A method is presented far the synthesis of fixed-order controllers with robustness to mixed real and complex uncertainties. The capabilities of the method are demonstrated on a two-mass/spring benchmark problem and on...
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A method is presented far the synthesis of fixed-order controllers with robustness to mixed real and complex uncertainties. The capabilities of the method are demonstrated on a two-mass/spring benchmark problem and on a flexible satellite example. Several fixed-order mixed mu controllers are designed. A comparison with both full-order and reduced-order controllers indicates that the method is capable of synthesizing low-order controllers achieving robust performance levels similar to full-order designs, and superior to reduced-order controllers.
It is well known that the spatial frequency spectrum of membrane and thin plate splines exhibit self-affine characteristics and, hence, behave as fractals. This behavior was exploited in generating the constrained fra...
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It is well known that the spatial frequency spectrum of membrane and thin plate splines exhibit self-affine characteristics and, hence, behave as fractals. This behavior was exploited in generating the constrained fractal surfaces, which were generated by using a Gibbs sampler algorithm in the work of Szeliski and Terzopoulos. The algorithm involves locally perturbing a constrained spline surface with white noise until the spline surface reaches an equilibrium state. In this paper, we introduce a fast generalized Gibbs sampler that combines two novel techniques, namely, a preconditioning technique in a wavelet basis for constraining the splines and a perturbation scheme in which, unlike the traditional Gibbs sampler, all sites (surface nodes) that do not share a common neighbor are updated simultaneously. In addition, we demonstrate the capability to generate arbitrary order fractal surfaces without resorting to blending techniques. Using this fast Gibbs sampler algorithm, we demonstrate the synthesis of realistic terrain models from sparse elevation data.
A novel Recurrent Neural Network(RNN) based blind equalization algorithm is proposed in the *** the first time, the conjugate gradient algorithm and a three point searching method are used in RNN *** results show th...
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A novel Recurrent Neural Network(RNN) based blind equalization algorithm is proposed in the *** the first time, the conjugate gradient algorithm and a three point searching method are used in RNN *** results show that our algorithm is suprior to the one proposed by Kechriotis and the Constant Modulus algorithm.
gradient-based homotopy algorithms have previously been developed for synthesizing H-2 optimal reduced-order dynamic compensators. These algorithms are made efficient and avoid high-order singularities along the homot...
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gradient-based homotopy algorithms have previously been developed for synthesizing H-2 optimal reduced-order dynamic compensators. These algorithms are made efficient and avoid high-order singularities along the homotopy path by constraining the controller realization to a minimal parameter basis. The resultant homotopy algorithms, however, sometimes experience numerical ill conditioning or failure due to the minimal parameterization constraint. A new homotopy algorithm is presented that is based on solving the optimal projection equations, a set of coupled Riccati and Lyapunov equations that characterize the optimal reduced-order dynamic compensator. Path following in the proposed algorithm is accomplished using a predictor/corrector scheme that computes the prediction and correction steps hy efficiently solving a set of four Lyapunov equations coupled by relatively low-rank linear operators. The algorithm does not suffer from ill conditioning because of constraining the controller basis and often exhibits better numerical properties than the gradient-based homotopy algorithms. The performance of the algorithm is illustrated by considering reduced-order control design for the benchmark four disk axial vibration problem and also reduced-order control of the Active Control Technique Evaluation for Spacecraft structure.
In this paper we present an implementation method for the conjugate gradient algorithm with geometric parallelization, also called domain decomposition. The results of some experiments on the Parsytec GCel are present...
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In this paper we present an implementation method for the conjugate gradient algorithm with geometric parallelization, also called domain decomposition. The results of some experiments on the Parsytec GCel are presented and we discuss further improvements for the implementation of CG on the Parsytec.
We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allo...
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We present a parallel iterative solver for discrete second order elliptic PDEs. It is based on the conjugate gradient algorithm with incomplete factorization preconditioning, using a domain decomposed ordering to allow parallelism in the triangular solves, and resorting to some special recently developed parallelization technique to avoid communication bottle-neck for the computation associated to the internal boundary nodes. Numerical results are given for a transputer network with up to 512 processors and a few workstation cluster.
We present a new preconditioner for n x n symmetric, positive definite Toeplitz, systems. This preconditioner is an element of the n-dimensional vector space of matrices that are diagonalized by the discrete sine tran...
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We present a new preconditioner for n x n symmetric, positive definite Toeplitz, systems. This preconditioner is an element of the n-dimensional vector space of matrices that are diagonalized by the discrete sine transform. Conditions are given for which the preconditioner is positive definite and for which the preconditioned system has asymptotically clustered eigenvalues. The diagonal form of the preconditioner can be calculated in O(n log(n)) operations if n = 2(k) - 1. Thus only n additional parameters need be stored. Moreover, complex arithmetic is not needed. To use the preconditioner effectively, we develop a new technique for computing a fast convolution using the discrete sine transform (also requiring only real arithmetic). The results of numerical experimentation with this preconditioner are presented. Our preconditioner is comparable, and in some cases superior, to the standard circulant preconditioner of Tony Chan. Possible generalizations for other fast transforms are also indicated.
We develop designs for the data parallel solution of quadratic programming problems subject to box constraints. In particular, we consider the class of algorithms that iterate between projection steps that identify ca...
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We develop designs for the data parallel solution of quadratic programming problems subject to box constraints. In particular, we consider the class of algorithms that iterate between projection steps that identify candidate active sets and conjugategradient steps that explore the working space. Using the algorithm of More and Toraldo [Report MCS-p77-05 89, Argonne National Laboratory, Illinois, 1989] as a specific instance of this class of algorithms we show how its components can be implemented efficiently on a data-parallel SIMD computer architecture. Alternative designs are developed for both arbitrary, unstructured Hessian matrices and for structured problems. Implementations are carried out on a Connection Machine CM-2. They are shown to be very efficient, achieving a peak computing rate over 2 Chops. Problems with several hundred thousand variables are solved within one minute of solution time on the 8K CM-2. Extremely large test problems, with up to 2.89 million variables, are also solved efficiently. The data parallel implementation outperforms a benchmark implementation of interior point algorithms on an IBM 3090-6009 vector supercomputer and a successive overrelaxation algorithm on an Intel iPSC/860 hypercube.
A computational method is proposed in this paper for a minimax problem in the time domain. A minimax problem for a linear system is formulated and analyzed by vector space methods. The uniqueness of the optimal soluti...
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A computational method is proposed in this paper for a minimax problem in the time domain. A minimax problem for a linear system is formulated and analyzed by vector space methods. The uniqueness of the optimal solution is analyzed readily in the present approach, and its geometric interpretation is presented. The further analysis based on duality shows that the infimum or a lower bound of the value of the performance index is calculated through supplementary optimization problems, and the minimax problem is solved as an optimization problem with an inequality constraint. The proposed approach provides a simple computational method for the minimax problem. Two numerical examples demonstrate simple implementation of the proposed method.
This paper describes a second-order projection method for the incompressible Navier-Stokes equations on multiply connected domains with a logically rectangular quadrilateral grid. The method uses a second-order fracti...
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This paper describes a second-order projection method for the incompressible Navier-Stokes equations on multiply connected domains with a logically rectangular quadrilateral grid. The method uses a second-order fractional step scheme in which one first solves diffusion-convection equations to determine intermediate velocities which are then projected onto the space of divergence-free vector fields. The spatial discretizations are accomplished by formally transforming the equations to a computational space with a uniform grid. The diffusion, pressure gradient, and divergence terms are discretized using standard finite difference approximations. The convection terms are discretized using a second-order Godunov method that provides a robust discretization of these terms at high Reynolds number. Numerical results are presented illustrating the performance of the method.
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