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On the utopian approach to the multiobjective LQ problem
Author(s) -
De Nicolao Giuseppe,
Locatelli Arturo
Publication year - 1993
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.4660140204
Subject(s) - mathematics , mathematical optimization , optimal control , quadratic equation , scalar (mathematics) , characterization (materials science) , point (geometry) , materials science , geometry , nanotechnology
The infinite horizon, multiobjective linear quadratic control problem for continuous time systems is considered. Following a utopian approach, the optimal solution is defined as the solution that minimizes the distance from the utopian point in the cost space. It is shown that under standard stabilizability and detectability assumptions the optimal solution always exists. The solution coincides with the solution of a scalar LQ problem in which the cost matrices are given by a suitably weighted sum of their counterparts in the individual criteria. By exploiting the characterization and properties of the optimal solution, it is shown that the problem can be efficiently solved by means of a Newton‐type algorithm.