In this article, a data-based compact Volterra model is constructed to carry out the silicon prediction task. The main motivations are to, on the one hand, make better use of the strong memory ability of the Volterra series, which is suitable for reflecting the large inertia of the blast furnace process, on the other hand, overcome the difficulty that high complexity of the original Volterra models may result in serious overfitting. Six kinds of models, including single-input and two-input linear, second-order and third-order compact Volterra models, are successively designed and verified through a real blast furnace case. The reasonable agreement between the predicted values and the observed values indicates the compact Volterra model, especially the single-input third-order Volterra model, are powerful and competitive for describing the complex blast furnace system. The experimental results can serve as a guide for the blast furnace operators to judge the in-furnace thermal state change in time and further provide an indication on how to control the blast furnace in advance.

This article contributes to extending the validity of Lyapunov function partial differential equations (PDEs) whose solution is conjectured to be able to behave as a Lyapunov function in stability analysis to more mass-action chemical reaction networks. First, we have proved that the Lyapunov function PDEs method is valid in capturing the asymptotic stability of the networks compounded of a complex balanced network and any species-dependent two-species autocatalytic network if some moderate conditions are included. Then, by defining a new class of networks, called complex balanced produced networks, we also show the asymptotic stability of this class of networks, and also to their compound with any species-independent one-dimensional network and with any species-dependent two-species autocatalytic network under some conditions by using the same method. A notable point is that these classes of networks are nonweakly reversible, of any dimension, and of any deficiency. Finally, we apply our results to some practical biochemical reaction networks, including birth-death processes, motifs related networks, etc., to illustrate validity.

It is a universal phenomenon that the state and input of the continuous stirred tank reactor (CSTR) systems are both disturbed. This paper proposes a (state, input)-disturbed port-Hamiltonian framework that can be used to model and further designs a stochastic passivity based controller to asymptotically stabilize in probability the (state, input)-disturbed CSTR (sidCSTR) systems. The opposite entropy function and the availability function are selected as the Hamiltonian for the model and control purposes, respectively. Furthermore, the proposed (state, input)-disturbed port-Hamiltonian model can simultaneously characterize the first law and the second law of thermodynamics when the opposite entropy function acts as the Hamiltonian. A simple CSTR example illustrates how the port-Hamiltonian method is utilized for modeling and controlling sidCSTR systems.

This paper contributes to extending the validity of Lyapunov function PDEs (in-vented by Fang and Gao in [SIAM Journal on Applied Dynamical Systems, 18(2019), pp. 1163-1199]and whose solution is conjectured to be able to behave as a Lyapunov function) in stability analysisto more mass-action chemical reaction networks. By defining a new class of networks, called complexbalanced produced networks, we have proved that the Lyapunov function PDEs method is validin capturing the asymptotic stability of this class of networks, and also to their compound withany 1-dimensional independent network according to species and with any two-species autocatalyticnon-independent network if some moderate conditions are included. A notable point is that thesethree classes of networks are non-weakly reversible, any dimensional and of any deficiency. We applyour results to some practical biochemical reaction networks including birth-death processes, motifsrelated networks etc., to illustrate validity.

We investigate a broad family of chemical reaction networks (CRNs) assigned with mass action kinetics, called complex-balanced-produced-CRNs (CBP-CRNs), which are generated by any given complex balanced mass action system (MAS) and whose structures depend on the selection of producing matrices. Unluckily, the generally applied pseudoHelmholtz free energy function may fail to act as a Lyapunov function for the CBP-CRNs. Inspired by the method of Lyapunov function partial differential equations (PDEs), we construct one solution of their corresponding Lyapunov function PDEs, termed as the generalized pseudoHelmholtz free energy function, and further show that solution can behave as a Lyapunov function to render the asymptotic stability for the CBP-CRNs. This work can be taken as an argument of the conjecture that Lyapunov function PDEs approach can serve for any MAS.