1 research outputs found
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
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.Comment: To appear in the SIAM journal on Control and Optimizatio