Zonotopic set-membership estimation for time-varying systems subject to dynamical biases and quantization effects

Abstract

In this paper, the zonotopic set-membership estimation (SME) problem is studied for time-varying systems subject to dynamical biases and uniform quantization. The considered dynamical bias evolves according to a certain dynamic process disturbed by unknown-but-bounded noises. The main objective of the paper is to propose a zonotopic SME method such that the real states are included in zonotopes described by linear image of an unit hypercube. By analyzing the dynamics of biases and states, the intersection set containing the state are first obtained based on the quantization measurements. Then, an auxiliary zonotope is constructed to bound the intersection where the center and generator matrix are presented recursively. Through orchestrating the correlation matrix, the F-Radius of such an auxiliary zonotope is further minimized. To reduce the computational burden, the desired zonotope with finite-dimensional generator matrix is constructed to externally approximate the auxiliary zonotope. Furthermore, the boundedness stability is analyzed for the developed zonotopic SME approach in the simulations presence of dynamical biases and uniform quantization. Finally, an example is provided to display the effectiveness of the SME method.