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discrete-time algorithm for Distributed Unconstrained Optimization Problem With Finite-time Computations

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2021年第1期68卷 351-355页

作者： Liu, Hongzhe Yu, Wenwu Southeast Univ Sch Math Nanjing 210096 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Peoples R China

This brief investigates the distributed unconstrained optimization problem, where its global objective function consists of the sum of N local objective functions. The aim for this brief is to design a discrete-time algorithm to solve the considered distributed optimization problem using only local computations and local information exchanges. To this end, a discrete-time algorithm resorting to the conjugate gradient method is proposed, and by it, the optimal solution to a class of distributed optimization problems over a static undirected graph can be obtained with finite-time computations under some mild conditions. Furthermore, simulations are given to verify the validity of the designed algorithm.

关键词： Distributed unconstrained optimization discrete-time algorithm conjugate gradient method finite-time computations

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discrete-time algorithm for Distributed Nash Equilibrium Seeking of A Class of Aggregative Games 36

Discrete-time Algorithm for Distributed Nash Equilibrium See...

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第36届中国控制会议

作者： Lingfei Wang Shu Liang Yiguang Hong NKU School of Mathematical Sciences Tianjin Key Laboratory of Systems and Control Institute of Systems ScienceChinese Academy of Sciences

ISBN: (纸本)9781538629185

In this paper,we investigate a distributed Nash equilibrium seeking problem for aggregative games with nonlinear aggregation *** our game model,the strategic interaction is associated with a sum of heterogeneous nonlinear mapping of local decisions,and the local cost functions are non-quadratic with the decision variables limited in local constraint *** propose a novel discrete-time distributed equilibrium seeking algorithm based on dynamic average consensus protocal and projected gradient *** virtue of variational inequalities and Lyapunov functions,we show that the algorithm can achieve the Nash equilibrium for the distributed aggregative game.

关键词： Distributed algorithm Aggregative game Nash equilibrium discrete-time algorithm

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Zhang neural network, Getz-Marsden dynamic system, and discrete-time algorithms for time-varying matrix inversion with application to robots' kinematic control

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NEUROCOMPUTING 2012年 97卷 22-32页

作者： Guo, Dongsheng Zhang, Yunong Sun Yat Sen Univ Sch Informat Sci & Technol Guangzhou 510006 Guangdong Peoples R China

In this paper, we present, develop and investigate a special kind of recurrent neural network termed Zhang neural network (ZNN) for time-varying matrix inversion. Comparing with the dynamic system proposed by Getz and Marsden (G-M) for time-varying matrix inversion, we show that such a G-M dynamic system depicted in an explicit dynamics can also be derived from the presented ZNN model depicted in an implicit dynamics. In other words, a novel result on the relationship between the ZNN model and others' model/method (i.e., the G-M dynamic system) is found for time-varying matrix inversion. In addition, we propose and investigate the discrete-time algorithms (depicted by systems of difference equations) of the aforementioned ZNN and G-M models in two situations, i.e., the time-derivative of the time-varying matrix to be inverted being known or unknown. Simulative and numerical results demonstrate the superior performance of the ZNN models for time-varying matrix inversion, as well as the efficacy of the G-M dynamic system (which has to be started with initial conditions sufficiently close to the desired initial inverse). Furthermore, the ZNN models and G-M dynamic system are applied to the kinematic control of a two-link planar manipulator via online solution of time-varying matrix inversion. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Zhang neural network Getz-Marsden dynamic system discrete-time algorithm time-varying matrix inversion Dynamics

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Distributed discrete-time algorithms for Convex Optimization With General Local Constraints on Weight-Unbalanced Digraph

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2021年第1期8卷 51-64页

作者： Liu, Hongzhe Zheng, Wei Xing Yu, Wenwu Southeast Univ Sch Math Nanjing 210096 Peoples R China Southeast Univ Sch Automat Nanjing 210096 Peoples R China Western Sydney Univ Sch Comp Data & Math Sci Sydney NSW 2751 Australia

This article investigates the convex optimization problem with general local constraints including N equality constraints, N inequality constraints, and N closed convex set constraints. Especially, the objective function of the considered problem is the sum of N convex functions, which are seen as local objective functions. First, for the distributed setting, a weight-unbalanced digraph with N nodes is introduced to describe the communication topology. Clearly, in the distributed setting, each node is responsible for a local objective function accompanied with an equality constraint, an inequality constraint, and a closed convex set constraint, which are viewed as local constraints. The aim of this article is to solve the considered convex optimization problem in a distributed manner, i.e., to lead the states of all nodes to a common optimal solution of the considered problem under the condition that each node only knows its own local objective function, and local constraints, and the information of its neighbors' states. Towards this end, by resorting to the exact penalty function method and the gradient descent-like method, two distinct distributed discrete-time algorithms are developed for two different cases, respectively. Furthermore, the convergence properties of the designed algorithms are rigorously analyzed under some common and standard assumptions, and the convergence rates are described in detail. Finally, simulation results are provided to verify the theoretical results.

关键词： Directed topology discrete-time algorithm distributed convex optimization general local constraints

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Distributed discrete-time optimization of heterogeneous multi-agent networks with unbounded position constraints and nonconvex velocity constraints

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NEUROCOMPUTING 2021年 466卷 92-101页

作者： Mo, Lipo Zhang, Zixin Yu, Yongguang Beijing Technol & Business Univ Sch Math & Stat Beijing 100048 Peoples R China Beijing Jiaotong Univ Sch Sci Beijing 100048 Peoples R China

The distributed discrete-time heterogeneous multi-agent optimization problem with unbounded position constraints and nonconvex velocity constraints was considered in this paper, where the models of agents are described by first-or second-order difference equations, the position constraints are assumed to be unbounded and convex and the velocity constraints are assumed to be bounded, closed and non convex. An improved distributed algorithm is adopted, under which, all agents could collaboratively minimize the entire objective function and the positions and velocities could always stay at the corresponding constraint sets. Then the convergence analysis is completed by the coordination transformation and the properties of projection operator and constraint operator. Finally, we give examples to illustrate the correctness of results. (c) 2021 Elsevier B.V. All rights reserved.

关键词： Heterogeneous multi-agent networks Distributed optimization discrete-time algorithm Nonconvex constraints Unbounded constraints

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Extension of discrete simple adaptive control with asymptotically perfect tracking

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INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING 2002年第2期16卷 107-121页

作者： Shibata, H Sun, Y Fujinaka, T Chen, G Univ Osaka Prefecture Coll Engn Dept Comp Sci & Syst Sakai Osaka 5998531 Japan

A discrete-time algorithm for simple adaptive control, proposed by one of authors, circumvents some drawbacks of the algorithm derived directly from continuous-time one. However, it leaves steady-state output error between a controlled plant and a reference model, This paper proposes a modified algorithm, which removes the steady-state output error. The stability of the algorithm is proved based on asymptotic output tracker theory, instead of command generator tracker theory. Finally, simulation results illustrate satisfactory control performance, that verifies the usefulness of the proposed algorithm. Copyright (C) 2002 John Wiley Sons, Ltd.

关键词： simple adaptive control discrete-time algorithm stability analysis feedforward compensator

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Selection in monotone matrices and computing kth nearest neighbors

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JOURNAL OF algorithmS 1996年第3期20卷 581-601页

作者： Agarwal, PK Sen, S INDIAN INST TECHNOL DEPT COMP SCINEW DELHIINDIA

An m x n matrix A = (a(i,j)), 1 less than or equal to i less than or equal to m and 1 less than or equal to j less than or equal to n, is called a totally monotone matrix if for all i(1), i(2),j(1),j(2), satisfying 1 less than or equal to i(1) < i(2) less than or equal to m, 1 less than or equal to j(1) < j(2) less than or equal to n. a(i1,J1) < a(i1,j2) double right arrow a(i2,j1) < a(i2,j2). We present an O((m + n)root n log n) time algorithm to select the kth smallest item from an m x n totally monotone matrix for any k less than or equal to mn. This is the first sub-quadratic algorithm for selecting an item from a totally monotone matrix Our method also yields an algorithm of the same time complexity for a generalized row-selection problem in monotone matrices. Given a set S = {p(1),..., p(n)} of n points in convex position and a vector k = {k(1),...,k(n)}, we also present an O(n(4/3)log(c) n) algorithm to compute the k(i)th nearest neighbor of p(i) for every i less than or equal to n;here c is an appropriate constant. This algorithm is considerably faster than the one based on a row-selection algorithm for monotone matrices. If the points of S are arbitrary, then the k(i)th nearest neighbor of p(i), for all i less than or equal to n, can be computed in time O(n(7/5) log(c) n), which also improves upon the previously best known result. (C) 1996 Academic Press, Inc.

关键词： Linear-time algorithm Simple polygon Upper-bounds Equal Proportional integral discrete-time algorithm Nearest neighbor Upper bound matrices Monotone complexity classes Less than or equal to

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CONTINUOUS-time APPROACH TO SELF-TUNING CONTROL - algorithm, IMPLEMENTATION AND ASSESSMENT

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1989年第6期136卷 333-340页

作者： PATRA, A RAO, GP Department of Electrical Engineering Indian Institute of Technology Kharagpur India

Inspired by the widely reported success of applications of piecewise-constant orthogonal functions to several problems of systems and control (in particular, to that of identification and the desirability of continuous-time treatment of the underlying design problem for self-tuning control), a completely continuous-time self-tuning algorithm based on block pulse functions is presented in the paper. It is found that the proposed algorithm is superior in performance to the corresponding discrete-time algorithm in the case of an example.

关键词： Self-adjusting control systems piecewise-constant orthogonal functions discrete-time algorithm block pulse functions control system analysis continuous time approach self-adjusting systems self-tuning control Control system analysis and synthesis methods adaptive control

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Distributed task assignment for mobile agents

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2007年第4期52卷 749-753页

作者： Moore, Brandon J. Passino, Kevin M. Ohio State Univ Dept Elect & Comp Engn Columbus OH 43210 USA

This note demonstrates how the distributed auction algorithm can be modified to assign mobile agents to spatially distributed tasks despite communication delays and the fact that agent movement may cause the benefit associated with each possible agent-task assignment to vary during the execution of the algorithm. Bounds on the convergence time of the algorithm and the sub-optimality of the resulting solution are provided. Monte Carlo simulations are provided to show the conditions under which the modified distributed auction can outperform centralized calculation.

关键词： discrete-time algorithm algorithms Mobile agents Monte Carlo technique Legal Executions Distribute

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WEIGHTED INPUT PREDICTIVE CONTROLLER

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IEE PROCEEDINGS-D CONTROL THEORY AND APPLICATIONS 1988年第1期135卷 16-20页

作者： WARWICK, K CLARKE, DW Department of Engineering Science University of Oxford Oxford UK

In the paper, a discrete-time algorithm is presented which is based on a predictive control scheme in the form of dynamic matrix control. A set of control inputs are calculated and made available at each time instant, the actual input applied being a weighted summation of the inputs within the set. The algorithm is directly applicable in a self-tuning format and is therefore suitable for slowly time-varying systems in a noisy environment.

关键词： discrete time systems discrete control systems self-tuning slowly time-varying systems discrete-time algorithm Optimal control dynamic matrix control predictive control polynomials Algebra matrix algebra weighted summation noisy environment

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