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Multistable systems with nested hidden and self-excited double scroll attractors

The European Physical Journal Special Topics 2021年第3期231卷 351-357页

作者： Escalante-González, R. J. Campos, Eric Electrical Electronic and Mechatronics Department Technological Institute of San Luis Potosí San Luis Potosí Mexico Division of Control and Dynamical Systems Institute for Scientific and Technological Research of San Luis Potosí San Luis Potosí Mexico

systems with multiscroll attractors have been studied extensively in recent decades. Some efforts have focused on understanding the mechanisms that generate complex dynamics in relatively simple systems. The chaotic properties of these systems have been found useful in cryptographic techniques. Recently, hidden chaotic attractors have raised interest in cryptographic algorithms due to the additional complexity they provide. Although several hidden chaotic attractors have been reported, the variety of mechanisms involved in the appearance of hidden attractors in multistable systems is not fully understood. Here we report an approach to generate multistable systems with nested hidden attractors. The idea behind the construction is to use a nonlinear function to produce coexisting self-excited attractors at specific locations. So, a hidden attractor emerges for each pair of self-excited attractors, each pair of these hidden attractors leads to the appearance of a larger hidden attractor. In this way, hidden nested attractors appear depending on the number of self-excited attractors. Therefore, the systems produced with the approach could possibly be used in a cryptographic algorithm. The new dynamical system to generate nested attractors starts by selecting three parameters which are related to the oscillatory behavior and appear in the linear part (matrix A) of the system equations. Then, using the proposed simplest system description, two parameters, which are related to the location of the equilibria, are adjusted in order to generate a bistable behavior with two self-excited attractors. Each of these self-excited attractors is generated by a pair of equilibrium points. Thus the two self-excited attractors emerge when the relationship between the separation of the two pairs of equilibria and the separation by pairs of equilibria is large enough, which is controlled by two parameters. The bistable behavior is found by choosing the appropriate parameters of the matrix

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Improving Generative Model-based Unfolding with Schrödinger Bridges

arXiv

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arXiv 2023年

作者： Diefenbacher, Sascha Liu, Guan-Horng Mikuni, Vinicius Nachman, Benjamin Nie, Weili Physics Division Lawrence Berkeley National Laboratory BerkeleyCA94720 United States Autonomous Control and Decision Systems Laboratory Georgia Institute of Technology AtlantaGA30332 United States National Energy Research Scientific Computing Center Berkeley Lab BerkeleyCA94720 United States Berkeley Institute for Data Science University of California BerkeleyCA94720 United States Machine Learning Research Group NVIDIA Research United States

Machine learning-based unfolding has enabled unbinned and high-dimensional differential cross section measurements. Two main approaches have emerged in this research area: one based on discriminative models and one based on generative models. The main advantage of discriminative models is that they learn a small correction to a starting simulation while generative models scale better to regions of phase space with little data. We propose to use Schrödinger Bridges and diffusion models to create SBUnfold, an unfolding approach that combines the strengths of both discriminative and generative models. The key feature of SBUnfold is that its generative model maps one set of events into another without having to go through a known probability density as is the case for normalizing flows and standard diffusion models. We show that SBUnfold achieves excellent performance compared to state of the art methods on a synthetic Z+jets dataset. © 2023, CC BY.

关键词： Phase space methods

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Riemannian Online Optimistic Algorithms with Dynamic Regret

引用

IEEE Transactions on Automatic control 2025年

作者： Wang, Xi Yuan, Deming Hong, Yiguang Hu, Zihao Wang, Lei Shi, Guodong University of New South Wales School of Electrical Engineering & Telecommunications SydneyNSW2052 Australia Nanjing University of Science and Technology School of Automation Nanjing210094 China Tongji University Shanghai Research Institute for Intelligent Autonomous Systems Shanghai201210 China Hong Kong University of Science and Technology Department of Mathematics Hong Kong Zhejiang University College of Control Science and Engineering Zhejiang 310058 China The University of Sydney Australian Center for Robotics School of Aerospace Mechanical and Mechatronic Engineering NSW2006 Australia

In this paper, we consider Riemannian online convex optimization with dynamic regret, which involves minimizing the cumulative loss difference between a learner's decisions and a sequence of adaptive decisions across dynamic environments over time on Riemannian manifolds. First, we propose Riemannian Online Optimistic Gradient Descent (R-OOGD), which extends the classical optimistic algorithms to Riemannian manifolds, requiring one gradient inquiry per round. We then propose Riemannian Adaptive Online Optimistic Gradient Descent (R-AOOGD) by incorporating the meta-expert framework into R-OOGD. We analyze the dynamic regret of R-OOGD and R-AOOGD in terms of the regularity of the sequence of cost functions and comparators. The dynamic regret bound matches the results in Euclidean space and with a scale adjustment of O(1+κ D2/√1-KD2) related to the sectional curvature lower bound κ, sectional curvature upper bound and feasible set diameter. Finally, we provide numerical experiments to illustrate the performance of the proposed algorithms. © 1963-2012 IEEE.

关键词： Optimization algorithms

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PARODIS: One MPC framework to control them all. Almost.

PARODIS: One MPC framework to control them all. Almost.

引用

control Technology and Applications (CCTA),

作者： Thomas Schmitt Jens Engel Matthias Hoffmann Tobias Rodemann Control Methods & Robotics Lab Technical University of Darmstadt Darmstadt Germany. Honda Research Institute Europe GmbH Offenbach Germany Systems Modeling and Simulation Systems Engineering Saarland University Germany

ISBN: (纸本)9781665436441

We introduce the MATLAB framework PARODIS, the Pareto optimal Model Predictive control framework for distributed systems. It is a general-purpose, flexible and easy-to-use framework for discrete state space models. Special features are the support of distributed (hierarchical) systems, scenario-based optimization and built-in methods for determination of the Pareto front and selection of a solution. It uses the popular MATLAB framework YALMIP for the symbolic formulation of optimization problems and models.

关键词： Adaptation models Object oriented modeling Conferences Hierarchical systems Pareto optimization Mathematical models Optimization

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Identifiability Analysis of Noise Covariances for LTI Stochastic systems with Unknown Inputs

arXiv

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arXiv 2022年

作者： Kong, He Sukkarieh, Salah Arnold, Travis J. Chen, Tianshi Mu, Biqiang Zheng, Wei Xing Shenzhen518055 China Guangdong Provincial Key Laboratory of Human-Augmentation and Rehabilitation Robotics in Universities SUSTech Shenzhen518055 China Sydney Institute for Robotics and Intelligent Systems The University of Sydney NSW2006 Australia Madison WI53704 United States School of Data Science Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Computer Data and Mathematical Sciences Western Sydney University SydneyNSW2751 Australia

Most existing works on optimal filtering of linear time-invariant (LTI) stochastic systems with arbitrary unknown inputs assume perfect knowledge of the covariances of the noises in the filter design. This is impractical and raises the question of whether and under what conditions one can identify the process and measurement noise covariances (denoted as Q and R, respectively) of systems with unknown inputs. This paper considers the identifiability of Q/R using the correlation-based measurement difference approach. More specifically, we establish (i) necessary conditions under which Q and R can be uniquely jointly identified;(ii) necessary and sufficient conditions under which Q can be uniquely identified, when R is known;(iii) necessary conditions under which R can be uniquely identified, when Q is known. It will also be shown that for achieving the results mentioned above, the measurement difference approach requires some decoupling conditions for constructing a stationary time series, which are proved to be sufficient for the well-known strong detectability requirements established by Hautus. © 2022, CC BY.

关键词： Stochastic systems

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Connecting the Dots: Context-Driven Motion Planning Using Symbolic Reasoning

arXiv

引用

arXiv 2023年

作者： van der Ploeg, Chris Braat, Michiel Masini, Beatrice Brouwer, Jochem Paardekooper, Jan-Pieter Netherlands Organisation for Applied Scientific Research Integrated Vehicle Safety Group Helmond5700 AT Netherlands Eindhoven University of Technology Dynamics and Control Group Mechanical Engineering Dept. P.O. Box 513 Eindhoven5600 MB Netherlands Netherlands Organisation for Applied Scientific Research Intelligent Autonomous Systems Group The Hague2597 AK Netherlands Radboud University Donders Institute for Brain Cognition and Behaviour P.O.Box 9010 Nijmegen6500 GL Netherlands

The introduction of highly automated vehicles on the public road may improve safety and comfort, although its success will depend on social acceptance. This requires trajectory planning methods that provide safe, proactive, and comfortable trajectories that are risk-averse, take into account predictions of other road users, and comply with traffic rules, social norms, and contextual information. To consider these criteria, in this article, we propose a non-linear model-predictive trajectory generator. The problem space is populated with risk fields. These fields are constructed using a novel application of a knowledge graph, which uses a traffic-oriented ontology to reason about the risk of objects and infrastructural elements, depending on their position, relative velocity, and classification, as well as depending on the implicit context, driven by, e.g., social norms or traffic rules. Through this novel combination, an adaptive trajectory generator is formulated which is validated in simulation through 4 use cases and 309 variations and is shown to comply with the relevant social norms, while taking minimal risk and progressing towards a goal area. Copyright © 2023, The Authors. All rights reserved.

关键词： Motion planning

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Fast control Strategy of Grid-forming Inverter Based on Power Feedforward

Fast Control Strategy of Grid-forming Inverter Based on Powe...

引用

第42届中国控制会议

作者： Sheng Zhang Zhijian Fang Qine Liu Muchao Xiang Dingbang Huang School of Automation China University of Geosciences Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems Engineering Research Center of Intelligent Technology for Geo-Exploration Ministry of Education State Grid Hubei Electric Power Co. LtdXiangyang Power Supply Company Electric Power Scientific Research Institute of State Grid Hubei Electric Power Co. Ltd

Grid-forming inverter is widely used in grid-connected systems of distributed generation because of its frequency and voltage support capacity and good stability in microgrid,but its large inertia will affect the dynamic response speed of grid-forming *** order to solve this problem,this paper introduces the loop that affects the dynamic response of grid-forming inverter,and carries out small signal modeling for active loop,analyzes the dynamic performance indicators and determinants of typical second-order ***,a method of adding power feedforward coefficient to the forward channel of the power loop is designed,and the response speed of the system with or without feedforward coefficient under the unit step response is ***,the simulation results show that adding the power feedforward coefficient can improve the response speed of the grid-forming inverter during startup and power switching,then achieves the effect of fast control.

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Intelligent system for real-time adaptive management of groups of small satellites: Design and experimenting 13

Intelligent system for real-time adaptive management of grou...

引用

13th Multiconference on control Problems, MCCP 2020

作者： Skobelev, P. Galuzin, V. Galitskaya, A. Travin, V. Samara Federal Research Scientific Center Ras Institute for the Control of Complex Systems Ras Sadovaya Str. 61 Samara443020 Russia Samara State Technical University Molodogvardeyskaya Str. 244 Samara443100 Russia Sec Smart Solutions Moskovskoye Shosse Office 1201 17 Samara443013 Russia

The paper considers development of an intelligent system for real-time management of groups of small satellites, as well as an approach to its implementation built on the basis of multi-agent technology. It discusses the main disadvantages of traditional planning systems currently used to manage various space missions, which complicate their application with new-generation multi-satellite orbital groups. A brief problem statement for planning the operation of a space observation system is given. The architecture of the developed system is proposed, describing the functions of the main modules and screens, which make it possible to process applications for imaging of observation objects entering the system in real time. Results of experimental studies are also presented. They demonstrate applicability of the proposed approach to solving problems of managing groups of small satellites to increase efficiency of using resources of the space system. Finally, the prospects for development and application of the system are discussed. © Published under licence by IOP Publishing Ltd.

关键词： Intelligent systems

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Maxwell's equations in homogeneous spaces for admissible electromagnetic fields

arXiv

引用

arXiv 2022年

作者： Obukhov, Valery V. Institute of Scientific Research and Development Tomsk State Pedagogical University Tomsk State Pedagogical University Tomsk634041 Russia Laboratory for Theoretical Cosmology International Center of Gravity and Cosmos Tomsk State University of Control Systems and Radio Electronics Tomsk634050 Russia

Maxwell's vacuum equations are integrated for admissible electromagnetic fields in homogeneous spaces. Admissible electromagnetic fields are those for which the space group generates an algebra of symmetry operators ( integrals of motion ) that is isomorphic to the algebra of group operators. Two frames associated with the group of motions are used to obtain systems of ordinary differential equations to which Maxwell's equations reduce. The solutions are obtained in quadratures. The potentials of the admissible electromagnetic fields and the metrics of the spaces contained in the obtained solutions depend on six arbitrary time functions, so it is possible to use them to integrate field equations in the theory of gravity. Copyright © 2022, The Authors. All rights reserved.

关键词： Maxwell equations

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Riemannian Optimistic Algorithms

arXiv

引用

arXiv 2023年

作者： Wang, Xi Yuan, Deming Hong, Yiguang Hu, Zihao Wang, Lei Shi, Guodong Australian Center for Robotics School of Aerospace Mechanical and Mechatronic Engineering The University of Sydney NSW2006 Australia Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Automation Nanjing University of Science and Technology Jiangsu210023 China Shanghai Research Institute for Intelligent Autonomous Systems Tongji University Shanghai201210 China College of Computing Georgia Institute of Technology AtlantaGA30339 United States College of Control Science and Engineering Zhejiang University Zhejiang310058 China

In this paper, we consider Riemannian online convex optimization with dynamic regret. First, we propose two novel algorithms, namely the Riemannian Online Optimistic Gradient Descent (R-OOGD) and the Riemannian Adaptive Online Optimistic Gradient Descent (R-AOOGD), which combine the advantages of classical optimistic algorithms with the rich geometric properties of Riemannian manifolds. We analyze the dynamic regrets of the R-OOGD and R-AOOGD in terms of regularity of the sequence of cost functions and comparators. Next, we apply the R-OOGD to Riemannian zero-sum games, leading to the Riemannian Optimistic Gradient Descent Ascent algorithm (R-OGDA). We analyze the average iterate and best-iterate of the R-OGDA in seeking Nash equilibrium for a two-player, zero-sum, g-convex-concave games. We also prove the last-iterate convergence of the R-OGDA for g-strongly convex-strongly concave problems. Our theoretical analysis shows that all proposed algorithms achieve results in regret and convergence that match their counterparts in Euclidean spaces. Finally, we conduct several experiments to verify our theoretical findings. Copyright © 2023, The Authors. All rights reserved.

关键词： Cost functions

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