Mixed L2 and L∞ problems by weight selection in quadratic optimal control

In an attempt to achieve more realistic control objectives, the weighting matrices in the standard LQI (linear quadratic impulse) problem are usually chosen by the designer in an ad hoc manner. The authors show several optimal control design problems that minimize a quadratic function of the control vector subject to multiple inequality constraints on the output L₂ norms, L_∞ norms, covariance matrix, and 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. It is shown how to construct these different weights. The practical significance of these results in 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 LQI controller for the continuous and discrete systems problem, rather than the stochastic LQG (linear quadratic Gaussian). The results are easily transferable to LQG