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 any
functional. Locally controllable affine systems and integral functionals depending on the program
control are considered. Local controllability of affine systems with nonnegative inputs is
proved in the case where the columns multiplying the controls form a positive basis. For such
systems, we introduce the local controllability coefficient and pose the problem of its maximization
depending on the choice of model parameters. As an example, we consider a very simplified
model of an underwater vehicle and study the problem of finding an arrangement of its control
propellers in which the energy consumption of the vehicle is minimal.