Maximin Approach to the Ship Collision Avoidance Problem via Multiple-Subarc Sequential Gradient-Restoration Algorithm View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2005-01

AUTHORS

A. Miele, T. Wang

ABSTRACT

The ideal strategy for ship collision avoidance under emergency conditions is to maximize wrt the controls the timewise minimum distance between a host ship and an intruder ship. This is a maximin problem or Chebyshev problem of optimal control in which the performance index being maximinimized is the distance between the two ships. Based on the multiple-subarc sequential gradient-restoration algorithm, a new method for solving the maximin problem is developed.Key to the new method is the observation that, at the maximin point, the time derivative of the performance index must vanish. With the zero derivative condition being treated as an inner boundary condition, the maximin problem can be converted into a Bolza problem in which the performance index, evaluated at the inner boundary, is being maximized wrt the controls. In turn, the Bolza problem with an added inner boundary condition can be solved via the multiple-subarc sequential gradient-restoration algorithm (SGRA).The new method is applied to two cases of the collision avoidance problem: collision avoidance between two ships moving along the same rectilinear course and collision avoidance between two ships moving along orthogonal courses. For both cases, we are basically in the presence of a two-subarc problem, the first subarc corresponding to the avoidance phase of the maneuver and the second subarc corresponding to the recovery phase. For stiff systems, the robustness of the multiple-subarc SGRA can be enhanced via increase in the number of subarcs. For the ship collision avoidance problem, a modest increase in the number of subarcs from two to three (one subarc in the avoidance phase, two subarcs in the recovery phase) helps containing error propagation and achieving better convergence results. More... »

PAGES

29-53

References to SciGraph publications

  • 1997-04. Collision Avoidance by a Ship with a Moving Obstacle: Computation of Feasible Command Strategies in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1988-01. Time optimal control computation with application to ship steering in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2003-01. Multiple-Subarc Gradient-Restoration Algorithm, Part 2: Application to a Multistage Launch Vehicle Design in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1999-12. Optimal Control of a Ship for Collision Avoidance Maneuvers in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1998-05. Optimal Control of a Ship for a Course-Changing Maneuver in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1999-11. Optimal Control of a Ship for Course Change and Sidestep Maneuvers in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2003-01. Multiple-Subarc Gradient-Restoration Algorithm, Part 1: Algorithm Structure in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 1993-06. On the control and guidance of the motion of an immersed body: Some problems in stochastic control in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10957-004-6464-y

    DOI

    http://dx.doi.org/10.1007/s10957-004-6464-y

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    https://app.dimensions.ai/details/publication/pub.1030995432


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