Principle of proportional damages in a multiple criteria LQR problem

Abstract

A multiple criteria linear quadratic regulator (LQR) problem is considered. The principle of proportional damages is worked out to minimize a norm of a difference between ideal and optimal values of the vector-performance criteria, while the distribution of the losses (damages) of the performance criteria are under control. A multiple criteria LQR problem solution via principle of proportional damages is obtained as a linear form of state variables and is invariant to the norm which is minimized.