A Differential Game Model of Ship Control Process

Abstract

In the paper the use of a differential game for describing the process of safe ship steering in the vicinity of a great number of ships is presented. It has been shown that a positional non-cooperative differential game of “j” participants is an adequate model of this process. The state equations of the process, the constraints for state variables and for control variables, initial and final conditions, and the form of pay-off have been formulated. Particular care was taken in considering different possible forms of the state equations. Different forms of state equations result from the possibility of identifying their coefficients, from the practical possibility of implementing control algorithms and from the scope of observability of process state when utilizing the information from the navigation system. As the optimum criterion for the differential game the minimum of loss of way caused by safety avoiding oncoming objects was adopted, as was at the same time the minimization of the risk of collision. The optimum strategies for the objects are calculated from the max min condition of the integral pay-off.