Quantitative Controllability Indices of Nonlinear Systems

The problem of optimal choice of system parameters with respect to a given optimalitycriterion is studied. To compare systems with different parameter values, a quantitativeestimation of controllability is introduced. This estimation is based on the average value ofa function that defines the optimality criterion. As an example, a very simplified model ofan underwater vehicle is considered. The problem of finding an arrangement of its controlpropellers for which either the motion time or the energy consumption of the vehicle is minimal isstudied. To test the approach used, the trajectories of the underwater vehicle are randomlygenerated. The energy consumption and the time of motion along these trajectories are comparedfor systems with different parameter values and different indices.