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Partition-based multi-agent optimization in the presence of lossy and asynchronous communication

AUTOMATICA 2020年 111卷 108648-000页

作者： Todescato, Marco Bof, Nicoletta Cavraro, Guido Carli, Ruggero Schenato, Luca BCAI Renningen Germany NREL Power Syst Engn Ctr Golden CO USA Dept Informat Engn DEI Padua Italy DEI Padua Italy NREL Golden CO USA US DOE Washington DC 20585 USA

We address the problem of multi-agent partition-based convex optimization which arises, for example, in robot localization problems and in regional state estimation in smart grids. More specifically, the global cost function is the sum of locally coupled cost functions that depend only on each agent variables and their neighbors' variables. Inspired by a generalized gradient descent strategy, namely the Block Jacobi iteration, we propose an algorithm amenable to a scalable distributed implementation, i.e., each agent eventually computes only the optimal values for its own variables via local communication with its neighbors. In particular, we provide sufficient conditions for global and semi-global exponential stability for the proposed algorithms even in the presence of lossy communications and asynchronous updates. The theoretical analysis relies on novel tools on Lyapunov theory based on separation of time scales and averaging theory for discrete-time systems. Finally, the proposed algorithm is numerically tested on the IEEE 123 nodes distribution feeder in the context of multi-area robust state estimation of smart grids in the presence of measurement outliers. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： convex programming Generalized gradient Distributed optimization Communication failures

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H_∞ robust exponential stability and memory state feedback control for uncertain singular time-delay systems with saturating actuators

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IET CONTROL THEORY AND APPLICATIONS 2016年第3期10卷 328-338页

作者： Ma, Yuechao Fu, Lei Yanshan Univ Coll Sci Qinhuangdao 066004 Hebei Peoples R China

This study is concerned with delay-dependent H robust exponential stability and memory state feedback stabilisation of singular time-delay systems with saturating actuators. First, a delay-dependent linear matrix inequality condition is obtained, which guarantees that the uncertain singular time-delay systems subject to actuator saturation are not only robustly exponential admissible, but also satisfy H performance via a tighter integral inequality and the method of free-weighting matrices. Then, using the conditions, the estimation of stability region and the controller with memory state feedback are given by solving a convex optimisation problem. Finally, some numerical examples are provided to demonstrate the merit of the obtained results.

关键词： delay systems uncertain systems asymptotic stability H control robust control linear matrix inequalities actuators convex programming state feedback memory state feedback control uncertain singular time-delay systems saturating actuators delay-dependent H robust exponential stability memory state feedback stabilisation delay-dependent linear matrix inequality condition actuator saturation integral inequality free-weighting matrices stability region estimation convex optimisation problem

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CONSISTENCY OF THE SCENARIO APPROACH

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SIAM JOURNAL ON OPTIMIZATION 2018年第1期28卷 135-162页

作者： Ramponi, Federico Alessandro Univ Brescia Dipartimento Ingn Informaz I-25123 Brescia Italy

This paper is meant to prove the consistency of the scenario approach a la Calafiore, Campi, and Garatti with convex constraints. Scenario convex problems are usually stated in two equivalent forms: first, as the minimum of a linear function over the intersection of a finite random sample of independent and identically distributed convex sets, or second, as the min-max of a finite random sample of independent and identically distributed convex functions. The paper shows that, under fairly general assumptions, as the size of the sample increases the minimum attained by the solution of a problem of the first kind converges almost surely to the minimum attained by a suitably defined "essential" robust problem (or diverges if such a robust problem is infeasible), and that the minimum attained by the solution of a scenario problem of the second kind converges almost surely to the minimum of the pointwise essential supremum taken over all the possible convex functions (or diverges if such essential supremum takes the only value +infinity). In both cases, if the solution of the essential problem exists and is unique, the solution of the scenario problem converges to it almost surely.

关键词： scenario approach stochastic programming convex programming sample-based optimization min-max optimization

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COUPLING POLICY ITERATION WITH SEMI-DEFINITE RELAXATION TO COMPUTE ACCURATE NUMERICAL INVARIANTS IN STATIC ANALYSIS

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LOGICAL METHODS IN COMPUTER SCIENCE 2012年第1期8卷

作者： Adje, Assale Gaubert, Stephane Goubault, Eric CNRS LSV F-94235 Cachan France ENS Cachan F-94235 Cachan France Ecole Polytech CMAP F-91128 Palaiseau France INRIA Saclay F-91128 Palaiseau France CEA LIST MeASI F-91191 Gif Sur Yvette France

We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of sub-level sets of non-linear functions, generalizes the domain of linear templates introduced by Manna, Sankaranarayanan, and Sipma. In the case of quadratic templates, we use Shor's semi-definite relaxation to derive safe and computable abstractions of semantic functionals, and we show that the abstract fixpoint can be over-approximated by coupling policy iteration and semi-definite programming. We demonstrate the interest of our approach on a series of examples (filters, integration schemes) including a degenerate one (symplectic scheme).

关键词： abstract interpretation policy iteration convex programming quadratic programming semi-definite programming Lyapunov functions

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Minimizing total travel time in a gravitational dense grid

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INTERNATIONAL JOURNAL OF INDUSTRIAL ENGINEERING-THEORY APPLICATIONS AND PRACTICE 2002年第1期9卷 78-85页

作者： Mesa, JA Arriola, R Ortega, FA Univ Seville Sch Ind Engn Dept Appl Math 2 Seville 41092 Spain Univ Seville Sch Architecture Dept Appl Math 1 E-41012 Seville Spain

Urban planning developed from 18th century has generated, in the majority of cities, a rectangular street grid which isadjacent to the original site. The historical center provides an attraction for the new built-up zones, giving rise to nonuniform submodels for land use, price of building sites and surface traffic. Mailing facilities, good distribution facilities and maintenance services locate their offices in the city in order to effectively serve preferred clients. The most convenient zones for such an end are the aforementioned areas, around the first annulus, which are characterized by the rectangular form of their streets and with easy access to the peripheral areas close to the center. An appropriate criterion to decide the location of such facilities consists of the minimization of total travel time on a discrete set of candidate points (the Weber problem). On the other hand, traffic density is a determinant factor for calculating the travel time between points in the city since it affects the vehicle speed. Although the displacement speed varies deterministicly and randomly in relation to many factors, it could be interesting to analyse a deterministic model based on the gravitational attraction. This model would establish different levels of velocity, in accordance with the distance to the axis in which the slowest speed measurement falls, and the trajectories are necessarily rectilinear. The planar curve, whose points are in travel time T with respect to a given point by using rectilinear displacements over a speed distribution which follows a gravitational framework, is determined in the current work. The analytical expression is established and the corresponding Weber problem is solved.

关键词： convex programming continuous location Weber problem

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H∞ observer-controller synthesis approach in low frequency for T-S fuzzy systems

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IET CONTROL THEORY AND APPLICATIONS 2020年第5期14卷 738-749页

作者： Xie, Wen-Bo Han, Zhao-Kun Wu, Fen Zhu, Song Harbin Univ Sci & Technol Coll Automat Harbin 150080 Peoples R China Shanghai Univ Shanghai Key Lab Power Stn Automat Technol Sch Mechatron Engn & Automat Shanghai 200444 Peoples R China North Carolina State Univ Dept Mech & Aerosp Engn Raleigh NC 27695 USA China Univ Min & Technol Sch Math Xuzhou 221116 Jiangsu Peoples R China

For the output feedback control problem of continuous-time T-S fuzzy systems with unknown premise variables, an H-infinity 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 H-infinity 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 infinity observer-controller design method H infinity observer-controller synthesis approach linear matrix inequality forms convex optimisation technique

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Continuous-Time H 2 - Control of Markovian Jump Linear Systems via convex Analysis

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IFAC Proceedings Volumes 1996年第1期29卷 1703-1708页

作者： O.L.V. Costa J.B.R. do Val J.C. Geromel University of Sāo Paulo Department of Electronic Engineering 05508-900 - São Paulo - SP - Brazil LAC-DT/Faculty of Electrical Engineering UNICAMP CP 6101 13081-970 - Campinas - SP - Brazil

A convex programming formulation to the continuous-time H 2 -control problem of linear systems with Markovian jumps (MJLS) is developed. The transition rate matrix II = [π ij ] for the Markov chain may be exactly known or belong to an appropriated convex set. The system state and jump variables may or may not be available to the controller. If they are not available, the H 2 -control problem can be viewed as a state-feed back control problem where the feedback gain is subject to structural constraints. These constraints possess important geometric properties, leading to cutting plane like algorithms.

关键词： convex programming H 2 -control continuous-time systems jump process

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-gain control on positive impulsive system via a hybrid proportional plus integral algorithm

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IET Control Theory & Applications 2019年第7期13卷 898-904页

作者： Hao Chen Tao Zhan Qinzhen Huang College of Electrical and Information Engineering Southwest Minzu University Chengdu 610041 People's Republic of China Department of Applied Mathematics University of Waterloo Waterloo Ontario N2L 3G1 Canada School of Mathematics Shandong University Jinan Shandong 250100 People's Republic of China

In this study, the -gain control issues on positive system are investigated. A hybrid proportional impulsive with integral (PII) control scheme is proposed. This impulse-time-dependent control algorithm uses the proportional control action at impulse instants for stabilising, and applies the integral control strategy between impulse time intervals for improving the state convergence, respectively. The average impulsive interval approach and co-positive Lyapunov function method are employed to derive the sufficient conditions. Then -gain performance of the impulsive positive system can be guaranteed by solving the linear programming problem. In addition, iterative convex optimisation algorithm is presented for the design of PII control gain matrices. Numerical examples illustrate the expected results of this design.

关键词： Lyapunov methods matrix algebra gain control control system synthesis linear programming time-varying systems iterative methods convex programming stability impulse time intervals co-positive Lyapunov function method impulsive positive system iterative convex optimisation algorithm PII control gain matrices positive impulsive system hybrid proportional plus integral algorithm integral control scheme impulse-time-dependent control algorithm impulse instants impulsive interval approach integral control strategy 𝒦1 stability proportional control action Kp ℒ1 -gain control issues linear programming problem

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Robust estimation of highly corrupted low-rank matrix via alternating direction method of multiplier

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IET SIGNAL PROCESSING 2023年第2期17卷

作者： Yimamu, Tuersunjiang Eisaka, Toshio Kitami Inst Technol Dept Mfg Engn Kitami Hokkaido Japan Kitami Inst Technol Div Informat & Commun Engn Kitami Hokkaido 0908507 Japan

Low-rank matrices play a central role in modelling and computational methods for signal processing and large-scale data analysis. Real-world observed data are often sampled from low-dimensional subspaces, but with sample-specific corruptions (i.e. outliers) or random noises. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and one encounters the problem of recovering the matrix given only incomplete and indirect observations. The authors aim to recover a low-rank component from incomplete and indirect observations and correct the possible errors. A new low-rank matrix recovery formula based on generalised Tikhonov regularisation and its solution algorithm are proposed. The proposed method determines the low-rank component for performing matrix recovery from highly corrupted observations. The authors' recommended algorithm reduces not only the outliers but also random corruptions in the recovering task. The experimental results obtained using both synthetic and real application data demonstrate the efficacy of the proposed method.

关键词： convex programming matrix algebra highly corrupted low-rank matrix signal processing low-dimensional subspaces data analysis computational methods alternating direction method of multiplier random corruptions robust estimation large-scale data analysis generalised Tikhonov regularisation low-rank component low-rank matrix recovery formula estimation theory

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Structured controller synthesis through block-diagonal factorization and parameter space optimization

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AUTOMATICA 2023年 147卷

作者： Yuan, Liming Chen, Silu Zhang, Chi Yang, Guilin Chinese Acad Sci Ningbo Inst Mat Technol & Engn Ningbo 315201 Zhejiang Peoples R China Univ Chinese Acad Sci Coll Mat Sci & Optoelect Technol Beijing 100049 Peoples R China

Constraints on the feedback structure arise in many control systems due to implementing cost, hardware limitations and operational reliability. The parameter space method aims to solve the robust structured controller design problems based on a convex reformulation technique. Despite its attractiveness, the structural constraints are limited to be either decentralized or linear dependence among entries within the same row or column in the current literature. And the global optimal solution is yet to be guaranteed, since a non-convex constraint is introduced in the parameter space after reformulating it as the output feedback synthesis problem. In this paper, we extend the parameter space method to a more generalized structured optimal control problem, such that the linear dependence can occur among its arbitrary entries. A bilinear factorization to the feedback gain matrix is proposed by a special Kronecker product decomposition. Subsequently, an equivalent transformation is proposed to convert this structured control design problem to a controller synthesis problem under decentralized full-state feedback. Thereby, the prior non-convex constraint in the parameter space is removed and the globally optimal structured controller is synthesized by convex programming. Examples such as integrated design and formation control demonstrate its practical appeals. (c) 2022 Elsevier Ltd. All rights reserved.

关键词： Optimal control Structured feedback gain Decentralized control Kronecker product Rank factorization convex programming Linear systems Parameter space

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