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Robust finite-time H-infinity control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation

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APPLIED MATHEMATICS AND COMPUTATION 2016年 286卷 213-227页

作者： Ma, Yuechao Jia, Xiaorui Liu, Deyou Yanshan Univ Coll Sci Qinhuangdao 066004 Hebei Peoples R China

In this paper, the problem of robust finite-time H-infinity control for discrete-time singular Markovian jump systems with time-varying delay and actuator saturation is studied. First, sufficient conditions that guarantee the systems singular stochastic finite-time boundedness are derived via constructing a delay-dependent Lyapunov-Krasonskii functional and linear matrix inequalities (LMI) approaches. Then the results are extended to singular stochastic finite-time H-infinity boundedness. Furthermore, with these conditions and convex optimization arithmetic, the design method of H-infinity controller and conditions that ensure the H-infinity disturbance attenuation level are obtained. Finally, some numerical examples are presented to illustrate the validity and efficiency of the proposed methods. (C) 2016 Elsevier Inc. All rights reserved.

关键词： Robust finite-time H-infinity control Singular stochastic finite-time boundedness Discrete-time singular system Actuator saturation Linear matrix inequality convex optimization problem

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2015年第12期14卷 6777-6791页

作者： Pourgharehkhan, Zahra Taherpour, Abbas Sala-Alvarez, Josep Khattab, Tamer Imam Khomeini Int Univ Dept Elect Engn Qazvin *** Iran Univ Politecn Cataluna Barcelona Tech Dept Signal Theory & Commun ES-08034 Barcelona Spain Qatar Univ Dept Elect Engn Doha Qatar

We address the problem of spectrum sensing in cognitive radios (CRs) when the secondary user (SU) is equipped with a multiantenna receiver. We consider scenarios with correlation between the received channels at different antennas and unequal per-antenna noise variances to accommodate calibration errors. First, we derive the exact as well as the asymptotic performance of the genie-aided (benchmark) detector with perfect knowledge of the antenna correlation coefficients, the primary user (PU) signal power and the noise covariance matrix. Then, we consider the sensing problem in which the SU is non-cognizant of the per-antenna noise variances, the PU signal power and the correlation of channel gains, starting with a specific treatment of the two-antenna case. For a general multiantenna receiver, we propose combining the derived test statistics among all antenna pairs. The related optimization problem to obtain the optimum combination weights is analyzed, which requires the analytical performance characterization of the constituent two-antenna detector. Thus, we compute the exact performance of the proposed detector in a special case (a particular case of the Hadamard ratio test) in terms of its detection and false alarm probabilities. Performance analyses are verified with simulations, showing that the proposed detector outperforms several recently-proposed multiantenna detectors for CR in the scenarios considered.

关键词： Cognitive radio spectrum sensing multiple antennas antenna correlations calibration uncertainty convex optimization problem

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ON THE BEHAVIOR OF THE DOUGLAS RACHFORD ALGORITHM FOR MINIMIZING A convex FUNCTION SUBJECT TO A LINEAR CONSTRAINT

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SIAM JOURNAL ON optimization 2020年第3期30卷 2559-2576页

作者： Bauschke, Heinz H. Moursi, Walaa M. Univ British Columbia Math Kelowna BC V1V 1V7 Canada Univ Waterloo Dept Combinator & Optimizat Waterloo ON N2L 3G1 Canada

The Douglas Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one minimizer. In the absence of minimizers, it was recently shown that for the case of two indicator functions, the DRA converges to a best approximation solution. In this paper, we present a new convergence result on the DRA applied to the problem of minimizing a convex function subject to a linear constraint. Indeed, a normal solution may be found even when the domain of the objective function and the linear subspace constraint have no point in common. As an important application, a new parallel splitting result is provided. We also illustrate our results through various examples.

关键词： convex optimization problem Douglas-Rachford splitting inconsistent constrained optimization least squares solution normal problem parallel splitting method projection operator proximal mapping

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Design and Implementation of Adaptive Multi-Tap Analog Interference Canceller

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2019年第3期18卷 1698-1706页

作者： Zhang, Liyuan Ma, Meng Jiao, Bingli Peking Univ Sch Elect Engn & Comp Sci Beijing 100871 Peoples R China

Due to the severity of self-interferences, analog interference canceller is an essential part of a full duplex radio system. As the self-interference can potentially be even much stronger than the received signal, it must be meritoriously suppressed before analog-to-digital conversion. This paper is aimed to provide an optimal radio frequency domain multi-tap interference cancellation design. To this end, the following two key problems are addressed: the hardware design problem and the adaptive weight adjusting problem. For optimal hardware design, a trade-off between widening effective delay range and maximizing the minimum cancellation capability is formulated. The principles and guidelines for optimal solution and hardware parameter design are derived. We also formulate adaptive weight adjusting as a multi-dimensional optimization problem, which is proved to be non-convex while adjusting the attenuators and phase shifters independently. By using a coordinate transformation technique, it is then converted into a convex optimization problem, and a convergent iterative algorithm based on the gradient descent method is applied to obtain the global optimum. The hardware implementation and experimental results substantiated the effectiveness of the proposed principles and algorithms.

关键词： Full-duplex self-interference cancellation convex optimization problem iterative algorithm

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Efficient algorithms for the inverse spanning-tree problem

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OPERATIONS RESEARCH 2003年第5期51卷 785-797页

作者： Hochbaum, DS Univ Calif Berkeley Dept Ind Engn & Operat Res Walter A Haas Sch Business Berkeley CA 94720 USA

The inverse spanning-tree problem is to modify edge weights in a graph so that a given tree T is a minimum spanning tree. The objective is to minimize the cost of the deviation. The cost of deviation is typically a convex function. We propose algorithms here that are faster than all known algorithms for the problem. Our algorithm's run time for any convex inverse spanning-tree problem is O(nm log(2) n) for a graph on n nodes and m edges plus the time required to find the minima of the n convex deviation functions. This not only improves on the complexity of previously known algorithms for the general problem, but also for algorithms devised for special cases. For the case when the objective is weighted absolute deviation, Sokkalingam et al. (1999) devised an algorithm with run time O(n(2)m log(nC)) for C the maximum edge weight. For the sum of absolute deviations our algorithm runs in time O(n(2) log n), matching the run time of a recent (Ahuja and Orlin 2000) improvement for this case. A new algorithm for bipartite matching in path graphs is reported here with complexity of O(n(1.5) log n). This leads to a second algorithm for the sum of absolute deviations running in O(n(1.5) log n log C) steps.

关键词： Programming: integer algorithms optimization in integers Network/graphs: flow algorithms parametric minimum cut Mathematics: convexity convex optimization problem

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Differential Stability Properties of convex optimization and Optimal Control problems

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JOURNAL OF optimization THEORY AND APPLICATIONS 2024年第2期201卷 609-630页

作者： Toan, Nguyen Thi Thuy, Le Quang Hanoi Univ Sci & Technol Sch Appl Math & Informat 1 Dai Co Viet Hanoi Vietnam

This paper studies the solution stability of convex optimization and discrete convexoptimal control problems in Banach spaces, where the solution set may be *** both the optimization problem and the optimal control problem, formulas forthe epsilon-subdifferential of the optimal value function are derived without qualificationconditions. We first calculate the epsilon-subdifferential of the optimal value function toa parametric optimization problem with geometrical and functional constraints. Wethen use the obtained results to derive a formula for computing the epsilon-subdifferentialof the optimal value function to a discrete convex optimal control problem with linearstate equations, control constraints and initial, terminal conditions

关键词： convex optimization problem convex discrete optimal control problem Optimal value function Conjugate function epsilon-subdifferentials epsilon-normal directions

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Sensor fusion noise suppression method based on finite impulse response complementary filters

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MEASUREMENT 2024年 232卷

作者： Wang, Jing Wang, Lei Lin, Jie Xiao, Ritao Chen, Jiamin Jin, Peng Harbin Inst Technol Sch Instrumentat Sci & Engn 92 Xidazhi St Harbin 150001 Heilongjiang Peoples R China

The noise of an inertial sensor is a major issue that limits low-frequency measurement in active control systems. In order to extend low-frequency measurement bandwidth, an optimal finite impulse response (FIR) complementary filter design method is proposed to fuse a displacement sensor and an inertial sensor in this paper. The equivalent relationship between the system noise and the super-sensor noise is analyzed. The mechanism of complementary filters affecting them is clarified. Then, a value function is first constructed as the optimization objective to minimize the cumulative power spectrum (CPS) of the super sensor noise. Based on this and filter amplitude constraints, a convex optimization problem is constructed for solving the optimal filter coefficients. Finally, the experimental results show that the super sensor based on the proposed filters has a wider lowfrequency bandwidth. The proposed filters are significantly superior to conventional IIR complementary filters.

关键词： Inertial sensor Super sensor Cumulative power spectrum FIR complementary filters convex optimization problem

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A Multi-Step Reconfiguration Model for Active Distribution Network Restoration Integrating DG Start-Up Sequences

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2020年第4期11卷 2879-2888页

作者： Sekhavatmanesh, Hossein Cherkaoui, Rachid Ecole Polytech Fed Lausanne EPFL Power Syst Res Grp Lausanne Switzerland

The ever-increasing penetration of Distributed Generators (DGs) in distribution networks suggests to enable their potentials in better fulfilling the restoration objective. The objective of the restoration problem is to resupply the maximum energy of loads considering their priorities using minimum switching operations. Basically, it is desired to provide a unique configuration that is valid regarding the load and generation profiles along the entire restorative period. However, this unique configuration may not satisfy at the same time: I) the DG start-up requirements at the beginning of the restoration plan and II) the topological conditions that would allow the DG to provide later on the most efficient support for the supply of loads. Therefore, it is proposed in this article to allow a limited number of reconfiguration steps according to the DG start-up requirements. In addition, this article presents a novel formulation for the reconfiguration problem that accounts for partial restoration scenarios where the whole unsupplied area cannot be restored. The decision variables of the proposed multi-step restoration problem are: I) the line switching actions at each step of the reconfiguration process, II) the load switching actions during the whole restorative period and, III) the active/reactive power dispatch of DGs during the whole restorative period. A relaxed AC power flow formulation is integrated to the optimization problem in order to ensure the feasibility of the solution concerning the operational safety constraints. The overall model is formulated in terms of a mixed-integer second-order cone programming. Two simulation scenarios are studied in order to illustrate different features of the proposed strategy and to demonstrate its effectiveness particularly in the case of large-scale outages in distribution networks.

关键词： Switches optimization Load flow Load modeling Generators Safety convex optimization problem distribution network DG load breaker multi-step reconfiguration restoration service sectionalizing switch tie-switch

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Weighted Sum Rate Maximization Under the Given PAPR Constraints for a Multi-user OFDM System

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WIRELESS PERSONAL COMMUNICATIONS 2019年第1期109卷 127-137页

作者： Falahati, Abolfazl Anarakifirooz, Elhamsadat Univ Sci & Technol Dept Elect Engn Tehran Iran

Orthogonal frequency division multiplexing (OFDM) is proved to be the best candidate to support the colossal increase in mobile users and their required high rate of transmission in frequency selective fading environments, where the inter-symbol interference is at highest. In an OFDM system, when the sinusoidal signals of the subcarriers are added constructively, the peak to average power ratio (PAPR) becomes very large causing major drawbacks for multicarrier signaling. Earlier efforts to address this problem have been mainly concentrated on the reduction of signal PAPR and various methods of achieving linear and efficient power amplification. However, all the deployed techniques suffer from different ambiguities such as high distortion, complexity, computational time, memory requirements, and above all, the data rate loss. This manuscript is mainly aimed at solving a convex optimization problem in which power and radio resources in an OFDM system are allocated among different subcarriers and users in order to, maximize the weighted sum rate for different users considering total power and PAPR limitations.

关键词： Orthogonal frequency division multiplexing (OFDM) Peak to average power ratio (PAPR) convex optimization problem Power and radio resources

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Higher Order Positive Semidefinite Diffusion Tensor Imaging

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SIAM JOURNAL ON IMAGING SCIENCES 2010年第3期3卷 416-433页

作者： Qi, Liqun Yu, Gaohang Wu, Ed X. Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China GanNan Normal Univ Sch Math & Comp Sci Jiangxi Key Lab Numer Simulat Technol Ganzhou 341000 Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Hong Kong Peoples R China

Due to the well-known limitations of diffusion tensor imaging, high angular resolution diffusion imaging (HARDI) is used to characterize non-Gaussian diffusion processes. One approach to analyzing HARDI data is to model the apparent diffusion coefficient (ADC) with higher order diffusion tensors. The diffusivity function is positive semidefinite. In the literature, some methods have been proposed to preserve positive semidefiniteness of second order and fourth order diffusion tensors. None of them can work for arbitrarily high order diffusion tensors. In this paper, we propose a comprehensive model to approximate the ADC profile by a positive semidefinite diffusion tensor of either second or higher order. We call this the positive semidefinite diffusion tensor (PSDT) model. PSDT is a convex optimization problem with a convex quadratic objective function constrained by the nonnegativity requirement on the smallest Z-eigenvalue of the diffusivity function. The smallest Z-eigenvalue is a computable measure of the extent of positive definiteness of the diffusivity function. We also propose some other invariants for the ADC profile analysis. Experiment results show that higher order tensors could improve the estimation of anisotropic diffusion and that the PSDT model can depict the characterization of diffusion anisotropy which is consistent with known neuroanatomy.

关键词： positive semidefinite diffusion tensor apparent diffusion coefficient Z-eigenvalue convex optimization problem invariants

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