On the utopian approach to the multiobjective LQ problem

On the utopian approach to the multiobjective LQ problem

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Article ID: iaor1994231
Country: United Kingdom
Volume: 14
Issue: 2
Start Page Number: 111
End Page Number: 124
Publication Date: Apr 1993
Journal: Optimal Control Applications & Methods
Authors: ,
Keywords: programming: multiple criteria, optimization
Abstract:

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.

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