The multiple linear quadratic gaussian problem

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Abstract
In this paper we define and solve the multiple linear quadratic gaussian (LQG) problem for discrete-time systems using Salukvadze's ideal point method which treats dynamic, but deterministic, multicriteria optimization problems. The solution consists in designing a scalar regulator where the weighting matrices are replaced by the sums of their counterparts in the individual criteria. The resulting control is optimal, in the sense that it minimizes the difference between the cost of the implemented policy from the cost that would occur if we optimized each criterion separately and added the outcomes. All the nice properties of the scalar LQG regulator are enjoyed by the multicriteria regulator as well. Extension to the continuous-time case is straightforward, yielding identical results.

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