Distributionally robust system identification for continuous fermentation nonlinear switched system under moment uncertainty of experimental data

• Published in: Applied mathematical modelling 2024-03, Vol.127, p.679-695
• Main Authors: Yuan, Jinlong, Lin, Sida, Zhang, Shaoxing, Liu, Chongyang
• Format: Article
• Language: English
• Subjects: Distributionally robust system identification; Error analysis; Optimization algorithm; Switched dynamical system; Uncertain experimental data
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2023.12.023

In this paper, we consider a nonlinear switched dynamical system (NSDS) with unknown system parameters in the context of uncertain experimental data. This system is employed to model the continuous fermentation for the production of 1,3-propanediol through glycerol bioconversion. The uncertain experimental data points are regarded as stochastic variables and only their first-order moment information of the probability distributions is available. The target of this paper is to optimize these system parameters under the environment of uncertain experimental data. Taking these factors into account, we propose a distributionally robust system identification (DRSI) problem (i.e., a bi-level system identification problem) governed by the NSDS. The objective functional comprises two level objectives: (i) the inner-level objective aims to maximize the expectation of the relative error between the solution of the NSDS and the uncertain experimental data with respect to their probability distributions at approximately stable time; and (ii) the outer-level objective is to minimize the expectation with respect to these system parameters. The DRSI problem is equivalently transformed into a single-level system identification (SLSI) problem with non-smooth term through the application of the duality theory in the probability space. A smoothing technique is employed to approximate the non-smooth term in the SLSI problem. Subsequently, an error analysis of the employed smoothing technique is derived. The gradients of the objective functional in the SLSI with respect to these system parameters are obtained. An optimization algorithm is designed to solve the SLSI problem. Finally, the paper concludes with simulation results. •The DRSI problem lies between RSI problem and SSI problem.•An optimization algorithm with the duality theory is proposed to solve the DRSI problem.•A smoothing technique is employed to approximate the non-smooth term in the objective functional.