiming at simultaneously designing
a controller and a communication policy for the networked system. We then analyze
and compare their structural and stability properties.
Given a continuous-time Linear Quadratic Regulator (LQR) problem we design a sampleddata
controller based on the continuous time LQR controller that takes into account the
limited communication medium and inter-sampling behavior. In contrast to former
work, the introduction of a periodic scheduler into the system dynamics will result in
a time-varying LQR problem with singularities in the system and weighting matrices.
To allow for a Riccati equation approach, singularities in the weighting matrices and
time-variance are accounted for using a lifting approach. We prove, for the first time,
that a communication sequence that avoids particularly defined pathological sampling
rates and updates each actuator signal only once is sufficient to preserve controllability
(and observability for the dual problem) with and without zero-order-hold logic. Optimal
scheduling for the multi-channel case is obtained by solving a complex combinatorial
optimization problem. Fast stochastic algorithms will be proposed to find a (sub)optimal
sequence and the associated optimal controller.

Translated title of the contribution | Optimal Scheduling and Control of Networked Control Systems I |
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Original language | English |

Publisher | University of Bristol |

Number of pages | 92 |

Publication status | Published - 2008 |

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## Cite this

Longo, S. (2008).

*Optimal Scheduling and Control of Networked Control Systems I*. University of Bristol.