ASYMPTOTIC METHODS IN PROBLEMS OF SUPERVISORY CONTROL OF AUTONOMOUS UNDERWATER ROBOTS
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 conditions of a volatile predictable environment, it is necessary to provide working tools, the use of which, together with 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-level control scheme, which can be called supervisory, is proposed in this paper to be implemented using two types 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 principle of 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 random perturbation in fast movements. Given that fast movements are stabilized, it is high probable that the noise influence averaged and does not significantly affect the behavior of slow variables. However, with sufficiently long observation it is possible to find a situation where at some period the perturbation values are not only uncompensated, but, on the contrary, line up in a sequence as specially intended to form an apparent deviation of the slow sub-vector from equilibrium. It is known from the theory of large deviations 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 this reason, the large deviations theory usage makes it possible to organize the control of deviations from a iven object’ t jecto y, capable of giving estimates on the probability of the controlled deviations critical values. As a result, it is shown that if accelerations are formed by fast subsystems, then in slow subsystems it is possible not only to achieve acceptable quality and accuracy at a fixed interval, but also to ensure this regardless of the disturbances. The validity of the proposed approach to synthesis, based on the separation of movements and the large deviations theory, is shown on the example of an autonomous underwater vehicle with two rudders (fore and aft) in the task of controlling longitudinal motion at a given depth. Simulation results and their discussion are presented.
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