Optimal dynamic bit assignment in noise-free quantized linear control systems

Abstract — This paper introduces a dynamic bit assignment policy (DBAP) for quantized feedback control systems without process or measurement noise. The proposed DBAP is a con-stant bit rate policy based on a similar policy analyzed in [1]. We prove that the new policy is optimal for diagonalizable systems in the sense of minimizing the summed square quantization error subject to a fixed number of quantization bits. For simplicity, this paper focuses on 2-dimensional discrete-time systems with diagonal system matrices. These results may be extended to more general systems. I