Parameter estimation in systems with binary-valued observations and structural uncertainties

• Published in: International journal of control Vol. 87; no. 5; pp. 1061 - 1075
• Main Authors: Kan, Shaobai, Yin, G., Wang, Le Yi
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 04.05.2014; Taylor & Francis Ltd
• Subjects: Algorithms; Bias; binary sensors; Dynamical systems; Empirical analysis; error bounds; Mathematical models; Nonlinear dynamics; nonlinear model mismatch; Nonlinearity; observation bias; Parameter estimation; system identification; Uncertainty; unmodelled dynamics
• ISSN: 0020-7179; 1366-5820
• DOI: 10.1080/00207179.2013.867363

This paper studies identification of linear systems with binary-valued observations generated via fixed thresholds. In addition to stochastic measurement noises, the systems are also subject to structural uncertainties, including deterministic unmodelled dynamics, nonlinear model mismatch, and sensor observation bias. Since binary-valued observations can supply only limited information on the signals, truncated empirical measures are introduced to extract further information for system identification. An effective identification algorithm is constructed based on the proposed empirical measures. Optimal identification errors, time complexity, optimal input design, and impact of disturbances, unmodelled dynamics, observation bias, and nonlinear model mismatch are thoroughly investigated in a stochastic information framework. Asymptotic upper and lower bounds are established on identification errors. Numerical experiments are presented to demonstrate the effectiveness of the algorithms and the main results.