Multi-step matrix game with the risk of ship collision

This paper describes the process of the safe ship control in a collision situation using a differential game model with j participants. The basic model of the process includes non-linear state equations and non-linear time-dependant constraints of the state variables as well as the quality game control index in the form of the game integral payment and the final payment. As an approximated model of the manoeuvring process, the model of multi-step matrix game has been adopted here. The Risk Game Manoeuvring (RGM) computer program has been designed in the MATLAB 6.5 language in order to determine the ship's safe trajectory. These considerations have been illustrated with examples of a computer simulation using an RGM program for determining the safe ship's trajectory in a real navigational situation.