LQG Control Performance With Low-Bitrate Periodic Coding

Several specific low-bitrate coding strategies are examined through their effect on linear–quadratic (LQ) control performance. By limiting the subject to these methods, we are able to identify principles underlying coding for control, a subject of significant recent interest but few tangible, i.e., implementable, results. In particular, we consider coding the quantized output signal deploying period-two codes of differing delay-versus-accuracy tradeoff. The quantification of coding performance is via the LQ control cost over a long but finite horizon up to a specified average escape time. Infinite-horizon stabilization is replaced by a mean-time-before-failure property, which is a new viewpoint but allows contact with uncoded controllers. The feedback control system comprises the coder–decoder in the path between the output and the state estimator, which is followed by linear state-variable feedback, as is optimal in the memoryless case. The static quantizer is treated as the functional composition of an infinitely long linear staircase function and saturation. This permits the analysis to subdivide into estimator computations, seemingly independent of the control performance criterion, and an escape time evaluation, which ties the control back into the choice of quantizer saturation bound. An example is studied, which illustrates the role of the control objective in determining the efficacy of coding using these schemes. The results mesh well with those observed in signal coding. However, the introduction of a realization-based escape time is a novelty departing significantly from mean square computations and from adaptive techniques.