Quantitative Controllability Indices of NonlinearSystems

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