Probabilistic stability and stabilization of human-machine system via hidden semi-Markov modeling approach

Yang-Fan Liu and Huai-Ning Wu

Applied Mathematics and Computation, 2025, vol. 489, issue C

Abstract: This paper investigates the probabilistic stability and stabilization issues of human-machine systems (H-MSs) through the use of hidden semi-Markov model (HS-MM) for human behavior modeling. Firstly, an HS-MM is employed to illustrate the sojourn-time-dependent HIS behavior, which considers the stochastic nature of human internal state (HIS) reasoning and the uncertainty from HIS observation. Next, by integrating HIS model, machine dynamic model, and human-machine interaction, a hidden semi-Markov jump system (HS-MJS) model is established to describe the H-MS. The initial machine state is considered to be Gaussian distributed with some given expected value and covariance matrix. By the tools of probabilistic reachable set computation and stochastic Lyapunov functional, a sufficient condition for the stochastic stability of the H-MS with some given confidence level is provided in terms of linear matrix inequalities (LMIs). Moreover, for a prescribed confidence level, an LMI-based human-assistance controller synthesis method is proposed to stabilize the H-MS with the confidence level. Finally, a driver-automation cooperative system is employed to verify the feasibility of the theoretical results.

Keywords: Human behavior modeling; Hidden semi-Markov model; Human-machine system; Probabilistic stability and stabilization (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324006143
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006143

DOI: 10.1016/j.amc.2024.129153

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().