Author(s)

J. Lisowski

Abstract

This paper describes the application of selected methods of optimal control theory for a ship to determine a safe trajectory during the passing of other ships encountered in restricted visibility at sea. The methods of comparison of safe ship control in a collision situation – multi-stage positional non-cooperative and cooperative game, multi-step matrix non-cooperative game, dynamic optimization with neural constrains of the state control process and kinematics optimization – have been introduced here. The synthesis of computer navigator decision supporting algorithms using dynamic programming and dual linear programming methods has been presented. The considerations have been used to illustrate examples of a computer simulation of the algorithms to determine the safe and optimal own ship trajectories in a navigational situation in restricted visibility on the North Sea. Keywords: differential games, positional games, matrix games, dual linear programming, dynamic programming, transport engineering, safe ship operations. 1 Optimal and safe ship control in the sea game environment The number of vessels operating on the seas and oceans has been increasing year by year, as have their speeds. This has necessitated further and more precise investigation into the problem of safe navigation. In order to ensure the safety of navigation the ships are obliged to comply with the regulations of the Convention, namely the International Regulations for Preventing Collisions at Sea (COLREG). However, these Rules refer only to two ships and under the conditions of good visibility [1, 2].

Keywords

differential games, positional games, matrix games, dual linearprogramming, dynamic programming, transport engineering, safe shipoperations