Asymptotic Methods of Monitoring and Control Algorithms Synthesis for Autonomous Vehicle Onboard Systems

We consider the problem of predicting potential collisions between two vehicles moving parallel to each other and subject to various disturbances. The algorithm for predicting the critical event (CE) of a collision is assumed to be implemented in real time, using onboard computers and sensors. We demonstrate that for linear models with Gaussian disturbances, such algorithms can be constructed based on the large deviation principle and the Wentzel-Freidlin CE quasipotential, along with its prototype in the form of a curve—the CE profile—leading from the attractor to the CE. This procedure is demonstrated in our article using the example of monitoring the relative motion of two autonomous underwater vehicles. As the applications of autonomous vehicles, such as unmanned aerial vehicles and unmanned surface and underwater vessels, expand, the need for models beyond those covered by traditional systems with Gaussian disturbances grows. In this paper, we attempt to use jump-type random processes of the Poisson type and birth-and-death processes as a disturbance model. Such models were considered in large deviation analysis problems by Schwartz and Weiss (A. Schwartz, A. Weiss). We use this approach to solve our forecasting problem based on the KS-profile or its analogue. We are talking specifically about an analogue, since there is no attractor in this case. Using the same problem for two spacecraft, but without Gaussian disturbances, we demonstrate that the curve connecting the equilibrium state and the KS fully corresponds to the role of the KS-profile in the forecast algorithm, although the equilibrium state in this case is not stable. Now we can formulate the problem of large deviation forecasting based on the KS-quasipotential and its preimage for a linear system with both Gaussian and Poisson disturbances, but this is the subject of future papers.