Multi-step matrix game of safe ship control at various safe passing distances

The paper introduces the process of safe ship control in collision situations using a differential game model with m participants. The basic model of process includes non-linear state equations and non-linear, time-varying constraints of the state variables as well as the quality game control index in the forms of game integral payment and final payment. As an approximated model of the manoeuvring process, a model of a multi-step matrix game in the form of a dual linear programming problem has been adopted here. The Game Control (gc) computer program has been designed in Matlab/Simulink software in order to determine the own ship safe trajectory. The considerations have been illustrated with computer simulation examples using the gc program for determining safe own ship trajectory in real navigation situations when passing commonly-encountered ships.