Analysis of a hybrid stochastic model of object movement along a complex trajectory

The paper addresses the analysis of the observability and controllability properties of an object model moving along a complex trajectory. The trajectory is represented by a set of pieces of a finite length, at each of which the object moves either uniformly and on a straight line, or makes a circular motion when turning to the right or to the left with constant velocity. Such trajectories are typical for many technical objects, including mobile robots. The hybrid stochastic model represented by a set of discrete linear stochastic models corresponding to various pieces of the object’s trajectory. The properties of complete observability and controllability of the hybrid stochastic model are analyzed. Based on the verification of the criterion for complete observability of a discrete linear dynamic system, the problem of choosing the optimal set of sensors was solved, in which the hybrid stochastic model retains the property of complete observability. It is proved that measurements of the coordinates of an object are mandatory to satisfy the criterion for complete observability.