A new kernel-based approach to system identification with quantized output data

In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo methods to provide an estimate of the system. In particular, we design two methods based on the so-called Gibbs sampler that allow also to estimate the kernel hyperparameters by marginal likelihood maximization via the expectation-maximization method. Numerical simulations show the effectiveness of the proposed scheme, as compared to the state-of-the-art kernel-based methods when these are employed in system identification with quantized data.Comment: 10 pages, 4 figure

Entropy of Highly Correlated Quantized Data

This paper considers the entropy of highly correlated quantized samples. Two results are shown. The first concerns sampling and identically scalar quantizing a stationary continuous-time random process over a finite interval. It is shown that if the process crosses a quantization threshold with positive probability, then the joint entropy of the quantized samples tends to infinity as the sampling rate goes to infinity. The second result provides an upper bound to the rate at which the joint entropy tends to infinity, in the case of an infinite-level uniform threshold scalar quantizer and a stationary Gaussian random process. Specifically, an asymptotic formula for the conditional entropy of one quantized sample conditioned on the previous quantized sample is derived. At high sampling rates, these results indicate a sharp contrast between the large encoding rate (in bits/sec) required by a lossy source code consisting of a fixed scalar quantizer and an ideal, sampling-rate-adapted lossless code, and the bounded encoding rate required by an ideal lossy source code operating at the same distortion

SMT-Based Bounded Model Checking of Fixed-Point Digital Controllers

Digital controllers have several advantages with respect to their flexibility and design's simplicity. However, they are subject to problems that are not faced by analog controllers. In particular, these problems are related to the finite word-length implementation that might lead to overflows, limit cycles, and time constraints in fixed-point processors. This paper proposes a new method to detect design's errors in digital controllers using a state-of-the art bounded model checker based on satisfiability modulo theories. The experiments with digital controllers for a ball and beam plant demonstrate that the proposed method can be very effective in finding errors in digital controllers than other existing approaches based on traditional simulations tools