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Optimal Tracking Control for a Class of Unknown Discrete-time Systems with Actuator Saturation via Data-based ADP algorithm

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Acta Automatica Sinica 2013年第9期39卷 1413-1420页

作者： Rui-Zhuo SONG Wen-Dong XIAO Chang-Yin SUN School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing 100083 China

A novel optimal tracking control method for a class of discrete-time systems with actuator saturation and unknown dynamics is proposed in this paper. The scheme is based on the iterative adaptive dynamic programming (ADP) algorithm. In order to implement the control scheme, a data-based identifier is first constructed for the unknown system dynamics. By introducing the M network, the explicit formula of the steady control is achieved. In order to eliminate the effect of the actuator saturation, a nonquadratic performance functional is presented, and then an iterative ADP algorithm is established to achieve the optimal tracking control solution with convergence analysis. For implementing the optimal control method, neural networks are used to establish the data-based identifier, compute the performance index functional, approximate the optimal control policy and solve the steady control, respectively. Simulation example is provided to verify the effectiveness of the presented optimal tracking control scheme.

关键词： Adaptive dynamic programming (ADP) iterative algorithm optimal tracking control data-based identifier

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An Improvement for the Calibration of Laser Gyro Strapdown IMU

An Improvement for the Calibration of Laser Gyro Strapdown I...

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32nd Chinese Control Conference (CCC)

作者： Yan Gong-min Zhao Chun-lian Wu Feng Qin Yong-yuan Northwestern Polytech Univ Dept Automat Control Xian 710072 Peoples R China

ISBN: (纸本)9781479900305

Under the condition of uniaxial rotation test and using norm restriction of the angular rotation vector, a nonlinear equations set including 6 uncorrelated rotations is established to define the SIMU calibration frame. A test scheme of clockwise & counter clockwise rotations is adopted to eliminate the effect of earth rotation and gyro drift errors. Linearization and iterative algorithm are put forward to resolve the nonlinear equations set with very high precision. In accelerometer calibration model, the two-order nonlinear coefficient and cross-coupling coefficient are both considered. The static multi-position method is used to calibrate accelerometers, but in each static position, it is necessary to conduct an extra vertical rotation test to determine gravitation vector in SIMU frame and the result can be used as accelerometer input reference. A static nine-position accelerometer calibration scheme is presented and the simulation results show that scale factor matrix and bias can be estimated with high accuracy, but the two-order nonlinear coefficient and cross-coupling coefficient are relatively affected by accelerometer measurement noise.

关键词： strapdown inertial navigation system calibration of SIMU iterative algorithm simulation tests

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Joint Design of Linear Transmitter and Receiver for the MIMO Interference Channel

Joint Design of Linear Transmitter and Receiver for the MIMO...

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2013 IEEE 5th International Symposium on Microwave,Antenna,Propagation and EMC Technologies for Wireless Communications

作者： Jin Li Youhua Fu Chen Liu Hua'an Zhao Nanjing University of Posts and Telecommunications National Mobile Communications Research Laboratory Southeast University

ISBN: (纸本)9781467360760

Interference alignment(IA) is a powerful scheme that has emerged out of recent work in the context of the MIMO X *** of the existing IA schemes are aimed to optimize the sum-capacity,the error probability,and the mean square errors(MSE) of the system,and less consider the system power *** paper proposes a new IA scheme to minimize the system transmit power under the condition of every user's MSE constraint through a joint design of linear transmitter and receiver for a K-user MIMO interference *** order to solve our optimization problem,we employ the Lagrange function and Karush-Kuhn-Tucker(KKT) conditions,then get the transmitter precoding and receiving filter matrices expressions by the analysis and ***,we use a joint iterative algorithm to solve the proposed optimization *** results verify that the provided scheme improves the power efficiency.

关键词： MIMO intereference channel joint transceiver mean square errors (MSE) KKT conditions iterative algorithm iterative algorithms Lagrangian dynamic efficiency Mean square error transmitter receivers Interference channels Receivers Error probability

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A Fully Implicit Finite Difference Scheme for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term

A Fully Implicit Finite Difference Scheme for the Variable-O...

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第二届国际计算科学与工程国际学术研讨会

作者： Wei-yuan Ma Ya-bin Shao Hai-dong Zhang School of Mathematics and Computer Science Northwest University for Nationalities

This paper proposes a finite difference scheme for variable-order nonlinear fractional diffusion equation, in which the nonlinear source term is considered implicit. A linear iterative algorithm for nonlinear scheme is introduced. The stability and convergence of the method are proved by discrete energy method. The convergence order of the method is O ( h). Some examples demonstrate that the method is efficient and reliable.

关键词： Variable-order nonlinear fractional diffusion equation Fully implicit difference scheme iterative algorithm Convergence Stability

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关于离散HJB方程的一种新的迭代法

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高等学校计算数学学报 2012年第2期34卷 179-184页

作者：邹战勇广东商学院数学与计算科学学院

A new iterative algorithm for discrete HJB equations is proposed. Monotone convergence has been proved for the *** example shows the efficiency of the algorithm.

关键词： HJB equation iterative algorithm monotone convergence.

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iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2008年第4期56卷 942-952页

作者： Ceng, Lu-Chuan Guu, Sy-Ming Yao, Jen-Chih Yuan Ze Univ Coll Management Dept Business Adm Chungli 330 Taoyuan Hsien Taiwan Shanghai Normal Univ Dept Math Shanghai 200234 Peoples R China Natl Sun Yat Sen Univ Dept Appl Math Kaohsiung 804 Taiwan

In the present paper, we introduce the concept of eta-relaxed strong convexity of a differentiable functional and extend Ding and Yao's auxiliary variational inequality technique [X.P. Ding, J.C. Yao, Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces, Computers and Mathematics with Applications, 49 (2005), 857-869] to develop iterative algorithms for finding the approximate solutions to the mixed quasi-variational-like inclusion problem (in short, MQVLIP) in a Banach space. On the one hand, we establish a result on the existence of a solution to the equilibrium problem by virtue of well-known Brouwer's fixed-point theorem. Moreover, by using this result we derive the existence and uniqueness of a solution to the MQVLIP and the existence of the approximate solutions generated by the algorithm for the MQVLIP. On the other hand, we use the concepts of eta-relaxed strong convexity of a differentiable functional and eta-cocoercivity of a composite map to prove the strong convergence of the approximate solutions to the unique solution of the MQVLIP. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： mixed quasi-variational-like inclusion Brouwer's fixed-point theorem auxiliary variational inequality iterative algorithm Banach space

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Two iterative algorithms for solving coupled matrix equations over reflexive and anti-reflexive matrices

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COMPUTATIONAL & APPLIED MATHEMATICS 2012年第2期31卷 353-371页

作者： Dehghan, Mehdi Hajarian, Masoud Shahid Beheshti Univ Fac Math Sci Dept Math GC Tehran 19839 Iran Amirkabir Univ Technol Fac Math & Comp Sci Dept Appl Math Tehran 15914 Iran

An n x n real matrix P is said to be a generalized reflection matrix if P-T = P and P-2 = I (where P-T is the transpose of P). A matrix A is an element of R-nxn is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A = PAP (A = -PAP). The reflexive and anti-reflexive matrices have wide applications in many fields. In this article, two iterative algorithms are proposed to solve the coupled matrix equations {A(1)XB(1) + (C1XD1)-D-T = M-1, A(2)XB(2) + (C2XD2)-D-T = M-2, over reflexive and anti-reflexive matrices, respectively. We prove that the first (second) algorithm converges to the reflexive (anti-reflexive) solution of the coupled matrix equations for any initial reflexive (anti-reflexive) matrix. Finally two numerical examples are used to illustrate the efficiency of the proposed algorithms.

关键词： iterative algorithm matrix equation reflexive matrix anti-reflexive matrix

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iterative algorithm FOR AXIALLY ACCELERATING STRINGS WITH INTEGRAL CONSTITUTIVE LAW

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Acta Mechanica Solida Sinica 2008年第5期21卷 449-456页

作者： Weijia Zhao Liqun Chen Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 China Department of Mathematics Qingdao University Qingdao 266071 China Department of Mechanics Shanghai University Shanghai 200444 China

A numerical method is proposed to simulate the transverse vibrations of a viscoelastic moving string constituted by an integral law. In the numerical computation, the Galerkin method based on the Hermite functions is applied to discretize the state variables, and the Runge- Kutta method is applied to solve the resulting differential-integral equation system. A linear iterative process is designed to compute the integral terms at each time step, which makes the numerical method more efficient and accurate. As examples, nonlinear parametric vibrations of an axially moving viscoelastic string are analyzed.

关键词： iterative algorithm partial-differential-integral equation Hermite function Galerkin method axially moving string integral constitutive law

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An Alternating Minimization algorithm for Binary Image Restoration

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2012年第2期21卷 883-888页

作者： Zhang, Jianjun Shanghai Univ Dept Math Shanghai 200444 Peoples R China

The problem we will consider in this paper is binary image restoration. It is, in essence, difficult to solve because of the combinatorial nature of the problem. To overcome this difficulty, we propose a new minimization model by making use of a new variable to enforce the image to be binary. Based on the proposed minimization model, we present a fast alternating minimization algorithm for binary image restoration. We prove the convergence of the proposed alternating minimization algorithm. Experimental results show that the proposed method is feasible and effective for binary image restoration.

关键词： Blur fast Fourier transform (FFT) Gaussian noise image restoration iterative algorithm regularization

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Strong stabilisation by output feedback controller for linear systems with delayed input

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IET CONTROL THEORY AND APPLICATIONS 2012年第10期6卷 1329-1340页

作者： Du, B. Lam, J. Shu, Z. Nanjing Univ Sci & Technol Dept Automat Nanjing 210094 Jiangsu Peoples R China Univ Hong Kong Dept Mech Engn Hong Kong Hong Kong Peoples R China Univ Southampton Fac Engn & Environm Electromech Grp Southampton SO17 1BJ Hants England

This study addresses the strong stabilisation problem for continuous-time linear systems with an unknown input delay via dynamic output feedback controllers. A new criterion for dynamic output feedback stabilisability is proposed in terms of matrix inequalities with the separation of the controller gain with the Lyapunov matrix and the system matrices. Based on these new characterisations, an iterative algorithm is given to design the dynamic output feedback controllers with the initial values obtained by some proposed state feedback stabilisation methods. The effectiveness and merits of the proposed approach are shown through several examples.

关键词： dynamic output feedback controller dynamic output feedback stabilisability Lyapunov matrix continuous time linear system stability Stability in control theory state feedback Lyapunov matrix equations linear systems feedback Algebra system matrices state feedback stabilisation method continuous time systems linear matrix inequalities matrix inequalities iterative algorithm delayed input controller gain strong stabilisation problem

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