arXiv subjects

Chuanhou Gao

Publications and source records attributed to Chuanhou Gao.

48 records · Page 3Linked to original sources

arXiv2020

Time-domain Boundedness of Noise-to-State Exponentially Stable Systems

In this paper we prove the time-domain boundedness for noise-to-state exponentially stable systems, and further make an estimation of its lower bound function, which allows to answer the question that how long the solution of a stochastic noise-to-state exponentially stable system stays in the domain of attraction and what happens with it if it escapes from this region for a while. The results will complement the probability-domain boundedness of noise-to-state exponentially stable systems, and provide a new insight into noise-to-state exponential stability.

math.DS↗

arXiv2020

Lyapunov Function PDEs Method to the Stability of Some Chemical Reaction Networks

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.

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arXiv2019

Lyapunov Function Partial Different Equations for Stability Analysis of a C of Chemical Reaction Networks

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.

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arXiv2019

Persistence of Delayed Complex Balanced Chemical Reaction Networks

In this paper, we derive two sufficient conditions to diagnose the persistence of two classes of delayed complex balanced chemical reaction network systems equipped with mass-action kinetics. One class is identified by $\dim Z_W=\dim\mathscr{S}-1$ ($Z_W$ is defined by \ref{eq:g} while $\mathscr{S}$ is the stoichiometric subspace of the network), the other class is identified through $\dim Z_W=0$ for any semilocking species set $W$ in the network. Then we also derive that delayed complex balanced systems with 2-d stoichiometric subspace are persistent. The results recur those proposed by Anderson et al. [D. F. Anderson, \textit{SIAM J. Appl. Math.}, 68 (2008), pp. 1464-1476; D. F. Anderson and A. Shiu, \textit{SIAM J. Appl. Math.}, 70 (2010), pp. 1840-1858] for checking the persistence of complex balanced reaction network systems without time delay. Further, we prove the above mentioned two classes of network systems are globally asymptotically stable at the corresponding positive equilibrium if the trajectory starts from a positive initial function. We illustrate the analysis by two numerical examples.

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arXiv2019

Two-stage Stochastic Lot-sizing Problem with Chance-constrained Condition in the Second Stage

In a given production planning horizon, the demands may only be comfirmed in part of the whole periods, and the others are uncertain. In this paper, we consider a two-stage stochastic lot-sizing problem with chance-constrained condition in the second stage. In the first stage, the demand is deterministic in each period, while in the second stage, the demands are random variables with finite distribution. We prove the optimality condition of the solutions under modified Wagner-Whitin condition and further develop a new equivalent MIP formulation which can depict the feasible region better. We also show that any subproblem fixing the selection of occurred scenarios has a complete linear description of its convex hull. A branch-and-bound algorithm is provided utilizing the character of the given subproblems.

math.OC↗

arXiv2019

Lyapunov Function Partial Differential Equations for Chemical Reaction Networks: Some Special Cases

In this paper, we develop a method to generate the Lyapunov function for stability analysis for chemical reaction networks. Based on the Chemical Master Equation, we derive the Lyapunov Function partial differential equations (PDEs), whose solution approximates the scaling non-equilibrium potential and serves as the candidate Lyapunov function for the given network. We further prove that for any chemical reaction network the solution (if exists) of the PDEs is dissipative. Moreover, the proposed method of Lyapunov Function PDEs is qualified for analyzing the asymptotic stability of complex balanced networks, all networks with $1$-dimensional stoichiometric subspace and some special networks with more than $2$-dimensional stoichiometric subspace if some moderate conditions are added. Several examples are presented to illustrate the efficiency of the method.

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arXiv2019

Enhancing Interpretability of Black-box Soft-margin SVM by Integrating Data-based Priors

The lack of interpretability often makes black-box models difficult to be applied to many practical domains. For this reason, the current work, from the black-box model input port, proposes to incorporate data-based prior information into the black-box soft-margin SVM model to enhance its interpretability. The concept and incorporation mechanism of data-based prior information are successively developed, based on which the interpretable or partly interpretable SVM optimization model is designed and then solved through handily rewriting the optimization problem as a nonlinear quadratic programming problem. An algorithm for mining data-based linear prior information from data set is also proposed, which generates a linear expression with respect to two appropriate inputs identified from all inputs of system. At last, the proposed interpretability enhancement strategy is applied to eight benchmark examples for effectiveness exhibition.

stat.ML↗

arXiv2019

Revisiting Persistence of Chemical Reaction Networks through Lyapunov Function Partial Differential Equations

In this paper, we propose a novel technique, referred to as the Lyapunov Function PDEs technique, to diagnose persistence of chemical reaction networks with mass-action kinetics. The technique allows that every network is attached to a Lyapuonv function PDE and a boundary condition whose solutions are expected to be Lyapunov functions for the network. By means of solution of the PDEs, either in the forms of itself or its time derivative, some checkable criteria are proposed for persistence of network systems. These criteria show high validity in proving that neither non-semilocking boundary points nor semilocking boundary non-equilibrium points (with additional conditions included) in mass-action systems are $ω$-$limit$ points. Further, we prove that a class of networks, called $\mathcal{W}_{I}$-endotactic networks that are regardless of values of the system parameters, a set larger than endotactic networks but smaller than $w_{I}$-endotactic networks, also give rise to persistent systems if the networks are $1$-dimensional. Although part of our results are covered by existing ones, part of them are still new. The proposed Lyapunov Function PDEs technique allows us to check persistence of mass action systems in an alternative corner, and is exhibiting large potential.

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arXiv2018

Complex Balancing Reconstructed to the Asymptotic Stability of Mass-action Chemical Reaction Networks with Conservation Laws

Motivated by the fact that the pseudo-Helmholtz function is a valid Lyapunov function for characterizing asymptotic stability of complex balanced mass action systems (MASs), this paper develops the generalized pseudo-Helmholtz function for stability analysis for more general MASs assisted with conservation laws. The key technique is to transform the original network into two different MASs, defined by reconstruction and reverse reconstruction, with an important aspect that the dynamics of the original network for free species is equivalent to that of the reverse reconstruction. Stability analysis of the original network is then conducted based on an analysis of how stability properties are retained from the original network to the reverse reconstruction. We prove that the reverse reconstruction possesses only an equilibrium in each positive stoichiometric compatibility class if the corresponding reconstruction is complex balanced. Under this complex balanced reconstruction strategy, the asymptotic stability of the reverse reconstruction, which also applies to the original network, is thus reached by taking the generalized pseudo-Helmholtz function as the Lyapunov function. To facilitate applications, we further provide a systematic method for computing complex balanced reconstructions assisted with conservation laws. Some representative examples are presented to exhibit the validity of the complex balanced reconstruction strategy.

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arXiv2018

Knowledge Integrated Classifier Design Based on Utility Optimization

This paper proposes a systematic framework to design a classification model that yields a classifier which optimizes a utility function based on prior knowledge. Specifically, as the data size grows, we prove that the produced classifier asymptotically converges to the optimal classifier, an extended version of the Bayes rule, which maximizes the utility function. Therefore, we provide a meaningful theoretical interpretation for modeling with the knowledge incorporated. Our knowledge incorporation method allows domain experts to guide the classifier towards correctly classifying data that they think to be more significant.

stat.ML↗

arXiv2017

Stabilization of (state, input)-disturbed CSTRs through the port-Hamiltonian systems approach

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.

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arXiv2016

Stochastic Weak Passivity Based Stabilization of Stochastic Systems with Nonvanishing Noise

For stochastic systems with nonvanishing noise, i.e., at the desired state the noise port does not vanish, it is impossible to achieve the global stability of the desired state in the sense of probability. This bad property also leads to the loss of stochastic passivity at the desired state if a radially unbounded Lyapunov function is expected as the storage function. To characterize a certain (globally) stable behavior for such a class of systems, the stochastic asymptotic weak stability is proposed in this paper which suggests the transition measure of the state to be convergent and the ergodicity. By defining stochastic weak passivity that admits stochastic passivity only outside a ball centered around the desired state but not in the whole state space, we develop stochastic weak passivity theorems to ensure that the stochastic systems with nonvanishing noise can be globally\locally stabilized in weak sense through negative feedback law. Applications are shown to stochastic linear systems and a nonlinear process system, and some simulation are made on the latter further.

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