Optimal Scheduling and Control of Networked Control Systems I

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.