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Exponential convergence for distributed smooth optimization under the restricted secant inequality condition

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arXiv 2019年

作者： Yi, Xinlei Zhang, Shengjun Yang, Tao Johansson, Karl H. Chai, Tianyou Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm100 44 Sweden Department of Electrical Engineering University of North Texas DentonTX76203 United States State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China

This paper considers the distributed smooth optimization problem in which the objective is to minimize a global cost function formed by a sum of local smooth cost functions, by using local information exchange. The standard assumption for proving exponential/linear convergence of first-order methods is the strong convexity of the cost functions, which does not hold for many practical applications. In this paper, we first show that the continuous-time distributed primal-dual gradient algorithm converges to one global minimizer exponentially under the assumption that the global cost function satisfies the restricted secant inequality condition. This condition is weaker than the strong convexity condition since it does not require convexity and the global minimizers are not necessary to be unique. We then show that the discrete-time distributed primal-dual algorithm constructed by using the Euler's approximation method converges to one global minimizer linearly under the same condition. The theoretical results are illustrated by numerical simulations. Copyright © 2019, The Authors. All rights reserved.

关键词： Continuous time systems

A Game Theoretic Approach to Design a Resilient controller For a Nonlinear Discrete System

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IFAC-PapersOnLine 2017年第1期50卷 387-392页

作者： Salehghaffari H. Krishnamurthy P. Khorrami F. Control/Robotics Research Laboratory (CRRL) Department of Electrical and Computer Engineering NYU Tandon School of EngineeringNY 11201 United States

In this paper, the problem of designing a cyber-resilient controller is studied for a class of nonlinear discrete systems subject to actuator attacks. We develop a coupled control design approach, which incorporates interaction between the intrusion detection system (IDS) and the attacker, with the controller design in the physical layer. In the considered cyber-attack scenario, the attacker attempts to first bypass the IDS to spoof the system actuator and then deteriorate the controller performance in the physical layer. The optimal attack strategy to deceive the IDS is obtained based on a zero-sum game in the detection layer. In the physical layer, it is assumed that the system has a secure compensator along with the actuator to deal with the injected attack values. Therefore, the controller and the compensator are designed based on the results of the game in the detection layer, and stochastic stability analysis and Lyapunov function methods are used to prove boundedness of the system state in the probabilistic sense. Finally, through numerical analysis of a representative example, the proposed design procedure is illustrated and its efficacy in maintaining robust stability of the cyber-physical system under actuator attacks is demonstrated. © 2017

关键词： attack strategy control systems security Cyber-physical system resilient control stochastic stability zero-sum game

Modeling and reachability analysis of synchronizing transitions bounded Petri net systems based upon semi-tensor product of matrices

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The Journal of China Universities of Posts and Telecommunications 2017年第1期24卷 77-86页

作者： Gao Na Han Xiaoguang Chen Zengqiang Zhang Qing College of Computer and Control Engineering Nankai University Tianjin 300350 China Tianjin Key Laboratory of Intelligent Robotics Tianjin 300350 China College of Science Civil Aviation University of China Tianjin 300300 China

The reachability problem of synchronizing transitions bounded Petri net systems （BPNSs） is investigated in this paper by constructing a mathematical model for dynamics of BPNS. Using the semi-tensor product （STP） of matrices, the dynamics of BPNSs, which can be viewed as a combination of several small bounded subnets via synchronizing transitions, are described by an algebraic equation. When the algebraic form for its dynamics is established, we can present a necessary and sufficient condition for the reachability between any marking （or state） and initial marking. Also, we give a corresponding algorithm to calculate all of the transition paths between initial marking and any target marking. Finally, an example is shown to illustrate proposed results. The key advantage of our approach, in which the set of reachable markings of BPNSs can be expressed by the set of reachable markings of subnets such that the big reachability set of BPNSs do not need generate, is partly avoid the state explosion problem of Petri nets （PNs）.

关键词： reachability Petri nets BPNSs semi-tensor product （STP） of matrices synchronizing transitions

Linear convergence of first- And zeroth-order primal-dual algorithms for distributed nonconvex optimization

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arXiv 2019年

作者： Yi, Xinlei Zhang, Shengjun Yang, Tao Chai, Tianyou Johansson, Karl H. Division of Decision and Control Systems School of Electrical Engineering and Computer Science Kth Royal Institute of Technology Digital Futures Stockholm100 44 Sweden Department of Electrical Engineering University of North Texas DentonTX76203 United States State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China

This paper considers the distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of local cost functions by using local information *** first propose a distributed first-order primal-dual algorithm. We show that it converges sublinearly to a stationary point if each local cost function is smooth and linearly to a global optimum under an additional condition that the global cost function satisfies the Polyak-Lojasiewicz condition. This condition is weaker than strong convexity, which is a standard condition for proving linear convergence of distributed optimization algorithms, and the global minimizer is not necessarily unique. Motivated by the situations where the gradients are unavailable, we then propose a distributed zeroth-order algorithm, derived from the proposed distributed first-order algorithm by using a deterministic gradient estimator, and show that it has the same convergence properties as the proposed first-order algorithm under the same conditions. The theoretical results are illustrated by numerical simulations. Copyright © 2019, The Authors. All rights reserved.

关键词： Cost functions

Distributed bandit online convex optimization with time-varying coupled inequality constraints

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arXiv 2019年

作者： Yi, Xinlei Li, Xiuxian Yang, Tao Xie, Lihua Johansson, Karl H. Chai, Tianyou Division of Decision and Control Systems School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm100 44 Sweden School of Electrical and Electronic Engineering Nanyang Technological University 50 Nanyang Avenue Singapore639798 Singapore State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Shenyang110819 China

This paper considers the problem of distributed bandit online convex optimization with time-varying coupled inequality constraints. This problem can be defined as a repeated game between a group of learners and an adversary. The learners attempt to minimize a sequence of global loss functions and at the same time satisfy a sequence of coupled constraint functions. The global loss and the coupled constraint functions are the sum of local convex loss and constraint functions, respectively, which are adaptively generated by the adversary. The local loss and constraint functions are revealed in a bandit manner, i.e., only the values of loss and constraint functions at sampled points are revealed to the learners, and the revealed function values are held privately by each learner. We consider two scenarios, one- and two-point bandit feedback, and propose two corresponding distributed bandit online algorithms used by the learners. We show that sublinear expected regret and constraint violation are achieved by these two algorithms, if the accumulated variation of the comparator sequence also grows sublinearly. In particular, we show that O(T θ1 ) expected static regret and O(T 7/4−θ1 ) constraint violation are achieved in the one-point bandit feedback setting, and O(T max{κ,1−κ}) expected static regret and O(T 1−κ/2) constraint violation in the two-point bandit feedback setting, where θ1 ∈ (3/4, 5/6] and κ ∈ (0, 1) are user-defined trade-off parameters. Finally, these theoretical results are illustrated by numerical simulations of a simple power grid example. Copyright © 2019, The Authors. All rights reserved.

关键词： Convex optimization

Variable population memetic search: A case study on the critical node problem

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arXiv 2019年

作者： Zhou, Yangming Hao, Jin-Kao Fu, Zhang-Hua Wang, Zhe Lai, Xiangjing School of Information Science and Engineering East China University of Science and Technology 130 Meilong Road Shanghai200237 China Key Laboratory of Advanced Control and Optimization for Chemical Processes Ministry of Education Department of Computer Science LERIA Université d'Angers 2 Boulevard Lavoisier Angers49045 France Institut Universitaire de France 1 rue Descartes Paris75231 France Robotics Laboratory for Logistics Service Institute of Robotics and Intelligent Manufacturing Chinese University of Hong Kong Shenzhen Institute of Artificial Intelligence and Robotics for Society Shenzhen518172 China Institute of Advanced Technology Nanjing University of Posts and Telecommunications Nanjing210023 China

Population-based memetic algorithms have been successfully applied to solve many difficult combinatorial problems. Often, a population of fixed size was used in such algorithms to record some best solutions sampled during the search. However, given the particular features of the problem instance under consideration, a population of variable size would be more suitable to ensure the best search performance possible. In this work, we propose variable population memetic search (VPMS), where a strategic population sizing mechanism is used to dynamically adjust the population size during the memetic search process. Our VPMS approach starts its search from a small population of only two solutions to focus on exploitation, and then adapts the population size according to the search status to continuously influence the balancing between exploitation and exploration. We illustrate an application of the VPMS approach to solve the challenging critical node problem (CNP). We show that the VPMS algorithm integrating a variable population, an effective local optimization procedure (called diversified late acceptance search) and a backbone-based crossover operator performs very well compared to state-of-the-art CNP algorithms. The algorithm is able to discover new upper bounds for 13 instances out of the 42 popular benchmark instances, while matching 23 previous best-known upper bounds. Copyright © 2019, The Authors. All rights reserved.

关键词： Population statistics

Looseness Detection of Rail Fasteners Using MEMS Sensor and Power Spectrum Entropy

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Looseness Detection of Rail Fasteners Using MEMS Sensor and ...

International Conference on Micro/Nano Sensors for AI, Healthcare, and robotics (NSENS)

作者： Hao Sun Zhikun Zhan Hongyu Zhang Junshan Liu Xiaopeng Sha Xiaodong Yu Jianing Yu Yuliang Zhao Lianqing Liu Key Lab of Industrial Computer Control Engineering of Hebei Province Yanshan University Qinhuangdao China School of Control Engineering Northeastern University at Qinhuangdao Qinhuangdao China State key Laboratory of Robotics Chinese Academy of Sciences

ISBN: (纸本)9781538694091;9781538694084

Rail fasteners, a key component of a railway track, are used to connect the rail and the sub-rail foundation together with the required degree of elasticity. Severely loose or failed fasteners may lead to serious safety hazards for rail transportation. However, current strategies for determining fastener looseness are mainly implemented manually, which is labor-intensive, inefficient and less-than-objective. In this paper, we propose a system that uses a MEMS acceleration meter and a wireless data transmission technique to detect railway fasteners. Vibration was generated by hitting the rail with a hammer. Then the acceleration data was transmitted to the cloud by the Global System for Mobile Communications (GSM) technique. The fastener looseness was analyzed using power spectrum entropy and frequency domain analysis. Results from the field experiments show that our method can identify the fastener's loosening state accurately and automatically. This wireless, low-cost fastener inspection system is expected to provide an effective approach to improving the efficiency of regular railway maintenance..

关键词： Conferences Artificial intelligence Medical services Robot sensing systems IP networks

Electrochemical Detection of Insulin Based on Screen Printed Electrode Modified by Nickel Hydroxide

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Electrochemical Detection of Insulin Based on Screen Printed...

International Conference on Micro/Nano Sensors for AI, Healthcare, and robotics (NSENS)

作者： Hongyu Zhang Zhikun Zhan Yuliang Zhao Xiaopeng Sha Xiaodong Yu Hui Sun Lijia Gu Jiali Liu Lianqing Liu Key Lab of Industrial Computer Control Engineering of Hebei Province Yanshan University Qinhuangdao China School of Control Engineering Northeastern University at Qinhuangdao Qinhuangdao China State key Laboratory of Robotics Chinese Academy of Sciences

ISBN: (纸本)9781538694091;9781538694084

This paper reports a novel electrochemical method for the detection of insulin in ultra-pure water. A screen printed electrode (SPE) modified by Nickel hydroxide was used as the working electrode, one with good activity of electro-catalytic oxidation-reduction for insulin. The SPE was modified by Nickel hydroxide using the electrodeposition method. The results showed that Nickel hydroxide was homogeneously electrodeposited on the surface of the working electrode. A coin-size electrolytic tank was fabricated with PDMS, which only requires 0.3ml of sample for the detection. The concentration of insulin was analyzed using the methods of Cyclic voltammetry (CV), Electrochemical impedance spectroscopy (EIS) and Chronoamperometry (i-t). The Nickel hydroxide used for detecting insulin showed good analytical characteristics, such as a high sensitivity of 14.797μA·μM -1 , a good linear detection range of 100nM-5μM, and a low detection limit of 93nM. This nickel hydroxide modified SPE electrode has a much smaller size and is easier to fabricate than traditional electrodes, making it a much more promising candidate for an insulin sensor.

关键词： Electrodes Insulin Nickel Oxidation Sensitivity Surface treatment Diabetes

Discrete effect on the anti-bounce-back boundary condition of lattice Bhatnagar-Gross-Krook model for convection-diffusion equations

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arXiv 2019年

作者： Wang, Liang Meng, Xuhui Wu, Hao-Chi Wang, Tian-Hu Lu, Gui Key Laboratory of Condition Monitoring and Control for Power Plant Equipment of Ministry of Eduction North China Electric Power University Beijing102206 China School of Energy Power and Mechanical Engineering North China Electric Power University Beijing102206 China Division of Applied Mathematics Brown University ProvidenceRI02912 United States School of Control and Computer Engineering North China Electric Power University Beijing102206 China

The discrete effect on the boundary condition has been a fundamental topic for the lattice Boltzmann method in simulating heat and mass transfer problems. In previous works based on the halfway anti-bounce-back (ABB) boundary condition for convection-diffusion equations (CDEs), it is reported that the discrete effect cannot be commonly removed in the Bhatnagar-Gross-Krook (BGK) model except for a special value of relaxation time. Targeting this point in the present paper, we still proceed within the framework of BGK model for two-dimensional CDEs, and analyze the discrete effect on a non-halfway ABB boundary condition which incorporates the effect of the distance ratio. By analyzing an unidirectional diffusion problem with a parabolic distribution, the theoretical derivations with three different discrete velocity models show that the numerical slip is a combined function of the relaxation time and the distance ratio. Different from previous works, we definitely find that the relaxation time can be freely adjusted by the distance ratio in a proper range to eliminate the numerical slip. Some numerical simulations are carried out to validate the theoretical derivations, and the numerical results for the cases of straight and curved boundaries confirm our theoretical analysis. Finally, it should be noted that the present analysis can be extended from the BGK model to other lattice Boltzmann (LB) collision models for CDEs, which can broaden the parameter range of the relaxation time to approach 0.5. Copyright © 2019, The Authors. All rights reserved.

关键词： Relaxation time