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

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...

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Bibliographic Details
Published inarXiv.org
Main Authors Maben Rabi, Chithrupa Ramesh, Johansson, Karl Henrik
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.02.2016
Subjects
Control systems design
Controllers
Equivalence
Feedback control
Optimal control
Quadratic equations
Separation
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Summary: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.
ISSN:2331-8422