Controller design for parameter sensitivity reduction in linear regulators

This paper addresses the problem of parameter sensitivity reduction in linear regulators. It is shown that the minimization of a modified performance index which includes a quadratic term of trajectory sensitivity (state, output, or control) subject to the augmented sensitivity system dynamics causes reduction not only in trajectory sensitivity but also in cost sensitivity. Inclusion of both state sensitivity and control sensitivity terms in the cost functional reduces cost sensitivity and facilitates the unification of two approaches previously treated independently: ‘trajectory sensitivity reduction’ and ‘cost sensitivity reduction’. Two control design methods, one based on a linear formulation and the other on a non-linear formulation, are given for both deterministic and stochastic systems. The improvement of these methods over existing methods is illustrated by examples.