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Robust filtering with guaranteed energy-to-peak performance — an LMI approach

IFAC Proceedings Volumes 1999年第2期32卷 1814-1819页

作者： Reinaldo M. Palhares Pedro L.D. Peres Pontifícia Universidade Católica de Minus Gerais Graduate Program in Electrical Engineering Av. Dom José Gaspar 500 Prédio 4 30535-610 Belo Hotizonte - MG - Brazil School of Electrical and Computer Engineering University of Campinas DT/FEEC/UNICAMP - CP 6101 13.081-970 Campinas - SP - Brazil

The problem of robust energy-to-peak filtering for linear systems with convex bounded uncertainties is investigated in this paper. The main purpose is to design a full order stable linear filter that minimizes the worst-case peak value of the filtering error output signal with respect to all bounded energy inputs, in such way that the filtering error system remains quadratically stable Necessary and sufficient conditions arc formulated in terms of Linear Matrix Inequalities - LMIs, for both continuous- and discrete-time cases.

关键词： Robust Estimation Filter Design Uncertain Linear Systems convex programming Energy-to-Peak Gain Linear- Matrix Inequalities

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Nonlinear H ∞ Control System Design via Extended Quadratic Lyapunov Function

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IFAC Proceedings Volumes 1998年第17期31卷 161-166页

作者： Seigo Sasaki Kenko Uchida Waseda University Dept. of Elect. Electr. and Computer Eng. Tokyo 169-8555 Japan

Using extended quadratic Lyapunov functions, we consider H ∞ control synthesis problems for input-affine polynomial type nonlinear systems, and characterize nonlinear H ∞ controllers, in the state feedback case and the output feedback case, via Riccati type matrix inequality conditions. The controllers can be given by solving linear matrix inequalities which are given at vertices of a convex hull enclosing a domain of states. We also detennine a domain of internal stability. We finally show that the proposed method is effective through a numerical example for output feedback control problem of bilinear system.

关键词： nonlinear control systems Lyapunov function H-infinity control convex programming control system synthesis

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Sequential convexifying Method (SCM) with Application to Optimization and Control

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IFAC Proceedings Volumes 1987年第5期20卷 97-102页

作者： Jie Lin Bai-wu Wan Institute of Systems Engineering Xi'an Jiaotong University Xi'an PRC

In the hierarchical optimization and control of large scale steady state systems, the Interaction Balance Method (IBM) is of great importance. However, there are many practical problems which are not IBM applicable. This paper introduces a objective convexifying technique---- Sequential convexifying Method (SCM), which turns most of the IBM unsolvable problems into solvable ones. Being different from the Augmented Lagrangian Method, SCM maintains the separability of the objective after convexification, which has eased the task of decomposation significantly. A convergence proof of SCM as well as the estimation of the convergence ratio is presented. Simulation is also provided.

关键词： Large scale systems optimization mathematical programming hierarchical systems convex programming interaction balance method augmented lagrangian method

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A Linear Matrix Inequality Approach for Guaranteed Cost Control

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IFAC Proceedings Volumes 1996年第1期29卷 3591-3596页

作者： A. Fischman J.M. Dion L. Dugard A. Trofino Neto Laboratoire d'Automatique de Grenoble (URA CNRS 228) E.N.S.I.E.G.-I.N.P.G. B.P. 46 38402 St Martin d'Heres France. Laboratório de Controle e Microinformática / EEL / CTC Universidade Federal de Santa Catarina PO 476 88010-970 Florianópolis Brazil.

This paper deals with the problem of the guaranteed cost control synthesis for systems with structured uncertainties. The main interest of the proposed approach is to generalize previous works in this area using a linear matrix inequality (LMI) framework. First of all, the inclusion of scaling matrices in the design avoids the need of an adequate a priori rank-1 decomposition for the uncertainties. In addition, the iterative search for a solution, as proposed in earlier works, is no longer needed. Then, a LMI procedure for the minimization of an upper bound for the guaranteed cost is presented. Comparisons with previous results in the context of guaranteed cost control are also presented on a numerical example.

关键词： convex programming robust control uncertainty quadratic stability

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On the solution of the discrete-time coupled algebraic riccati equations

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IFAC Proceedings Volumes 1999年第2期32卷 4947-4952页

作者： R.P. Marques O.L.V. Costa University of São Paulo Department of Electronic Engineering 05508-900 São Paulo SP Brazil

Conditions for existence of maximal and stabilizing liermitian solutions for a set of discrete-time coupled algebraic Riccati equations are considered. Such equations play an important role in optimal control of discrete-time Markovian jump linear systems. The matrix cost is only assumed to be liermitian. First, conditions for existence of a maximal liermitian solution are derived in terms of the concept of mean square stabilizability and a convex set not being empty. A connection with convex optimization is also established, leading to a numerical algorithm. Next, a necessary and sufficient condition for existence of a stabilizing solution (in the mean square sense) is derived. These results generalize and unify several previous results presented in the literature of discrete-time coupled Riccati equations of Markovian jump linear systems.

关键词： Riccati equations Optimal control Jump process Markov parameters convex programming

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observer–controller synthesis approach in low frequency for T–S fuzzy systems

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IET Control Theory & Applications 2020年第5期14卷 738-749页

作者： Wen-Bo Xie Zhao-Kun Han Fen Wu Song Zhu College of Automation Harbin University of Science and Technology Harbin 150080 People's Republic of China Shanghai Key Laboratory of Power Station Automation Technology School of Mechatronic Engineering and Automation Shanghai University Shanghai 200444 People's Republic of China Department of Mechanical and Aerospace Engineering North Carolina State University Raleigh NC 27695 USA School of Mathematics China University of Mining and Technology Xuzhou 221116 People's Republic of China

For the output feedback control problem of continuous-time T–S fuzzy systems with unknown premise variables, an observer–controller design method in the low-frequency domain is proposed. First, an observer–controller structure is given, the unknown premise variables are limited by Lipschitz conditions. Then, the system stability conditions are obtained by the negativeness of eigenvalues' real parts. To achieve better control performance of the system in low frequency, the index for attenuating the unknown low-frequency disturbance is guaranteed by generalised Kalman–Yakubovich–Popov lemma. Then, the stability and robustness conditions are converted into linear matrix inequality forms, which can be solved directly by a convex optimisation technique. Finally, several simulation examples carried out to show the effectiveness of the proposed method.

关键词： convex programming observers linear matrix inequalities robust control feedback fuzzy systems eigenvalues and eigenfunctions control system synthesis fuzzy control continuous time systems Lipschitz conditions system stability conditions eigenvalues generalised Kalman–Yakubovich–Popov lemma robustness conditions output feedback control problem continuous-time T–S fuzzy systems H∞ observer–controller design method H∞ observer–controller synthesis approach linear matrix inequality forms convex optimisation technique

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Type parameter estimation of 2D-GTD model based on ADMM approach

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ELECTRONICS LETTERS 2024年第10期60卷

作者： Jin, Mingming Wang, Jun Wei, Shaoming Zeng, Zhiqiang Zhang, Chi Qu, Fangrui Beihang Univ Sch Elect & Informat Engn Beijing Peoples R China Beihang Univ Hangzhou Innovat Inst Hangzhou Peoples R China Tsinghua Univ Sch Aerosp Engn Beijing Peoples R China

The type parameter helps in scattering mechanism analysis and scattering centre identification. However, current approximate solution methods based on spectral estimation are noise-sensitive and exhibit low accuracy. In this letter, a high-precision approach for the type parameter based on the alternating direction method of multipliers (ADMM) is proposed. Logarithmic transformation is used to separate the type parameter and the amplitude from the coupling term, and initially obtain the closed-form solution of the type parameter. Then, the regularization term of l2-norm is used for denoising. Finally, a joint optimization model based on ADMM is constructed to effectively estimate the type parameter. Simulation results confirm the high accuracy of the proposed approach. In this letter, a high-precision approach for the type parameter based on the alternating direction method of multipliers (ADMM) is proposed. Logarithmic transformation is used to separate the type parameter and the amplitude from the coupling term, and initially obtain the closed-form solution of the type parameter. Then, the regularization term of l2-norm is used for denoising and a joint optimization model based on ADMM is constructed to effectively estimate the type parameter. image

关键词： convex programming geometrical theory of diffraction parameter estimation radar signal processing

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ON THE CONVERGENCE OF GRADIENT-LIKE FLOWS WITH NOISY GRADIENT INPUT

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SIAM JOURNAL ON OPTIMIZATION 2018年第1期28卷 163-197页

作者： Mertikopoulos, Panayotis Staudigl, Mathias Univ Grenoble Alpes CNRS INRIA LIG F-38000 Grenoble France Maastricht Univ Dept Quantitat Econ POB 616 NL-6200 MD Maastricht Netherlands

In view of solving convex optimization problems with noisy gradient input, we analyze the asymptotic behavior of gradient-like flows under stochastic disturbances. Specifically, we focus on the widely studied class of mirror descent schemes for convex programs with compact feasible regions, and we examine the dynamics' convergence and concentration properties in the presence of noise. In the vanishing noise limit, we show that the dynamics converge to the solution set of the underlying problem (a.s.). Otherwise, when the noise is persistent, we show that the dynamics are concentrated around interior solutions in the long run, and they converge to boundary solutions that are sufficiently "sharp." Finally, we show that a suitably rectified variant of the method converges irrespective of the magnitude of the noise (or the structure of the underlying convex program), and we derive an explicit estimate for its rate of convergence.

关键词： convex programming dynamical systems mirror descent noisy feedback stochastic differential equations

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Duality Based Risk Mitigation Method for Construction of Joint Hydro-Wind Coordination Short-Run Marginal Cost Curves

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ENERGIES 2018年第5期11卷 1254页

作者： Ilak, Perica Rajsl, Ivan Dakovic, Josip Delimar, Marko Univ Zagreb Fac Elect Engn & Comp Dept Energy & Power Syst Unska 3 HR-10000 Zagreb Croatia

This study analyzes the short-run hydro generation scheduling for the wind power differences from the contracted schedule. The approach for construction of the joint short-run marginal cost curve for the hydro-wind coordinated generation is proposed and applied on the real example. This joint short-run marginal cost curve is important for its participation in the energy markets and for economic feasibility assessment of such coordination. The approach credibly describes the short-run marginal costs which this coordination bears in "real life". The approach is based on the duality framework of a convex programming and as a novelty combines the shadow price of risk mitigation, which quantifies the hourly cost of mitigating risk, and the water shadow price, which quantifies the marginal cost of electricity production. The proposed approach is formulated as a stochastic linear program and tested on the case of the Vinodol hydropower system and the wind farm Vratarusa in Croatia. The result of the case study is a family of 24 joint short-run marginal cost curves. The proposed method is expected to be of great interest to investors as it enables risk mitigation for investors with diverse risk preferences, from risk-averse to risk-seeking.

关键词： convex programming wind power hydropower risk mitigation CVaR short-run marginal cost curve

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H∞ filtering for discrete-time 2D T-S fuzzy systems with finite frequency disturbances

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IET CONTROL THEORY AND APPLICATIONS 2019年第13期13卷 1983-1994页

作者： Duan, Zhaoxia Shen, Jian Ghous, Imran Fu, Jinna Hohai Univ Coll Energy & Elect Engn Nanjing 211100 Jiangsu Peoples R China China Elect Technol Grp Corp Res Inst 28 Nanjing 210007 Jiangsu Peoples R China COMSATS Inst Informat Technol Dept Elect & Comp Engn Lahore Campus Lahore 54000 Pakistan

This study investigates the filter design problem for two-dimensional (2D) discrete-time non-linear systems in Takagi-Sugeno (T-S) fuzzy model. The frequency of the exogenous disturbances is assumed to belong to a known finite frequency (FF) domain. An FF H infinity performance is defined for 2D discrete-time systems, which generalises the standard one and makes use of the frequency-domain characteristics of practical signals. By virtue of the defined FF H infinity performance, sufficient conditions are proposed for analysing the disturbance attenuation performance of the filtering error system. Efficient conditions are obtained to guarantee the existence of a filter and such that the error system is asymptotically stable with an FF H infinity performance index. A systematic filter design scheme is developed by converting the corresponding fuzzy filter design into a convex optimisation problem. Finally, a gas absorption system is employed to illustrate the validity of the proposed methods.

关键词： discrete time systems asymptotic stability convex programming fuzzy systems H-infinity filters nonlinear systems discrete-time 2D T-S fuzzy systems finite frequency disturbances filter design problem two-dimensional discrete-time nonlinear systems Takagi-Sugeno fuzzy model exogenous disturbances frequency-domain characteristics filtering error system systematic filter design scheme gas absorption system H-infinity filtering disturbance attenuation performance fuzzy filter design finite frequency domain convex optimisation problem FF H-infinity performance index

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