Vector quantization and signal compression
Vector quantization and signal compression
Foundations of Quantization for Probability Distributions
Foundations of Quantization for Probability Distributions
Stabilizability of Stochastic Linear Systems with Finite Feedback Data Rates
SIAM Journal on Control and Optimization
SIAM Journal on Control and Optimization
Optimal dynamic quantizers for discrete-valued input control
Automatica (Journal of IFAC)
Brief Quadratic stabilization of sampled-data systems with quantization
Automatica (Journal of IFAC)
Stochastic stability for feedback quantization schemes
IEEE Transactions on Information Theory
Hi-index | 22.14 |
Existing analyses of 'zooming' quantisation schemes for bit-rate-limited control systems rely on the encoder and controller being initialised with identical internal states. Due to the quantiser discontinuity and the plant instability, it was not clear if closed-loop stability was possible if the encoder and controller commenced from different initial conditions. In this article, we consider partially observed, unstable linear time-invariant plants, with unbounded and possibly non-Gaussian noise, and propose a modified zooming-like scheme with finite-dimensional internal encoder and controller states that may not initially be identical. Using a stochastic pseudo-norm, we prove that this scheme yields mean-square stability in all closed-loop state variables, not just the plant state, under a sufficient condition involving this initial error, the plant dynamics and the channel data rate. With diminishing initial error, this condition approaches a known universal lower bound on data rates and becomes tight. Furthermore, we show that the scheme automatically corrects itself, in the sense that the errors between the internal states of the encoder and controller tend to zero stochastically with time. This suggests that the policy will maintain stability in the presence of channel errors, for sufficiently low bit error rates. We support these conclusions with simulations.