Article
Automation & Control Systems
Dong-Nan Liu, Lisheng Tong, Bin Liu, Bo Xu, Qin Gao
Summary: This paper studies the problem of impulsive observers in continuous-time dynamical systems using event-triggered impulsive control. The output-based event-triggered impulsive control schemes are designed and full-order event-triggered impulsive observers are obtained. The concept of impulsive observer with K-asymptotic gain is proposed and shown to have tracking capability and K-asymptotic gain properties.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Physics, Fluids & Plasmas
Konstantinos Sakellariou, Thomas Stemler, Michael Small
Summary: A computationally simple and efficient network-based method for approximating topological entropy of low-dimensional chaotic systems is proposed, which outperforms existing techniques through the construction of complex network sequences for increasingly finer partitions, resulting in more accurate approximations.
Review
Automation & Control Systems
Pauline Bernard, Vincent Andrieu, Daniele Astolfi
Summary: This paper reviews the main design techniques of state observer design for continuous-time dynamical systems, which involve algorithms that reconstruct the full information of a dynamical process based on partially measured data. The available methods are classified based on the detectability/observability assumptions they require. The paper shows how each class of observer relies on transforming the system dynamics in a particular normal form, which allows the design of an observer, and how each observability condition guarantees the invertibility of its associated transformation and the convergence of the observer. Finally, some implementation aspects and open problems are briefly discussed.
ANNUAL REVIEWS IN CONTROL
(2022)
Article
Automation & Control Systems
Jeongho Kim, Insoon Yang
Summary: Maximum entropy reinforcement learning methods have been successfully applied to a range of challenging sequential decision-making and control tasks. However, there is a need to extend these methods to continuous-time systems. This article studies the theory of maximum entropy optimal control in continuous time and derives a novel class of equations. The results demonstrate the performance of the maximum entropy method in continuous-time optimal control and reinforcement learning problems.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Mathematics, Interdisciplinary Applications
Hui Wang, Runzhe Liu, Yang Zhao, Xiaohui Du
Summary: By establishing time-lag financial system risk models and analyzing the dynamical behavior with chaos theory, it is found that different parameter values lead to different motion states in the system, and the time-lag risk intensity parameter strongly influences system motion. Proper measures with certain delay effects must be taken to control risk and select the appropriate time-lag control intensity for the system to operate in a stable state.
Article
Computer Science, Artificial Intelligence
O. Andrianova, A. Poznyak, R. Q. Fuentes-Aguilar, Isaac Chairez
Summary: This study aims to design a robust nonparametric identifier for singular perturbed systems (SPSs) with uncertain mathematical models. The identifier uses a novel differential neural network (DNN) structure, which takes into account the multirate nature of SPS. A rational form of the DNN and a mixed learning law are proposed to solve the identification of the fast dynamics in SPS. The study also proposes a control Lyapunov function and a nonlinear parameter identification methodology for the design of the learning laws. A complementary matrix inequality-based optimization method is used to obtain the smallest attainable convergence invariant region. A numerical example of an enzymatic-substrate-inhibitor system is provided to demonstrate the application of the DNN identifier. The benefits of using the rational form for the identifier in terms of mean square error (MSE) are highlighted in the comparison with a classical identifier.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Mathematics, Applied
Bin Liu, Meng Yang, Bo Xu, Guohua Zhang
Summary: This paper investigates the exponential stabilization of continuous-time dynamical systems through aperiodic intermittent controls (APIC), proposing time-triggered and event-triggered APIC schemes, as well as an E-APIC with state-based control widths (SCW). The study shows that E-APIC with SCW has better performance and can achieve the least total control time compared to other intermittent control schemes.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Automation & Control Systems
Md Arzoo Jamal, Rakesh Kumar, Santwana Mukhopadhyay, Subir Das
Summary: The present article investigates the fixed-time stability analysis of nonlinear dynamical systems with impulsive effects. Novel criteria are derived to achieve stability in fixed-time under stabilizing and destabilizing impulses. Theoretical results show that the estimated fixed-time in this study is less conservative and more accurate compared to existing theorems. The theoretical findings are also applied to impulsive control of general neural network systems.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Bin Liu, Bo Xu, Zhijie Sun
Summary: This paper investigates incremental stability and contraction via impulsive control for continuous-time dynamical systems. Criteria for incremental stability including delta GAS and delta GES are established using Lyapunov-like function and average dwell-time methods. The robustness of delta GES via impulsive control is demonstrated with respect to time-delays and data dropout. Some less conservative criteria are derived for global contracting/delta GES via impulsive control.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2021)
Article
Computer Science, Artificial Intelligence
R. C. Budzinski, S. R. Lopes, C. Masoller
Summary: The study investigates bursting neurons coupled with a small world topology, using ordinal analysis to characterize burst sequences and distinguish different dynamical regimes based on symbol probabilities, which are influenced by coupling strength and network topology. Different spatio-temporal properties of these regimes can be visualized with raster plots.
Article
Automation & Control Systems
Shaojie Wang, Jin Xiao, Xiaoguang Hu, Zongyu Zuo, Tianyou Chen
Summary: This paper solves the finite-time consensus problem for discrete time multi-agent systems (MASs) with agents updating their values via linear iteration and interactions described by signed digraphs. A sufficient condition is presented for agents to reach consensus on any given linear function of multiple initial signals in finite time. The method extends the existing linear iterative framework for unsigned graphs to computation for signed graphs with appropriate modifications.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2023)
Article
Acoustics
Tamas Haba, Csaba Budai
Summary: This paper investigates the continuous-time behavior of sampled-data control systems. It shows that the traditional methods for obtaining continuous-time models can be inaccurate between the sampling instants, even when Shannon's sampling theorem is satisfied. A new method is introduced in this paper to characterize the continuous-time dynamics of sampled-data control systems, and the derived model is verified through simulations.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Automation & Control Systems
Linna Wei, Wu-Hua Chen, Shixian Luo, Ganji Huang
Summary: This paper investigates the impulsive average-consensus problem of first-order multi-agent systems with dynamically changing topologies. The continuous-time dynamics and impulsive protocols are both affected by nonuniform time-varying communication delays. By utilizing Razumikhin techniques and time-varying Lyapunov function method, some impulse-delay-dependent sufficient criteria for the average-consensus of multi-agent systems are derived. Numerical simulations are conducted to demonstrate the effectiveness and validity of the theoretical results.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2022)
Article
Automation & Control Systems
Xinxin Guo, Weisheng Yan, Rongxin Cui, Raja Rout, Shouxu Zhang
Summary: This article proposes a self-triggered adaptive neural network tracking controller for a class of continuous-time nonlinear systems, with unknown drift and input dynamics, by using neural networks to approximate the unknown tracking control. Robust exact differentiator technique and an auxiliary compensator are employed to handle unknown drift, input dynamics, and input constraints, and the effectiveness of the controller is demonstrated through rigorous Lyapunov analyses.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2022)
Article
Materials Science, Multidisciplinary
Angel L. Corps, Pavel Stransky, Pavel Cejnar
Summary: Dynamical phase transitions are defined by the nonanalytic behavior of the survival probability at certain critical times, which originate from the zeros of the survival amplitude. We introduce the complex-time survival amplitude by extending the time variable onto the complex domain, where the complex zeros near the time axis correspond to nonanalytic points where the survival probability abruptly vanishes in the infinite-size limit. We illustrate our results numerically in the fully connected transverse-field Ising model, which exhibits a symmetry-broken phase delimited by an excited-state quantum phase transition, and explore the behavior of the complex-time survival amplitude under changes in the out-of-equilibrium protocol, as well as the influence of the excited-state quantum phase transition.
Article
Mathematics, Applied
Xinyu Han, Yi Zhao, Michael Small
Summary: While reservoir computing has shown remarkable performance in various practical scenarios, its ability to generalize on unseen data is still limited. This paper proposes a novel generalization bound for reservoir computing, based on empirical Rademacher complexity, which explores the relationship between the model's performance and hyperparameters. The proposed bound is tighter and validated through numerical experiments. Additionally, the generalization bound for reservoir computing with a directed acyclic graph (DAG) is found to be lower and less sensitive to hyperparameters compared to that with an Erdos-Renyi undirected random graph (ER graph).
Article
Mathematics, Applied
Braden Thorne, Thomas Jungling, Michael Small, Debora Correa, Ayham Zaitouny
Summary: Reservoir Time Series Analysis (RTSA) is a method that uses the state space representation generated by a reservoir computing model for time series analysis, showing superior performance in feature distinction and accuracy compared to benchmark methods.
Article
Chemistry, Analytical
Ayham Zaitouny, Athanasios D. Fragkou, Thomas Stemler, David M. Walker, Yuchao Sun, Theodoros Karakasidis, Eftihia Nathanail, Michael Small
Summary: This paper proposes a recurrence-based technique for incident detection using time series traffic volume data. The results show that the proposed method can effectively detect incidents and differentiate between different types of congestion.
Article
Computer Science, Artificial Intelligence
Thomas Jungling, Thomas Lymburn, Michael Small
Summary: This study investigates the propagation and distribution of information-carrying signals injected in dynamical systems acting as reservoir computers. By using multivariate correlation analysis, measures known as the consistency spectrum and consistency capacity were revealed to be high-dimensional portraits of the nonlinear functional dependence between input and reservoir state. A hierarchy of capacities characterizes the interference of signals from each source, while time-resolved capacities form a profile of the reservoir's nonlinear fading memory for individual inputs.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2022)
Article
Mathematics, Interdisciplinary Applications
Jinming Wan, Genki Ichinose, Michael Small, Hiroki Sayama, Yamir Moreno, Changqing Cheng
Summary: This study presents a multi-layer network model to study contagion dynamics and behavioral adaptation. The model reveals the interaction between physically isolated communities and the coevolution of behavioral change and spreading dynamics. The analytical insights provide compelling guidelines for coordinated policy design to enhance preparedness for future pandemics.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Zahra Shahriari, Shannon D. Algar, David M. Walker, Michael Small
Summary: We propose a robust algorithm for constructing first return maps of dynamical systems from time series without embedding. Our method is based on ordinal partitions of the time series, and the first return map is constructed from successive intersections with specific ordinal sequences. We define entropy-based measures to guide our selection of the ordinal sequence for a good first return map and show that this method can robustly be applied to time series from classical chaotic systems.
Review
Mathematics, Applied
Eugene Tan, Shannon Algar, Debora Correa, Michael Small, Thomas Stemler, David Walker
Summary: Delay embedding methods are important tools in time series analysis and prediction. The selection of embedding parameters can greatly impact the analysis, leading researchers to develop various methods for optimization. This paper provides a comprehensive overview of embedding theory, outlining existing methods for selecting embedding lag in both uniform and non-uniform cases. The proposed method, SToPS, combines dynamical and topological arguments to select embedding lags, and performs similarly to existing methods for non-uniform embedding. It also outperforms other methods when predicting fast-slow time series.
Article
Computer Science, Information Systems
Tongfeng Weng, Xiaolu Chen, Zhuoming Ren, Huijie Yang, Jie Zhang, Michael Small
Summary: We adopt reservoir computing, a machine learning technique, to study synchronization phenomena in complex networks. By constructing a coupled configuration, we demonstrate that coupled reservoir oscillators exhibit synchrony with the learned dynamical system. Through this synchronization scheme, we recover the observed system's bifurcation behavior solely based on its chaotic dynamics. Our work provides an alternative framework for studying synchronization phenomena in nature when only observed data are available.
INFORMATION SCIENCES
(2023)
Article
Physics, Multidisciplinary
Siyang Jiang, Jin Zhou, Michael Small, Jun-an Lu, Yanqi Zhang
Summary: Searching for key nodes and edges in a network has been a longstanding problem. Recently, there has been increased attention on the cycle structure in networks. This study proposes a ranking algorithm for cycle importance by identifying key cycles that contribute significantly to the network's dynamics. The researchers provide a concrete definition of importance using the Fiedler value and present a neat index for ranking cycles based on the sensitivity of the Fiedler value to different cycles. Numerical examples demonstrate the effectiveness of this method.
PHYSICAL REVIEW LETTERS
(2023)
Article
Mathematics, Applied
Lixiang Liu, Shanshan Chen, Michael Small, Jack Murdoch Moore, Keke Shang
Summary: This paper presents a novel SIRS model on scale-free networks that considers behavioral memory and time delay to depict an adaptive behavioral feedback mechanism in the spread of epidemics. The study includes a rigorous analysis of the dynamics of the model, determines the basic reproduction number R0, uniform persistence, and global asymptotic stability of equilibria. The model exhibits a sharp threshold property, and optimal control strategies for effective vaccination and treatment are demonstrated. Stochastic network simulations validate the findings and indicate that time delay does not affect R0, but behavioral memory does.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Editorial Material
Biology
Shannon D. Algar, Jennifer Rodger, Michael Small
PHYSICS OF LIFE REVIEWS
(2023)
Article
Engineering, Industrial
Yucheng Hao, Limin Jia, Enrico Zio, Yanhui Wang, Michael Small, Man Li
Summary: The researchers studied the optimization repair strategy for high-speed trains by establishing an interdependent network and introducing a resilience metric based on network theory. They developed an interdependent machine-electricity-communication network and related cascading failure models and proposed comprehensive robustness metrics for the network and nodes. They solved the resilience optimization model of the network using a tabu search algorithm. They analyzed the optimal repair strategy for different numbers of failed nodes and analyzed the characteristics of the preferentially repaired node. The optimal repair strategy is not necessarily determined by topological metrics.
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2023)
Article
Physics, Fluids & Plasmas
Jack Murdoch Moore, Haiying Wang, Michael Small, Gang Yan, Huijie Yang, Changgui Gu
Summary: The network correlation dimension controls the distribution of network distance in terms of a power-law model and has significant impacts on both structural properties and dynamical processes. We have developed new maximum likelihood methods that can robustly and objectively identify network correlation dimension as well as a bounded interval of distances where the model accurately represents the structure. We have also compared the traditional practice of estimating correlation dimension with a proposed alternative method using the fraction of nodes at a distance modeled as a power law.
Article
Physics, Multidisciplinary
Eugene Tan, Shannon D. Algar, Debora Correa, Thomas Stemler, Michael Small
Summary: A method of constructing a discretised network representation of a system's attractor is proposed and its applicability in identifying dynamical change points in different systems is demonstrated.
COMMUNICATIONS PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Tongfeng Weng, Xiaolu Chen, Zhuoming Ren, Huijie Yang, Jie Zhang, Michael Small
Summary: This study investigates the collective behavior of multiply moving reservoir computing oscillators. These oscillators gradually exhibit coherent rhythmic behavior when their number is large enough, showing excellent agreement with their learned dynamical system. Furthermore, the oscillators can exhibit significantly distinct collective behaviors resembling bifurcation phenomenon when changing a critical reservoir parameter. Intermittent synchronization emerges among the oscillators when studying a continuous chaotic system.
CHAOS SOLITONS & FRACTALS
(2023)
