Numerical Study on Low-Rank Approximate Solutions to Large-Scale Algebraic Riccati Equations

  • 李 建穎

Student thesis: Master's Thesis

Abstract

In recent years large-scale computing has become an important research topic Algebraic Riccati equations is a control problem comes from the quadratic optimization In this paper we study the relationship between the large-scale sparse algebraic Riccati equations low-rank approximate solutions and the control systems the control system controllability and observability that can be used to obtain low-rank approximate solution of large sparse algebriac Riccati equations; we use Newton's method solving the algebriac Riccati equations the convergence rate of Newton's method is quadratic but each iteration requires solving the Lyapunov equation so that the convergence rate significantly lower for solving the Lyapunov equations Cholesky Factor Alternating Direction Implicit iterative method can be kept low-rank structure of the solution thereby reducing its computation; further use of two strategies: Guess initial value Relaxed CFADI reducing the total number of inner iteration to accelerate the convergence rate of Newton's method and finally provide some numerical results
Date of Award2014 Jan 14
Original languageEnglish
SupervisorChern-Shuh Wang (Supervisor)

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