АСИМПТОТИЧЕСКИЕ МЕТОДЫ В ЗАДАЧАХ СУПЕРВИЗОРНОГО УПРАВЛЕНИЯ АВТОНОМНЫХ ПОДВОДНЫХ РОБОТОВ

Abstract

The work is devoted to the relevant problem of control synthesis for autonomous underwater vehicles(AUVs). Since AUVs must perform actions in accordance with a given program under conditionsof a volatile predictable environment, it is necessary to provide working tools, the use of which, togetherwith the AUV position and orientation control requires, along with continuous local stabilization means,implementation of supervising and coordinated control algorithms at the upper level. Such a two-levelcontrol scheme, which can be called supervisory, is proposed in this paper to be implemented using twotypes of asymptotic methods: to separate movements into fast and slow, an apparatus for analyzing singularly perturbed differential equations is used, and the upper level control is based on the principleof large deviations. The general synthesis task is to control slow movements and stabilize fast movements.At the same time, in the stochastic problem formulation, it is assumed that there is a randomperturbation in fast movements. Given that fast movements are stabilized, it is high probable that thenoise influence averaged and does not significantly affect the behavior of slow variables. However, withsufficiently long observation it is possible to find a situation where at some period the perturbation valuesare not only uncompensated, but, on the contrary, line up in a sequence as specially intended toform an apparent deviation of the slow sub-vector from equilibrium. It is known from the theory of largedeviations that such a trajectory is the only and most likely of all those leading to a certain critical event.At the same time, the phase of this process can be used to judge the critical event proximity. For thisreason, the large deviations theory usage makes it possible to organize the control of deviations from aiven object’ t jecto y, capable of giving estimates on the probability of the controlled deviationscritical values. As a result, it is shown that if accelerations are formed by fast subsystems, then in slowsubsystems it is possible not only to achieve acceptable quality and accuracy at a fixed interval, but alsoto ensure this regardless of the disturbances. The validity of the proposed approach to synthesis, basedon the separation of movements and the large deviations theory, is shown on the example of an autonomousunderwater vehicle with two rudders (fore and aft) in the task of controlling longitudinal motion ata given depth. Simulation results and their discussion are presented.