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On the solution of the linear‐quadratic optimal control problem by extended invariant imbedding
Author(s) -
Breitenecker Felix
Publication year - 1983
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.4660040203
Subject(s) - linear quadratic regulator , mathematics , riccati equation , boundary value problem , algebraic riccati equation , mathematical analysis , linear differential equation , linear system , optimal control , differential equation , mathematical optimization
The solution of the linear‐quadratic output regulator problem by Pontryagin's maximum principle results in an unstable linear boundary value problem. The method of invariant imbedding, which requires the integration of a matrix Riccati differential equation, solves certain boundary value problems in a stable manner. In order to make this well known method applicable, an extension algorithm is defined, which maps the boundary value problem into a problem of double dimension. The resulting algorithm of extended invariant imbedding does not depend on the boundary values. So the matrix Riccati equation has to be integrated only once ‘offline’: The unknown boundary values, the state, and the control are calculated by solution of systems of linear equations (‘online’). So, if the boundary values change, only systems of linear equations have to be solved once more. The algorithm has two variants with usually contrary stability behaviour.