Abstract
Abstract Nonlinear biochemical systems such as the anaerobic digestion process experience the problem of the multi-stability phenomena, and thus, the dynamic spectrum of the system has several undesired equilibrium states. As a result, the selection of initial conditions and operating parameters to avoid such states is of importance. In this work, we present a data-driven approach, which relies on the generation of several system trajectories of the anaerobic digestion system and the construction of a data-driven Koopman operator to give a concise criterion for the classification of arbitrary initial conditions in the state space. Unlike other approximation methods, the criterion does not rely on difficult geometrical analysis of the identified boundaries to produce the classification.
Highlights
The biological process through which multiple organisms break down organic matter in the absence of oxygen is called the Anaerobic Digestion process
We present a data-driven approach, which relies on the generation of several system trajectories of the anaerobic digestion system and the construction of a data-driven Koopman operator to give a concise criterion for the classi cation of arbitrary initial conditions in the state space
In this paper we propose a new approach based on a dynamical system representation of the anaerobic digesthe integration of such numerical representations from dif- tion process, the fact that it does not subsequently rely on ferent initial conditions to estimate the discrete-time ap- the manipulation of the di erential equation model is an proximation of the Koopman operator
Summary
The biological process through which multiple organisms break down organic matter in the absence of oxygen is called the Anaerobic Digestion process. This paper analyzes the inherent di culties of the process, such as nonlinearities and the multi-stability phenomena with a data-driven linear operator framework. This analysis allows the identi cation of essential conditions in the operation of the reactor for control purposes. The analysis of multi-stability phenomena present in some nonlinear systems is closely related to the concept of attraction or stability regions. This subject is as important as the notion of stability because the stable operating points of a nonlinear system are rarely globally stable [4]. For the anaerobic digestion process, it is essential to know the attraction region of the desired operating point where the biological species interact and coexist, and the attraction region of the di erent washout points where bacterial life has disappeared
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