Approximate Linear Quadratic Regulator Problem and Its Application to Optimal Control in Discrete-Time LTI Systems

Chapter
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 110)

Abstract

It is considered to approximately solve an linear quadratic (LQ) regulator problem in the case of discrete-time LTI systems. It leaves parameters as symbols in the evaluation function. The notion of the approximate LQ regulator problem is introduced. Also a computation method to solve the problem is proposed. A numerical example of the approximate LQ regulator problem is also presented, which is applied to an inverted pendulum on a cart.

Keywords

Linear system theory Optimal control Discrete-time LTI system Symbolic computation 

References

  1. 1.
    Kitamoto T (1994) Approximate eigenvalues, eigenvectors and iverse of a matrix with polynomial entries. Jpn J Ind Appl Math 11(1):73–85CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Kučera V (1979) Discrete linear control: the polynomial approach. John Wiley & Sons, Chichester, UKMATHGoogle Scholar
  3. 3.
    Mori K (2011) Approximate riccati equation and its application to optimal control in discrete-time systems. In: Proceedings of the international multiconference of engineers and computer scientists 2011 (IMECS 2011), Hong Kong, 16–18 March. Lecture notes in engineering and computer science, pp 808–812Google Scholar
  4. 4.
    Mori K, Abe K (1997) Approximate spectral factorization and its application to optimal control—case of discrete-time siso with 1 parameter—. In: Proceedings of the second asian control conference (ASCC ’97), pp 421–424Google Scholar
  5. 5.
    Ogata K (1994) Discrete-time control systems, 2nd edn. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  6. 6.
    Sasaki T, Suzuki M, Kolár̆ M, Sasaki M (1991) Approximate factorization of multivariate polynomials and absolute irreducibility testing. Jpn J Ind Appl Math 8(3):357–375Google Scholar
  7. 7.
    Zhou K, Doyle J, Glover K (1996) Robust and optimal control. Prentice Hall, Upper Saddle River, NJMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Computer Science and EngineeringThe University of AizuAizu-WakamatsuJapan

Personalised recommendations