Mixed L2and L∞problems by weight selection in quadratic optimal control

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Abstract
In an attempt to achieve more realistic control objectives, the weighting matrices in the standard LQ1 problem are usually chosen by the designer in an ad hoc manner. This paper shows several optimal control design problems that minimize a quadratic function of the control vector subject to multiple inequality constraints on the output L 2 norms, L ∞ norms, covariance matrix, and the maximum singular value of the output covariance matrix. The solutions of all four of these problems reduce to standard LQI control problems with different choices of weights. This paper shows how to construct these different weights. The practical significance of these results is that many robustness properties relate directly to these four entities. Hence the given control design algorithm delivers a specified degree of robustness to both parameter errors and disturbances. The results are presented in the deterministic terms of the linear quadratic impulse (LQI)for continuous and discrete systems problem rather than the stochastic LQG problem. The results are easily transferable to the LQG problem.

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