Multi-level Approach to the Large-scale Control Problem

Abstract

Let us consider a multivariable control problem. From the theory of the optimal control [1], [5] we know that it is possible to find for some speciale case the so-called “feed-back” solution of the optimal control problem

$$ {\text{u = c (x)}} $$

where u — is a n-dimensional optimal control vector which minimized the index of performance

$$ {\text{I = }}\int_{{{\text{t}}_{\text{o}}}}^{{{\text{t}}_{\text{1}}}} {\;{\text{g(x,u) dt}}} $$

x — is a n-dimensional state vector of the controlled process

$$ \dot x = f\left( {x,u} \right) $$

Let us introduce the complexity measure of the optimal controller.