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Browsing by Author "Yuzhen, Ge"

Now showing 1 - 9 of 9
  • Cost-Effective Parallel Processing for H-squared/H-to infinity Controller Synthesis
    Yuzhen, Ge; Watson, Layne T.; Collins, Emmanuel G. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1995-07-01)
    A distributed version of a homotopy algorithm for solving the H-squared/H-to infinity mixed-norm controller synthesis problem is presented. The main purpose of the study is to explore the possibility of achieving high performance with low cost. Existing UNIX workstations running PVM (Parallel Virtual Machine) are utilized. Only the Jacobian matrix computation is distributed and therefore the modification to the original sequential code is minimal. The same algorithm has also been implemented on an Intel Paragon parallel machine. Our implementation shows that acceptable speedup is achieved and the larger the problem sizes, the higher the speedup. Comparing with the results from the Intel Paragon, the study concludes that utilizing the existing UNIX workstations can be a very cost-effective approach to shorten computation time. Furthermore, this economical way to achieve high performance computation can easily be realized and incorporated in a practical industrial design environment.
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    Globally Convergent Homotopy Algorithms for the Combined H-squared/ H-to Infinity Model Reduction Problem
    Yuzhen, Ge; Watson, Layne T.; Collins, Emmanuel G.; Bernstein, Dennis S. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1993-06-01)
    The problem of finding a reduced order model, optimal in the H-squared sense, to a given system model is a fundamental one in control system analysis and design. The addition of a H-to infinity constraint to the H-squared optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probablity-one homotopy methods the combined H-squared/H-to infinity model reduction problem is difficult to solve. Several approaches based on homotopy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations -- input normal, Ly, Bryson, and Cannon's 2 x 2 block parametrization -- are developed and compared here.
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    A Homotopy Algorithm for the Combined H-squared/H-to Infinity Model Reduction Problem
    Yuzhen, Ge; Collins, Emmanuel G.; Watson, Layne T.; Bernstein, Dennis S. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1993-05-01)
    The problem of finding a reduced order model, optimal in the H-squared sense, to a given system model is a fundamental one in control system analysis and design. The addition of a H-to infinity constraint to the H-squared optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probability-one homotopy methods the combined H-squared/H-to infinity model reduction problem is difficult to solve. Several approaches based on homotoppy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on two formulations - input normal form; Ly, Bryson, and Cannon's 2 x 2 block parametrization - are developed and compared here.
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    A Homotopy Algorithm for the Combined H2/H&infin Model Reduction Problem
    Yuzhen, Ge; Collins, Emmanuel G.; Watson, Layne T.; Bernstein, Dennis S. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1992)
    The problem of finding a reduced order model, optimal in the H2 sense, to a given system model is a fundamental one in control system analysis and design. The addition of an H∞ constraint to the H2 optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probability-one homotopy methods the combined H2 /H∞ model reduction problem is difficult to solve. Several approaches based on homotopy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on two formulations---input normal form; Ly, Bryson, and Cannon's 2x2 block parametrization are developed and compared.
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    An Input Normal Form Homotopy for the L2 Optimal Model Order Reduction Problem
    Yuzhen, Ge; Collins, Emmanuel G.; Watson, Layne T.; Davis, L. D. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1993-06-01)
    In control system analysis and design, finding a reduced order model, optimal in the L-squared sense, to a given system model is a fundamental problem. The problem is very difficult without the global convergence of homotopy methods, and a homotopy based approach has been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. A homotopy algorithm based on the input normal form characterization of the reduced order model is developed here and is compared with the homotopy algorithms based on Hyland and Bernstein's optimal projection equations. The main conclusions are that the input normal form algorithm can be very efficient, but can also be very ill conditioned or even fail.
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    Minimal Parameter Homotopies for the L2 Optimal Model Order Reduction Problem
    Yuzhen, Ge; Collins, Emmanuel G.; Watson, Layne T.; Davis, L. D. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1992)
    The problem of finding a reduced order model, optimal in the L2 sense, to a given system model is a fundamental one in control system analysis and design. The problem is very difficult without the global convergence of homotopy methods, and a number of homotopy based approaches have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on several formulations are developed and compared here. The main conclusions are that dimensionality is inversely related to numerical well conditioning and algorithmic efficiency is inversely related to robustness of the algorithm.
  • An Object-oriented Approach to Semidefinite Programming
    Yuzhen, Ge; Watson, Layne T.; Emmanuel G. Collins, Jr. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1996-05-01)
    An object-oriented design and implementation of a primal-dual algorithm for solving the semidefinite programming problem is presented. The advantages of applying the object-oriented methodology to numerical computations, in particular to an interior point algorithm for semidefinite programming, or for solving other types of linear matrix inequalities are discussed. One object-oriented design of the primal-dual algorithm and its implementation using C++ is presented. The performance of the C++ implementation is compared with that of a procedural C implementation, and while the performance of the C++ implementation is comparable to that of the C implementation, the resulting code is easier to read, modify, and maintain.
  • Probability-One Homotopy Algorithms for Full and Reduced Order H-squared/H-to Infinity Controller Synthesis
    Yuzhen, Ge; Watson, Layne T.; Collins, Emmanuel G.; Bernstein, Dennis S. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1994)
    Homotopy algorithms for both full- and reduced-order LQG controller design problems with an H-to infinity constraint on disturbance attenuation are developed. The H-to infinity constraint is enforced by replacing the covariance Lyapunov equation by a Riccati equation whose solution gives an upper boundary on H-squared performance. The numerical algorithm, based on homotopy theory, solves the necessary conditions for a minimum of the upper bound on H-squared performance. The algorithms are based on two minimal parameter formulations: Ly, Bryson, and Cannon's 2X2 block parametrization and the input normal Riccati form parametrization. An over-parametrization formulation is also proposed. Numerical experiments suggest that the combination of a globally convergent homotopy method and a minimal parameter formulation applied to the upper bound minimization gives excellent results for mixed-norm H-squared/H-to infinity synthesis. The nonmonocity of homotopy zero curves is demonstrated, proving that algorithms more sophisticated that standard continuation are necessary.
  • Quantum Computing Applied to Optimization
    Yuzhen, Ge; Watson, Layne T. (Department of Computer Science, Virginia Polytechnic Institute & State University, 1999-09-01)
    Optimization problems represent a class of problems that can be time consuming to solve and very complex. In this paper, a quantum algorithm for solving optimization problems is proposed. The algorithm utilizes the encoding scheme from genetic algorithms to encode the problem and then uses Grover's unitary transformation to seek out a solution. The efficiency of the algorithm depends on the length of the chromosome or the coded variable. As a simple example the satisfiability problem, an NP-complete problem, is examined using the algorithm and the time complexity of solving this problem is greatly improved. The traveling salesman and minimum spanning tree problems are also briefly discussed.