Advertisement

Orthogonal Decomposition Applications

  • Alexander Weinmann

Abstract

The orthogonal component coefficient vector x is given by Eq.(36.16). Thus, x(t) is decomposed into k terms. Starting now with the orthogonal expansion coefficient vector associated with (t) and using h o(t) = 1, the original function x(t) can be expressed as follows
$$x(t) = \int_o^t {\dot x(t)dt + x(0) = \int_o^t {{{\dot x}^{\neg T}}} } hdt + x(0) = {\dot x^{\neg T}}\int_o^t {h(t)dt + x(0)}$$
(38.1)
$$x(t) = {\dot x^{\neg T}}{{\rm{P}}_M}{\rm{h(}}t) + x(0){h_o}(t) = {\dot x^{\neg T}}{{\rm{P}}_M}{\rm{h + x}}_o^Th;{\rm{ }}{{\rm{x}}_o} \buildrel \Delta \over = {\left[ {x(0){\rm{ 0 0}}...} \right]^T}$$
(38.2)

Keywords

Operational Matrix Laguerre Polynomial Orthogonal Expansion Riccati Differential Equation Linear Optimal Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • Alexander Weinmann
    • 1
  1. 1.Department of Electrical EngineeringTechnical University ViennaAustria

Personalised recommendations