Approximation of low rank solutions for linear quadratic control of partial differential equations

Academic Article

Abstract

  • Algebraic Riccati equations (ARE) of large dimension arise when using approximations to design controllers for systems modeled by partial differential equations. We use a modified Newton method to solve the ARE that takes advantage of several special features of these problems. The modified Newton method leads to a right-hand side of rank equal to the number of inputs regardless of the weights. Thus, the resulting Lyapunov equation can be more efficiently solved. The Cholesky-ADI algorithm is used to solve the Lyapunov equation resulting at each step. The algorithm is straightforward to code. Performance is illustrated with a number of standard examples. An example on controlling the deflection of the Euler-Bernoulli beam indicates that for weakly damped problems a low rank solution to the ARE may not exist. Further analysis supports this point. © 2008 Springer Science+Business Media, LLC.
  • Digital Object Identifier (doi)

    Start Page

  • 93
  • End Page

  • 111
  • Volume

  • 46
  • Issue

  • 1