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For a networked control system, we consider the problem of encoder and controller design. We study a discrete-time linear plant with a finite horizon performance cost, comprising of a quadratic function of the states and controls, and an additive communication cost. We study separation in design of the encoder and controller, along with related closed-loop properties such as the dual effect and certainty equivalence. We consider three basic formats for encoder outputs: quantized samples, real-valued samples at event-triggered times, and real-valued samples over additive noise channels. If the controller and encoder are dynamic, then we show that the performance cost is minimized by a separated design: the controls are updated at each time instant as per a certainty equivalence law, and the encoder is chosen to minimize an aggregate quadratic distortion of the estimation error. This separation is shown to hold even though a dual effect is present in the closed-loop system. We also show that this separated design need not be optimal when the controller or encoder are to be chosen from within restricted classes.

Abstract-In this paper, we show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of a sub-optimal scheduler with a certainty equivalent controller. Furthermore, we show that a mapping of the statebased scheduler into one which fulfills this condition, and consequently has an optimal certainty equivalent controller, does not result in an equivalent class of design in the sense of Witsenhausen. Computing the estimate remains hard, but can be simplified by introducing a symmetry constraint on the scheduler.

Innovations-based priority assignment for control over CAN-like networks.In: 54th IEEE Conference on Abstract-We present an innovations-based prioritization mechanism to efficiently use network resources for data gathering, without compromising the real-time decision making capability of the control systems. In the envisioned protocol, each sensor assigns the Value of Information (VoI) contained in its current observations for the network as the priority. Tournaments are used to compare priorities and assign transmission slots, like in the CAN bus protocol. By using a rollout strategy, we derive feasible algorithms for computing the VoI-based priorities for the case of coupled and decoupled systems. In the case of decoupled systems, performance guarantees with regard to the control cost of the VoI-based strategy are identified. We illustrate the efficiency of the proposed approach on a platooning example in which the vehicles receive measurements from multiple sensors.

Abstract-In this paper, we identify sufficient conditions for Lyapunov Mean Square Stability (LMSS) of a contention-based network of first-order systems, with state-based schedulers. The stability analysis helps us to choose policies for adapting the scheduler threshold to the delay from the network and scheduler. We show that three scheduling laws can result in LMSS: constant-probability laws and additively increasing or decreasing probability laws. Our results counter the notions that increasing probability scheduling laws alone can guarantee stability of the closed-loop system, or that decreasing probability scheduling laws are required to mitigate congestion in the network.