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About: Linearization is a(n) research topic. Over the lifetime, 20520 publication(s) have been published within this topic receiving 383929 citation(s). more


Open accessJournal ArticleDOI: 10.1109/JPROC.2003.823141
Simon Julier, Jeffrey Uhlmann1Institutions (1)
08 Nov 2004-
Abstract: The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT. more

  • Fig. 12. Fourth-order sigma points.
    Fig. 12. Fourth-order sigma points.
  • Table 1 Points and Weights for n = 3 Dimensions for the Fourth-Order UT
    Table 1 Points and Weights for n = 3 Dimensions for the Fourth-Order UT
Topics: Unscented transform (65%), Extended Kalman filter (64%), Linearization (57%) more

5,559 Citations

Open accessBook
12 May 1974-
Abstract: This book is about dynamical aspects of ordinary differential equations and the relations between dynamical systems and certain fields outside pure mathematics. A prominent role is played by the structure theory of linear operators on finite-dimensional vector spaces; the authors have included a self-contained treatment of that subject. more

2,847 Citations

Journal ArticleDOI: 10.1016/S0020-7462(98)00048-1
Ji-Huan He1Institutions (1)
Abstract: In this paper, a new kind of analytical technique for a non-linear problem called the variational iteration method is described and used to give approximate solutions for some well-known non-linear problems. In this method, the problems are initially approximated with possible unknowns. Then a correction functional is constructed by a general Lagrange multiplier, which can be identified optimally via the variational theory. Being different from the other non-linear analytical methods, such as perturbation methods, this method does not depend on small parameters, such that it can find wide application in non-linear problems without linearization or small perturbations. Comparison with Adomian’s decomposition method reveals that the approximate solutions obtained by the proposed method converge to its exact solution faster than those of Adomian’s method. more

Topics: Adomian decomposition method (64%), Iterative method (56%), Numerical analysis (55%) more

2,223 Citations

Journal ArticleDOI: 10.1109/9.618250
L. El Ghaoui1, François Oustry1, M. Ait-Rami1Institutions (1)
Abstract: This paper describes a linear matrix inequality (LMI)-based algorithm for the static and reduced-order output-feedback synthesis problems of nth-order linear time-invariant (LTI) systems with n/sub u/ (respectively, n/sub y/) independent inputs (respectively, outputs). The algorithm is based on a "cone complementarity" formulation of the problem and is guaranteed to produce a stabilizing controller of order m/spl les/n-max(n/sub u/,n/sub y/), matching a generic stabilizability result of Davison and Chatterjee (1971). Extensive numerical experiments indicate that the algorithm finds a controller with order less than or equal to that predicted by Kimura's generic stabilizability result (m/spl les/n-n/sub u/-n/sub y/+1). A similar algorithm can be applied to a variety of control problems, including robust control synthesis. more

Topics: Complementarity theory (53%), Linear system (50%), Linearization (50%)

1,856 Citations

Open accessBook
22 Jun 1999-
Abstract: 1 Linear vs. Nonlinear.- 2 Planar Dynamical Systems.- 3 Mathematical Background.- 4 Input-Output Analysis.- 5 Lyapunov Stability Theory.- 6 Applications of Lyapunov Theory.- 7 Dynamical Systems and Bifurcations.- 8 Basics of Differential Geometry.- 9 Linearization by State Feedback.- 10 Design Examples Using Linearization.- 11 Geometric Nonlinear Control.- 12 Exterior Differential Systems in Control.- 13 New Vistas: Multi-Agent Hybrid Systems.- References. more

Topics: Linearization (65%), Lyapunov function (64%), Feedback linearization (63%) more

1,827 Citations

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Topic's top 5 most impactful authors

Zhongsheng Hou

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62 papers, 483 citations

Gerasimos Rigatos

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Peng Shi

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Henk Nijmeijer

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