Orthogonal Decomposition Applications

  • Alexander Weinmann


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
$$x(t) = \int_o^t {\dot x(t)dt + x(0) = \int_o^t {{{\dot x}^{\neg T}}} } hdt + x(0) = {\dot x^{\neg T}}\int_o^t {h(t)dt + x(0)}$$
$$x(t) = {\dot x^{\neg T}}{{\rm{P}}_M}{\rm{h(}}t) + x(0){h_o}(t) = {\dot x^{\neg T}}{{\rm{P}}_M}{\rm{h + x}}_o^Th;{\rm{ }}{{\rm{x}}_o} \buildrel \Delta \over = {\left[ {x(0){\rm{ 0 0}}...} \right]^T}$$


Operational Matrix Laguerre Polynomial Orthogonal Expansion Riccati Differential Equation Linear Optimal Control 
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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

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

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