# Separated design of encoder and controller for networked linear quadratic optimal control

arXiv: https://arxiv.org/abs/1405.0135 · HTML: https://mlsanity.com/paper/1405.0135/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2014.

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning for Jointly Optimal Coding and Control Policies for a Controlled Markovian System over a Communication Channel](https://mlsanity.com/paper/2411.13884/) (2024)

## Abstract (arXiv)

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.