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In this work, we develop an analytical framework that integrates opinion dynamics with a recommendation system. By incorporating elements such as collaborative filtering, we provide a precise characterization of how recommendation systems shape interpersonal interactions and influence opinion formation. Moreover, the property of the coevolution of both opinion dynamics and recommendation systems is also shown. Specifically, the convergence of this coevolutionary system is theoretically proved, and the mechanisms behind filter bubble formation are elucidated. Our analysis of the maximum number of opinion clusters shows how recommendation system parameters affect opinion grouping and polarization. Additionally, we incorporate the influence of propagators into our model and propose a reinforcement learning-based solution. The analysis and the propagation solution are demonstrated in simulation using the Yelp data set.

Recent research on social contagion processes has revealed the limitations of traditional networks, which capture only pairwise relationships, to characterize complex multiparty relationships and group influences properly. Social contagion processes on higher-order networks (simplicial complexes and general hypergraphs) have therefore emerged as a novel frontier. In this work, we investigate discrete-time Susceptible-Infected-Susceptible (SIS) social contagion processes occurring on weighted and directed hypergraphs and their extensions to bivirus cases and general higher-order SIS processes with the aid of tensor algebra. Our focus lies in comprehensively characterizing the healthy state and endemic equilibria within this framework. The emergence of bistability or multistability behavior phenomena, where multiple equilibria coexist and are simultaneously locally asymptotically stable, is demonstrated in view of the presence of the higher-order interaction. The novel sufficient conditions of the appearance for system behaviors, which are determined by both (higher-order) network topology and transition rates, are provided to assess the likelihood of the SIS social contagion processes causing an outbreak. More importantly, given the equilibrium is locally stable, an explicit domain of attraction associated with the system parameters is constructed. Moreover, a learning method to estimate the transition rates is presented. In the end, the attained theoretical results are supplemented via numerical examples. Specifically, we evaluate the effectiveness of the networked SIS social contagion process by comparing it with the $2^n$-state Markov chain model. These numerical examples are given to highlight the performance of parameter learning algorithms and the system behaviors of the discrete-time SIS social contagion process.

Consensus control in multi-agent systems has received significant attention and practical implementation across various domains. However, managing consensus control under unknown dynamics remains a significant challenge for control design due to system uncertainties and environmental disturbances. This paper presents a novel learning-based distributed control law, augmented by an auxiliary dynamics. Gaussian processes are harnessed to compensate for the unknown components of the multi-agent system. For continuous enhancement in predictive performance of Gaussian process model, a data-efficient online learning strategy with a decentralized event-triggered mechanism is proposed. Furthermore, the control performance of the proposed approach is ensured via the Lyapunov theory, based on a probabilistic guarantee for prediction error bounds. To demonstrate the efficacy of the proposed learning-based controller, a comparative analysis is conducted, contrasting it with both conventional distributed control laws and offline learning methodologies.

M-N-C single-atom catalysts (SACs) have emerged as a potential substitute for the costly platinum-group catalysts in oxygen reduction reaction (ORR). However, several critical aspects of M-N-C SACs in ORR remain poorly understood, including their pH-dependent activity, selectivity for 2- or 4-electron transfer pathways, and the identification of the rate-determining steps. Herein, analyzing >100 M-N-C structures and >2000 sets of energetics, we unveil a pH-dependent evolution in ORR activity volcanos from a single-peak in alkaline media to a double-peak in acids. We found that this pH-dependent behavior in M-N-C catalysts fundamentally stems from their moderate dipole moments and polarizability for O* and HOO* adsorbates, as well as unique scaling relations among ORR adsorbates. To validate our theoretical discovery, we synthesized a series of molecular M-N-C catalysts, each characterized by well-defined atomic coordination environments. Impressively, the experiments matched our theoretical predictions on kinetic current, Tafel slope, and turnover frequency in both acidic and alkaline environments. These new insights also refine the famous Sabatier principle by emphasizing the need to avoid an "acid trap" while designing M-N-C catalysts for ORR or any other pH-dependent electrochemical applications., Comment: 24 pages, 5 Figures

While conventional graphs only characterize pairwise interactions, higher-order networks (hypergraph, simplicial complex) capture multi-body interactions, which is a potentially more suitable modeling framework for a complex real system. However, the introduction of higher-order interactions brings new challenges for the rigorous analysis of such systems on a higher-order network. In this paper, we study a series of SIS-type diffusion processes with both indirect and direct pathways on a directed hypergraph. In a concrete case, the model we propose is based on a specific choice (polynomial) of interaction function (how several agents influence each other when they are in a hyperedge). Then, by the same choice of interaction function, we further extend the system and propose a bi-virus competing model on a directed hypergraph by coupling two single-virus models together. Finally, the most general model in this paper considers an abstract interaction function under single-virus and bi-virus settings. For the single-virus model, we provide the results regarding healthy state and endemic equilibrium. For the bi-virus setting, we further give an analysis of the existence and stability of the healthy state, dominant endemic equilibria, and coexisting equilibria. All theoretical results are finally supported by some numerical examples.

This paper proposes a novel distributed coverage controller for a multi-agent system with constant-speed unicycle robots (CSUR). The work is motivated by the limitation of the conventional method that does not ensure the satisfaction of hard state- and input-dependent constraints and leads to feasibility issues for multi-CSUR systems. In this paper, we solve these problems by designing a novel coverage cost function and a saturated gradient-search-based control law. Invariant set theory and Lyapunov-based techniques are used to prove the state-dependent confinement and the convergence of the system state to the optimal coverage configuration, respectively. The controller is implemented in a distributed manner based on a novel communication standard among the agents. A series of simulation case studies are conducted to validate the effectiveness of the proposed coverage controller in different initial conditions and with control parameters. A comparison study in simulation reveals the advantage of the proposed method in terms of avoiding infeasibility. The experiment study verifies the applicability of the method to real robots with uncertainties. The development procedure of the method from theoretical analysis to experimental validation provides a novel framework for multi-agent system coordinate control with complex agent dynamics.

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.

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.

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.

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.

The learning inefficiency of reinforcement learning (RL) from scratch hinders its practical application towards continuous robotic tracking control, especially for high-dimensional robots. This work proposes a data-informed residual reinforcement learning (DR-RL) based robotic tracking control scheme applicable to robots with high dimensionality. The proposed DR-RL methodology outperforms common RL methods regarding sample efficiency and scalability. Specifically, we first decouple the original robot into low-dimensional robotic subsystems; and further utilize one-step backward (OSBK) data to construct incremental subsystems that are equivalent model-free representations of the above decoupled robotic subsystems. The formulated incremental subsystems allow for parallel learning to relieve computation load and offer us mathematical descriptions of robotic movements for conducting theoretical analysis. Then, we apply DR-RL to learn the tracking control policy, a combination of incremental base policy and incremental residual policy, under a parallel learning architecture. The incremental residual policy uses the guidance from the incremental base policy as the learning initialization and further learns from interactions with environments to endow the tracking control policy with adaptability towards dynamically changing environments. Our proposed DR-RL based tracking control scheme is developed with rigorous theoretical analysis of system stability and weight convergence. The effectiveness of our proposed method is validated numerically on a 7-DoF KUKA iiwa robot manipulator and experimentally on a 3-DoF robot manipulator that would fail for other counterpart RL methods.

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.

Mobile robots are desired with resilience to safely interact with prior-unknown environments and finally accomplish given tasks. This paper utilizes instantaneous local sensory data to stimulate the safe feedback motion planning (SFMP) strategy with adaptability to diverse prior-unknown environments without building a global map. This is achieved by the numerical optimization with the constraints, referred to as instantaneous local control barrier functions (IL-CBFs) and goal-driven control Lyapunov functions (GD-CLFs), learned from perceptional signals. In particular, the IL-CBFs reflecting potential collisions and GD-CLFs encoding incrementally discovered subgoals are first online learned from local perceptual data. Then, the learned IL-CBFs are united with GD-CLFs in the context of quadratic programming (QP) to generate the safe feedback motion planning strategy. Rather importantly, an optimization over the admissible control space of IL-CBFs is conducted to enhance the solution feasibility of QP. The SFMP strategy is developed with theoretically guaranteed collision avoidance and convergence to destinations. Numerical simulations are conducted to reveal the effectiveness of the proposed SFMP strategy that drives mobile robots to safely reach the destination incrementally in diverse prior-unknown environments.

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.

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.

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.

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.

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., Comment: Submitted to IFAC 2020