Application of the bio-inspired optimization methods in the solar sail optimal open-loop control problem


DOI: 10.34759/trd-2022-122-24

Аuthors

Panteleyev A. V.1*, Belyakov I. A.2**

1. ,
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: avpanteleev@inbox.ru
**e-mail: vanbelyakov@yandex.ru

Abstract

This article discusses application of bio-inspired metaheuristic global optimization methods: Grey Wolf Optimizer (GWO) and Whale Optimization Algorithm (WOA) for the problem of optimal loop-open control. Optimal control needs to manipulate space probe with solar sail. These algorithms belong to the class of swarm optimization methods, which feature is possibility of data transfer between individuals. At the same time GWO and WOA were inspired by nature, therefore we may relate them to bio-inspired category. The behavior of a nonlinear deterministic continuous model of a plant is described by a system of differential equations with given initial conditions and a non-fixed terminal time. It is assumed that only time information is available during control, i.e. the open-loop control is used. Numerical solution is found in the form of saturation function, which guarantees fulfillment of parallelepiped control constraints. Function arguments are finding in the linear combination of given base functions. Since terminal moment is undefined, this article applies method of transformation to the fixed terminal time problem, which introduces new independent variable, related with time.

The task is to find optimal control law for realizing solar system mission flight from the Earth’s orbit to the Mercury’s orbit in the shortest possible time. Algorithm of two bio-inspired metaheuristic optimization methods application and software were created for numerical solution solar sail open-loop control problem. Software gives mathematical modelling with various parameters for a subsequent visualization. Comparison with known results was provided. Recommendations were provided for parameters choose to solve typical model optimization and applied solar sail control problem.

Keywords:

optimal open-loop control problems, global optimization algorithm, software, bio-inspired algorithm, metaheuristic, time optimal control, solar sail

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