arXiv subjects

Ming Cao

Publications and source records attributed to Ming Cao.

At least 91 records · Page 5Linked to original sources

arXiv2021

Modelling the Effect of Vaccination and Human Behaviour on the Spread of Epidemic Diseases on Temporal Networks

Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread of recurrent epidemic diseases in a partially vaccinated population. The model encapsulates several realistic features, such as the different effectiveness of the vaccine against transmission and development of severe symptoms, testing practices, the possible implementation of non-pharmaceutical interventions to reduce the transmission, isolation of detected individuals, and human behaviour. Using a mean-field approach, we analytically derive the epidemic threshold of the model and, if the system is above such a threshold, we compute the epidemic prevalence at the endemic equilibrium. These theoretical results show that precautious human behaviour and effective testing practices are key toward avoiding epidemic outbreaks. Interestingly, we found that, in many realistic scenarios, vaccination is successful in mitigating the outbreak by reducing the prevalence of seriously ill patients, but it could be a double-edged sword, whereby in some cases it might favour resurgent outbreaks, calling for higher testing rates, more cautiousness and responsibility among the population, or the reintroduction of non-pharmaceutical interventions to achieve complete eradication.

math.DS↗

arXiv2021

Singularity-free Guiding Vector Field for Robot Navigation

Most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in vector-field guided path-following (VF-PF) navigation algorithms. These algorithms are based on a vector field, and the singular points are exactly where the vector field diminishes. In this paper, we show that it is mathematically impossible for conventional VF-PF algorithms to achieve global convergence to desired paths that are self-intersected or even just simple closed (precisely, homeomorphic to the unit circle). Motivated by this new impossibility result, we propose a novel method to transform self-intersected or simple closed desired paths to non-self-intersected and unbounded (precisely, homeomorphic to the real line) counterparts in a higher-dimensional space. Corresponding to this new desired path, we construct a singularity-free guiding vector field on a higher-dimensional space. The integral curves of this new guiding vector field is thus exploited to enable global convergence to the higher-dimensional desired path, and therefore the projection of the integral curves on a lower-dimensional subspace converge to the physical (lower-dimensional) desired path. Rigorous theoretical analysis is carried out for the theoretical results using dynamical systems theory. In addition, we show both by theoretical analysis and numerical simulations that our proposed method is an extension combining conventional VF-PF algorithms and trajectory tracking algorithms. Finally, to show the practical value of our proposed approach for complex engineering systems, we conduct outdoor experiments with a fixed-wing airplane in windy environment to follow both 2D and 3D desired paths.

cs.RO↗

arXiv2021

Optimal policy design to mitigate epidemics on networks using an SIS model

Understanding how to effectively control an epidemic spreading on a network is a problem of paramount importance for the scientific community. The ongoing COVID-19 pandemic has highlighted the need for policies that mitigate the spread, without relying on pharmaceutical interventions, that is, without the medical assurance of the recovery process. These policies typically entail lockdowns and mobility restrictions, having thus nonnegligible socio-economic consequences for the population. In this paper, we focus on the problem of finding the optimum policies that "flatten the epidemic curve" while limiting the negative consequences for the society, and formulate it as a nonlinear control problem over a finite prediction horizon. We utilize the model predictive control theory to design a strategy to effectively control the disease, balancing safety and normalcy. An explicit formalization of the control scheme is provided for the susceptible--infected--susceptible epidemic model over a network. Its performance and flexibility are demonstrated by means of numerical simulations.

q-bio.PE↗

arXiv2021

Game-theoretic modeling of collective decision-making during epidemics

The spreading dynamics of an epidemic and the collective behavioral pattern of the population over which it spreads are deeply intertwined and the latter can critically shape the outcome of the former. Motivated by this, we design a parsimonious game-theoretic behavioral--epidemic model, in which an interplay of realistic factors shapes the co-evolution of individual decision-making and epidemics on a network. Although such a co-evolution is deeply intertwined in the real-world, existing models schematize population behavior as instantaneously reactive, thus being unable to capture human behavior in the long term. Our model offers a unified framework to model and predict complex emergent phenomena, including successful collective responses, periodic oscillations, and resurgent epidemic outbreaks. The framework also allows to assess the effectiveness of different policy interventions on ensuring a collective response that successfully eradicates the outbreak. Two case studies, inspired by real-world diseases, are presented to illustrate the potentialities of the proposed model.

q-bio.PE↗

arXiv2021

Different Environment Feedback in Fast-slow Eco-evolutionary Dynamics

The fast-slow dynamics of an eco-evolutionary system are studied, where we consider the feedback actions of environmental resources that are classified into those that are self-renewing and those externally supplied. We show although these two types of resources are drastically different, the resulting closed-loop systems bear close resemblances, which include the same equilibria and their stability conditions on the boundary of the phase space, and the similar appearances of equilibria in the interior. After closer examination of specific choices of parameter values, we disclose that the global dynamical behaviors of the two types of closed-loop systems can be fundamentally different in terms of limit cycles: the system with self-renewing resources undergoes a generalized Hopf bifurcation such that one stable limit cycle and one unstable limit cycle can coexist; the system with externally supplied resources can only have the stable limit cycle induced by a supercritical Hopf bifurcation. Finally, the explorative analysis is carried out to show the discovered dynamic behaviors are robust in even larger parameter space.

eess.SY↗

arXiv2021

Distributed coordinated path following using guiding vector fields

It is essential in many applications to impose a scalable coordinated motion control on a large group of mobile robots, which is efficient in tasks requiring repetitive execution, such as environmental monitoring. In this paper, we design a guiding vector field to guide multiple robots to follow possibly different desired paths while coordinating their motions. The vector field uses a path parameter as a virtual coordinate that is communicated among neighboring robots. Then, the virtual coordinate is utilized to control the relative parametric displacement between robots along the paths. This enables us to design a saturated control algorithm for a Dubins-car-like model. The algorithm is distributed, scalable, and applicable for any smooth paths in an $n$-dimensional configuration space, and global convergence is guaranteed. Simulations with up to fifty robots and outdoor experiments with fixed-wing aircraft validate the theoretical results.

cs.RO↗

arXiv2021

Pole-like Objects Mapping and Long-Term Robot Localization in Dynamic Urban Scenarios

Localization on 3D data is a challenging task for unmanned vehicles, especially in long-term dynamic urban scenarios. Due to the generality and long-term stability, the pole-like objects are very suitable as landmarks for unmanned vehicle localization in time-varing scenarios. In this paper, a long-term LiDAR-only localization algorithm based on semantic cluster map is proposed. At first, the Convolutional Neural Network(CNN) is used to infer the semantics of LiDAR point clouds. Combined with the point cloud segmentation, the long-term static objects pole/trunk in the scene are extracted and registered into a semantic cluster map. When the unmanned vehicle re-enters the environment again, the relocalization is completed by matching the clusters of the local map with the clusters of the global map. Furthermore, the continuous matching between the local and global maps stably outputs the global pose at 2Hz to correct the drift of the 3D LiDAR odometry. The proposed approach realizes localization in the long-term scenarios without maintaining the high-precision point cloud map. The experimental results on our campus dataset demonstrate that the proposed approach performs better in localization accuracy compared with the current state-of-the-art methods. The source of this paper is available at: http://www.github.com/HITSZ-NRSL/long-term-localization.

cs.RO↗

arXiv2021

Convergence Analysis of Dual Decomposition Algorithm in Distributed Optimization: Asynchrony and Inexactness

Dual decomposition is widely utilized in distributed optimization of multi-agent systems. In practice, the dual decomposition algorithm is desired to admit an asynchronous implementation due to imperfect communication, such as time delay and packet drop. In addition, computational errors also exist when individual agents solve their own subproblems. In this paper, we analyze the convergence of the dual decomposition algorithm in distributed optimization when both the asynchrony in communication and the inexactness in solving subproblems exist. We find that the interaction between asynchrony and inexactness slows down the convergence rate from $\mathcal{O} ( 1 / k )$ to $\mathcal{O} ( 1 / \sqrt{k} )$. Specifically, with a constant step size, the value of objective function converges to a neighborhood of the optimal value, and the solution converges to a neighborhood of the exact optimal solution. Moreover, the violation of the constraints diminishes in $\mathcal{O} ( 1 / \sqrt{k} )$. Our result generalizes and unifies the existing ones that only consider either asynchrony or inexactness. Finally, numerical simulations validate the theoretical results.

math.OC↗

arXiv2021

Analysis, Prediction, and Control of Epidemics: A Survey from Scalar to Dynamic Network Models

During the ongoing COVID-19 pandemic, mathematical models of epidemic spreading have emerged as powerful tools to produce valuable predictions of the evolution of the pandemic, helping public health authorities decide which intervention policies should be implemented. The study of these models -- grounded in the systems theory and often analyzed using control-theoretic tools -- is an extremely important research area for many researchers from different fields, including epidemiology, engineering, physics, mathematics, computer science, sociology, economics, and management. In this survey, we review the history and present the state of the art in the modeling, analysis, and control of epidemic dynamics. We discuss different approaches to epidemic modeling, either deterministic or stochastic, ranging from the first implementations of scalar systems of differential equations to describing the epidemic spreading at the population level, and to more recent models on dynamic networks, which capture the spatial spread and the time-varying nature of human interactions.

math.DS↗

arXiv2021

Highway Traffic Control via Smart e-Mobility -- Part I: Theory

In this paper, we study how to alleviate highway traffic congestion by encouraging plug-in hybrid and electric vehicles to stop at a charging station around peak congestion times. Specifically, we design a pricing policy to make the charging price dynamic and dependent on the traffic congestion, predicted via the cell transmission model, and the availability of charging spots. Furthermore, we develop a novel framework to model how this policy affects the drivers' decisions by formulating a mixed-integer potential game. Technically, we introduce the concept of "road-to-station" (r2s) and "station-to-road" (s2r) flows, and show that the selfish actions of the drivers converge to charging schedules that are individually optimal in the sense of Nash. In the second part of this work, submitted as a separate paper (Part II: Case Study), we validate the proposed strategy on a simulated highway stretch between The Hague and Rotterdam, in The Netherlands.

eess.SY↗

arXiv2021

Highway Traffic Control via Smart e-Mobility -- Part II: Dutch A13 Case Study

In this paper, we study how to alleviate highway traffic congestions by encouraging plug-in electric and hybrid vehicles to stop at charging stations around peak congestion times. Specifically, we focus on a case study and simulate the adoption of a dynamic charging price depending on the traffic congestion. We use real traffic data of the A13 highway stretch between The Hague and Rotterdam, in The Netherlands, to identify the Cell Transmission Model. Then, we apply the algorithm proposed in (Part I: Theory) to different scenarios, validating the theoretical results and showing the benefits of our strategy in terms of traffic congestion alleviation. Finally, we carry out a sensitivity analysis of the proposed algorithm and discuss how to optimize its performance.

eess.SY↗

arXiv2021

Exerting Control in Repeated Social Dilemmas with Thresholds

Situations in which immediate self-interest and long-term collective interest conflict often require some form of influence to prevent them from leading to undesirable or unsustainable outcomes. Next to sanctioning, social influence and social structure, it is possible that strategic solutions can exist for these social dilemmas. However, the existence of strategies that enable a player to exert control in the long-run outcomes can be difficult to show and different situations allow for different levels of strategic influence. Here, we investigate the effect of threshold nonlinearities on the possibilities of exerting unilateral control in finitely repeated n-player public goods games and snowdrift games. These models can describe situations in which a collective effort is necessary in order for a benefit to be created. We identify conditions in terms of a cooperator threshold for the existence of generous, extortionate and equalizing zero-determinant (ZD) strategies. Our results show that, for both games, the thresholds prevent equalizing ZD strategies from existing. In the snowdrift game, introducing a cooperator threshold has no effect on the region of feasible extortionate ZD strategies. For extortionate strategies in the public goods game, the threshold only restricts the region of enforceable strategies for small values of the public goods multiplier. Generous ZD strategies exist for both games, but introducing a cooperator threshold forces the slope more towards the value of a fair strategy, where the player has approximately the same payoff as the average payoff of his opponents.

cs.MA↗

arXiv2021

Stability of Remote Synchronization in Star Networks of Kuramoto Oscillators

Synchrony of neuronal ensembles is believed to facilitate information exchange among cortical regions in the human brain. Recently, it has been observed that distant brain areas which are not directly connected by neural links also experience synchronization. Such synchronization between remote regions is sometimes due to the presence of a mediating region connecting them, e.g., \textit{the thalamus}. The underlying network structure of this phenomenon is star-like and motivates us to study the \textit{remote synchronization} of Kuramoto oscillators, {modeling neural dynamics}, coupled by a directed star network, for which peripheral oscillators get phase synchronized, remaining the accommodating central mediator at a different phase. We show that the symmetry of the coupling strengths of the outgoing links from the central oscillator plays a crucial role in enabling stable remote synchronization. We also consider the case when there is a phase shift in the model which results from synaptic and conduction delays. Sufficient conditions on the coupling strengths are obtained to ensure the stability of remotely synchronized states. To validate our obtained results, numerical simulations are also performed.

nlin.CD↗

arXiv2021

A two-layer model for coevolving opinion dynamics and collective decision-making in complex social systems

Motivated by the literature on opinion dynamics and evolutionary game theory, we propose a novel mathematical framework to model the intertwined coevolution of opinions and decision-making in a complex social system. In the proposed framework, the members of a social community update their opinions and revise their actions as they learn of others' opinions shared on a communication channel, and observe of others' actions through an influence channel; these interactions determine a two-layer network structure. We offer an application of the proposed framework by tailoring it to study the adoption of a novel social norm, demonstrating that the model is able to capture the emergence of several real-world collective phenomena such as paradigm shifts and unpopular norms. Through the establishment of analytical conditions and Monte Carlo numerical simulations, we shed light on the role of the coupling between opinion dynamics and decision-making, and of the network structure, in shaping the emergence of complex collective behavior in social systems.

cs.SI↗

arXiv2020

Applications of the Poincaré--Hopf Theorem: Epidemic Models and Lotka--Volterra Systems

This paper focuses on the equilibria and their regions of attraction for continuous-time nonlinear dynamical systems. The classical Poincaré--Hopf Theorem from differential topology is used to derive a result on a sufficient condition on the Jacobian for the existence of a unique equilibrium for the system, which is in fact locally exponentially stable. We show how to apply this result to the deterministic SIS networked model, and a nonlinear Lotka--Volterra system. We apply the result further to establish an impossibility conclusion for a class of distributed feedback controllers whose goal is to drive the SIS network to the zero equilibrium. Specifically, we show that if the uncontrolled system has a unique nonzero equilibrium (a diseased steady-state), then the controlled system also has a unique nonzero equilibrium. Applying results from monotone dynamical systems theory, we further show that both the uncontrolled and controlled system will converge to their nonzero equilibrium from all nonzero initial conditions exponentially fast. A counterpart sufficient condition for the existence of a unique equilibrium for a nonlinear discrete-time dynamical system is also presented.

math.DS↗

arXiv2020

Forced variational integrator for distance-based shape control with flocking behavior of multi-agent systems

A multi-agent system designed to achieve distance-based shape control with flocking behavior can be seen as a mechanical system described by a Lagrangian function and subject to additional external forces. Forced variational integrators are given by the discretization of Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. We derive forced variational integrators that can be employed in the context of control algorithms for distance-based shape with velocity consensus. In particular, we provide an accurate numerical integrator with a lower computational cost than traditional solutions, while preserving the configuration space and symmetries. We also provide an explicit expression for the integration scheme in the case of an arbitrary number of agents with double integrator dynamics. For a numerical comparison of the performances, we use a planar formation consisting of three autonomous agents.

eess.SY↗

arXiv2020

Vector Field Guided Path Following Control: Singularity Elimination and Global Convergence

Vector field guided path following (VF-PF) algorithms are fundamental in robot navigation tasks, but may not deliver the desirable performance when robots encounter singular points where the vector field becomes zero. The existence of singular points prevents the global convergence of the vector field's integral curves to the desired path. Moreover, VF-PF algorithms, as well as most of the existing path following algorithms, fail to enable following a self-intersected desired path. In this paper, we show that such failures are fundamentally related to the mathematical topology of the path, and that by "stretching" the desired path along a virtual dimension, one can remove the topological obstruction. Consequently, this paper proposes a new guiding vector field defined in a higher-dimensional space, in which self-intersected desired paths become free of self-intersections; more importantly, the new guiding vector field does not have any singular points, enabling the integral curves to converge globally to the "stretched" path. We further introduce the extended dynamics to retain this appealing global convergence property for the desired path in the original lower-dimensional space. Both simulations and experiments are conducted to verify the theory.

eess.SY↗

arXiv2020

Learning enables adaptation in cooperation for multi-player stochastic games

Interactions among individuals in natural populations often occur in a dynamically changing environment. Understanding the role of environmental variation in population dynamics has long been a central topic in theoretical ecology and population biology. However, the key question of how individuals, in the middle of challenging social dilemmas (e.g., the "tragedy of the commons"), modulate their behaviors to adapt to the fluctuation of the environment has not yet been addressed satisfactorily. Utilizing evolutionary game theory and stochastic games, we develop a game-theoretical framework that incorporates the adaptive mechanism of reinforcement learning to investigate whether cooperative behaviors can evolve in the ever-changing group interaction environment. When the action choices of players are just slightly influenced by past reinforcements, we construct an analytical condition to determine whether cooperation can be favored over defection. Intuitively, this condition reveals why and how the environment can mediate cooperative dilemmas. Under our model architecture, we also compare this learning mechanism with two non-learning decision rules, and we find that learning significantly improves the propensity for cooperation in weak social dilemmas, and, in sharp contrast, hinders cooperation in strong social dilemmas. Our results suggest that in complex social-ecological dilemmas, learning enables the adaptation of individuals to varying environments.

q-bio.PE↗