Sufficient Conditions for Absolute Minimum of the Maximal Functional in the Multi — Criterial Problem of Optimal Control

Abstract

One possible approach to the problem of optimization of a dynamical system

$$ x(t) = f(x,u,t) $$

((1))

, when the simultaneous minimization of the given set Ω of performance criteria-functionals J _ω (x, u), ω ∈ Ω is required, consists in reducing it to a mono-criterial problem with the single functional

$$ J(x,u) = \mathop {\max }\limits_{\omega \in \Omega } \left\{ {{J_\omega }(x,u)} \right\}$$

((2))

to be minimized.