Sensitivity reduction of the linear quadratic regulator by matrix modification
Cristina Verde, P.M. Frank · International Journal of Control · 1988
The power of sensitivity theory used for the design of linear quadratic optimal regulators is discussed. It is shown that a reduction in the L2-norm of the trajectory sensitivity function and in the maximal magnitude of the inverse of the return difference can be obtained modifying the weighting matrix Q according to the sensitivity with respect to parameter variations for each state variable. A general rule is given that provides a trade-off of sensitivity reduction versus increase in the performance index. The efficiency for the continuous and discrete case of the LQR is demonstrated with two examples.