Searching for Parameters of a Model with the Best Local Controllability

Abstract

We study the problem of optimal choice of model parameters with respect to anyfunctional. Locally controllable affine systems and integral functionals depending on the programcontrol are considered. Local controllability of affine systems with nonnegative inputs isproved in the case where the columns multiplying the controls form a positive basis. For suchsystems, we introduce the local controllability coefficient and pose the problem of its maximizationdepending on the choice of model parameters. As an example, we consider a very simplifiedmodel of an underwater vehicle and study the problem of finding an arrangement of its controlpropellers in which the energy consumption of the vehicle is minimal.