Wyniki wyszukiwania - BazTech

1

Zero-sum games on a product of staircase-function finite spaces

Romanuke Vadim

Journal of Mathematics and Applications

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2021

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Vol. 44

75--91

EN

A tractable method of solving zero-sum games defined on a product of staircase-function finite spaces is presented. The method is based on stacking solutions of “smaller” matrix games, each defined on an interval where the pure strategy value is constant. The stack is always possible, even when only time is discrete, so the set of pure strategy possible values can be continuous. Any combination of the solutions of the “smaller” matrix games is a solution of the initial zero-sum game.

2

Multi-criteria optimization of multi-step matrix game in collision avoidance of ships

Lisowski J.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2019

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Vol. 13, no. 1

125--131

EN

This research article formulates a mathematical model of the matrix game of the safe ship control process containing: state variables and control, collision risk definition and the form of a collision risk matrix. Multicriteria optimization of the matrix game was introduced, leading to non-cooperative and cooperative game control algorithms and non-game control. Simulation safe trajectories of own ship for various types of control were compared to the example of the real situation at sea.

3

The Safe Control Sensitivity Functions in Matrix Game of Ships

Lisowski J.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2018

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Vol. 12, no. 3

527--532

EN

The paper describes the use of matrix game theory for the synthesis of safe control of a ship in collision situations. An analysis of the sensitivity of the ship control algorithm to the inaccuracy of process state information and changes in its parameters was presented. Sensitivity characteristics were compared on the example of the navigational situation in the Kattegat Strait for good and restricted visibility at sea.

4

Comparison of dynamic games in application to safe ship control

Lisowski J.

Polish Maritime Research

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2014

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nr 3

3--12

EN

The paper introduces methods of dynamic games for automation of ship control in the collision situation, the game control processes in marine navigation and the fundamental mathematical model of the game ship control. First, state equations, control and state constraints and then control goal function in the form of payments : the integral payment and the final one, have been defined. Multi-stage positional , and multi-step matrix, non-cooperative and cooperative, game and optimum control algorithms for a collision situation, have been presented. The considerations have been illustrated with an exemplary computer simulation of algorithms to determine a safe own ship’s trajectory in the process of passing the ships encountered in Kattegat Strait.

5

Sensitivity of computer support game algorithms of safe ship control

Lisowski J.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 2

439--446

EN

The paper investigates the sensitivity of safe ship control to inaccurate data from the ARPA anti-collision radar system and to changes in the process control parameters. The system structure of safe ship control in collision situations and computer support programmes exploring information from the ARPA anti-collision radar are presented. Sensitivity characteristics of the multistage positional non-cooperative and cooperative game and kinematics optimization control algorithms are determined through examples of navigational situations with restricted visibility at sea.