arXiv subjects

Fangzhou Liu

Publications and source records attributed to Fangzhou Liu.

31 records · Page 2Linked to original sources

arXiv2023

Discrete-time Layered-network Epidemics Model with Time-varying Transition Rates and Multiple Resources

This paper studies a discrete-time time-varying multi-layer networked SIWS (susceptible-infected-water-susceptible) model with multiple resources under both single-virus and competing multi-virus settings. Besides the human-to-human interaction, we also consider that the disease can diffuse on different types of medium. We use \emph{resources} to refer to any media that the pathogen of a virus can spread through, and do not restrict the resource only to be water. In the single-virus case, we give a full analysis of the system's behaviour related to its healthy state and endemic equilibrium. In the multi-virus case, we show analytically that different equilibria appear driven by the competition among all viruses. We also show that some analytical results of the time-invariant system can be expanded into time-varying cases. Finally, we illustrate the results through some simulations.

eess.SY↗

arXiv2023

A Persistent-Excitation-Free Method for System Disturbance Estimation Using Concurrent Learning

Observer-based methods are widely used to estimate the disturbances of different dynamic systems. However, a drawback of the conventional disturbance observers is that they all assume persistent excitation (PE) of the systems. As a result, they may lead to poor estimation precision when PE is not ensured, for instance, when the disturbance gain of the system is close to the singularity. In this paper, we propose a novel disturbance observer based on concurrent learning (CL) with time-variant history stacks, which ensures high estimation precision even in PE-free cases. The disturbance observer is designed in both continuous and discrete time. The estimation errors of the proposed method are proved to converge to a bounded set using the Lyapunov method. A history-sample-selection procedure is proposed to reduce the estimation error caused by the accumulation of old history samples. A simulation study on epidemic control shows that the proposed method produces higher estimation precision than the conventional disturbance observer when PE is not satisfied. This justifies the correctness of the proposed CL-based disturbance observer and verifies its applicability to solving practical problems.

eess.SY↗

arXiv2023

Simultaneous Recursive Identification of Parameters and Switching Manifolds Identification of Discrete-Time Switched Linear Systems

A novel procedure for the online identification of a class of discrete-time switched linear systems, which simultaneously estimates the parameters and switching manifolds of the systems, is proposed in this paper. Firstly, to estimate the parameters of the subsystems, a discrete-time concurrent learning-based recursive parameter estimator is designed to guarantee the exponential convergence of the estimation errors to zero. Secondly, as an assistant procedure of the identification framework, an online switching detection method is proposed by making use of the history stacks produced by the concurrent learning estimators. Thirdly, techniques of incremental support vector machine are applied to develop the recursive algorithm to estimate the system switching manifolds, with its stability proven by a Lynapunov-based method. At the end of the paper, the stability and precision of the proposed identification methods are confirmed by the numerical simulation of a 2-order switched linear system. Compared to the traditional offline identification methods, the proposed online identification framework possesses superior efficiency with respect to large amounts of data, while the limitations and outlook of this framework are also discussed within the conclusion.

eess.SY↗

arXiv2022

Off-Policy Risk-Sensitive Reinforcement Learning Based Constrained Robust Optimal Control

This paper proposes an off-policy risk-sensitive reinforcement learning based control framework for stabilization of a continuous-time nonlinear system that subjects to additive disturbances, input saturation, and state constraints. By introducing pseudo controls and risk-sensitive input and state penalty terms, the constrained robust stabilization problem of the original system is converted into an equivalent optimal control problem of an auxiliary system. Then, aiming at the transformed optimal control problem, we adopt adaptive dynamic programming (ADP) implemented as a single critic structure to get the approximate solution to the value function of the Hamilton-Jacobi-Bellman (HJB) equation, which results in the approximate optimal control policy that is able to satisfy both input and state constraints under disturbances. By replaying experience data to the off-policy weight update law of the critic artificial neural network, the weight convergence is guaranteed. Moreover, to get experience data to achieve a sufficient excitation required for the weight convergence, online and offline algorithms are developed to serve as principled ways to record informative experience data. The equivalence proof demonstrates that the optimal control strategy of the auxiliary system robustly stabilizes the original system without violating input and state constraints. The proofs of system stability and weight convergence are provided. Simulation results reveal the validity of the proposed control framework.

eess.SY↗

arXiv2022

Adaptive Observer for a Class of Systems with Switched Unknown Parameters Using DREM

In this note, we develop an adaptive observer for a class of nonlinear systems with switched unknown parameters to estimate the states and parameters simultaneously. The main challenge lies in how to eliminate the disturbance effect of zero-input responses caused by the switching on the parameter estimation. These responses depend on the unknown states at switching instants (SASI) and constitute an additive disturbance to the parameter estimation, which obstructs parameter convergence to zero. Our solution is to treat the zero-input responses as excitations instead of disturbances. This is realized by first augmenting the system parameter with the SASI and then developing an estimator for the augmented parameter using the \textit{dynamic regression extension and mixing} (DREM) technique. Thanks to its property of element-wise parameter adaptation, the system parameter estimation is decoupled from the SASI. As a result, the estimation errors of system states and parameters converge to zero asymptotically. Furthermore, the robustness of the proposed adaptive observer is guaranteed in the presence of disturbances and noise. A numerical example validates the effectiveness of the proposed approach.

eess.SY↗

arXiv2021

FedXGBoost: Privacy-Preserving XGBoost for Federated Learning

Federated learning is the distributed machine learning framework that enables collaborative training across multiple parties while ensuring data privacy. Practical adaptation of XGBoost, the state-of-the-art tree boosting framework, to federated learning remains limited due to high cost incurred by conventional privacy-preserving methods. To address the problem, we propose two variants of federated XGBoost with privacy guarantee: FedXGBoost-SMM and FedXGBoost-LDP. Our first protocol FedXGBoost-SMM deploys enhanced secure matrix multiplication method to preserve privacy with lossless accuracy and lower overhead than encryption-based techniques. Developed independently, the second protocol FedXGBoost-LDP is heuristically designed with noise perturbation for local differential privacy, and empirically evaluated on real-world and synthetic datasets.

cs.LG↗

arXiv2021

Model-Free Incremental Adaptive Dynamic Programming Based Approximate Robust Optimal Regulation

This paper presents a new formulation for model-free robust optimal regulation of continuous-time nonlinear systems. The proposed reinforcement learning based approach, referred to as incremental adaptive dynamic programming (IADP), exploits measured data to allow the design of the approximate optimal incremental control strategy, which stabilizes the controlled system incrementally under model uncertainties, environmental disturbances, and input saturation. By leveraging the time delay estimation (TDE) technique, we first exploit sensory data to reduce the requirement of a complete dynamics, where measured data are adopted to construct an incremental dynamics that reflects the system evolution in an incremental form. Then, the resulting incremental dynamics serves to design the approximate optimal incremental control strategy based on adaptive dynamic programming, which is implemented as a simplified single critic structure to get the approximate solution to the value function of the Hamilton-Jacobi-Bellman equation. Furthermore, for the critic artificial neural network, experience data are used to design an off-policy weight update law with guaranteed weight convergence. Rather importantly, to address the unintentionally introduced TDE error, we incorporate a TDE error bound related term into the cost function, whereby the TDE error is attenuated during the optimization process. The system stability proof and the weight convergence proof are provided. Numerical simulations are conducted to validate the effectiveness and superiority of our proposed IADP, especially regarding the reduced control energy expenditure and the enhanced robustness.

eess.SY↗

arXiv2020

Distributed Link Removal Strategy for Networked Meta-Population Epidemics and its Application to the Control of the COVID-19 Pandemic

In this paper, we investigate the distributed link removal strategy for networked meta-population epidemics. In particular, a deterministic networked susceptible-infected-recovered (SIR) model is considered to describe the epidemic evolving process. In order to curb the spread of epidemics, we present the spectrum-based optimization problem involving the Perron-Frobenius eigenvalue of the matrix constructed by the network topology and transition rates. A modified distributed link removal strategy is developed such that it can be applied to the SIR model with heterogeneous transition rates on weighted digraphs. The proposed approach is implemented to control the COVID-19 pandemic by using the reported infected and recovered data in each state of Germany. The numerical experiment shows that the infected percentage can be significantly reduced by using the distributed link removal strategy.

physics.soc-ph↗

arXiv2020

Interplay Between Homophily-Based Appraisal Dynamics and Influence-Based Opinion Dynamics: Modeling and Analysis

In social systems, the evolution of interpersonal appraisals and individual opinions are not independent processes but intertwine with each other. Despite extensive studies on both opinion dynamics and appraisal dynamics separately, no previous work has ever combined these two processes together. In this paper, we propose a novel and intuitive model on the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics. We assume that individuals' opinions are updated via the influence network constructed from their interpersonal appraisals, which are in turn updated based on the individual opinions via the homophily mechanism. By theoretical analysis, we characterize the set of equilibria and some transient behavior of our model. Moreover, we establish the equivalence among the convergence of the appraisal network to social balance, the modulus consensus of individual opinions, and the non-vanishing appraisals. Monte Carlo validations further show that the non-vanishing appraisals condition holds for generic initial conditions. Compared with previous works that explain the emergence of social balance via person-to-person homophily mechanism, our model provides an alternative explanation in terms of the person-to-entity homophily mechanism. In addition, our model also describes how individuals' opinions on multiple irrelevant issues become correlated and converge to modulus consensus over time-varying influence networks.

eess.SY↗

arXiv2020

On the Stability of the Endemic Equilibrium of A Discrete-Time Networked Epidemic Model

Networked epidemic models have been widely adopted to describe propagation phenomena. The endemic equilibrium of these models is of great significance in the field of viral marketing, innovation dissemination, and information diffusion. However, its stability conditions have not been fully explored. In this paper we study the stability of the endemic equilibrium of a networked Susceptible-Infected-Susceptible (SIS) epidemic model with heterogeneous transition rates in a discrete-time manner. We show that the endemic equilibrium, if it exists, is asymptotically stable for any nontrivial initial condition. Under mild assumptions on initial conditions, we further prove that during the spreading process there exists no overshoot with respect to the endemic equilibrium. Finally, we conduct numerical experiments on real-world networks to demonstrate our results.

eess.SY↗

arXiv2015

Environment tensor as order parameter for symmetry breaking and (symmetry-protected) topological orders

Spontaneous symmetry breaking is well understood through the classical "Mexican Hat" picture, which describes many quantum phases of matter. Recently, several new classes of quantum phases of matter, such as topological orders and symmetry protected topological (SPT) orders, were discovered. In an attempt to address the transitions between all those phases of quantum matter under the same framework, we introduced an analogous yet very simple picture for phase transitions in the context of tensor-networks. Using a very simple iteration process, we found that both symmetry breaking and some topological phase transitions (for topological orders described by gauge theory and 1D SPT orders) could be marked by a sudden change in the symmetry structure of the so-called "environment matrix". In this process, the environment matrix serves as an "order parameter" that captures patterns of entanglement in topological phases. The symmetry change in the environment matrix is very much like the symmetry breaking of conventional order parameters. We applied this method to both the transverse Ising model (1D and 2D honeycomb), spin-1 model (1D), and the Toric Code model in a magnetic field (2D honeycomb), and explored the corresponding symmetry structure changes in their environment matrices in details. With just a few variational parameters and a few minutes' run time on a laptop, we could get the corresponding phase transition points within a few percent error compared with the Quantum Monte Carlo results.

cond-mat.str-el↗

arXiv2014

Modular transformations and topological orders in two dimensions

The string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen provided ways to systematically label non-chiral topological orders in 2D. In those approaches, different topologically ordered many-body wave functions were characterized by different fixed-point tensors. Though extremely powerful, the resulting fixed-point tensors were mathematical abstractions and thus lacked a physical interpretation. As a result it was hard to judge if two different fixed-point tensors described the same quantum phase or not. We want to improve that approach by giving a more physical description of the topological orders. We find that the non-Abelian Berry's phases, $T$- and $S$-matrices, of the topological protected degenerate ground states on a torus give rise to a more physical description of topological orders. Using the Verlinde conjecture, we can even choose the canonical basis for the $T$- and $S$-matrices. It is conjectured that the $T$ and $S$-matrices form a complete and one-to-one characterization of non-chiral topological orders and can replace the fixed-point tensor description to give us a more physical label for topological orders. As a result, all the topological properties can be obtained from the $T$- and $S$-matrices, such as number of quasiparticle types (from the dimension of $T$ or $S$), the quasiparticle statistics (from the diagonal elements of $T$), the quantum dimensions of quasiparticles (from the first row of $S$), \etc.

cond-mat.str-el↗

arXiv2009

Magnetization of the Shastry-Sutherland antiferromagnet near the Ising limit

Motivated by recent experiments on TmB4 (arXiv:0712.1537), we examine the phase diagram of the Shastry-Sutherland antiferromagnet in an applied magnetic field in the limit of strong Ising anisotropy. In classical Ising limit, we demonstrate that the only fractional magnetization plateau is at 1/3 of the saturated magnetization. We study the perturbative influence of transverse quantum spin fluctuations, and present evidence that they can stabilize a narrow 1/2 magnetization plateau.

cond-mat.str-el↗