Synthesis of Optimal Control for Cooperative Collision Avoidance for Aircraft (Ships) with Unequal Turn Capabilities

T. Tarnopolskaya () and N. Fulton ()
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T. Tarnopolskaya: CSIRO Mathematical & Information Sciences
N. Fulton: CSIRO Mathematical & Information Sciences

Journal of Optimization Theory and Applications, 2010, vol. 144, issue 2, No 9, 367-390

Abstract: Abstract This paper presents a synthesis of an optimal control solution for cooperative collision avoidance strategies for aircraft (ships) with unequal turn capabilities in a close proximity coplanar encounter. The analytic expressions for the extremals are presented and their properties are analyzed. Simple algorithms for the synthesis of optimal control are developed. The structure of the synthesis is analyzed and its behavior with a change in the nondimensional turn rate ratio is studied. It is shown that Merz’s solution for identical aircraft (see Merz in Proc. Joint Automatic Control Conf., Paper 15-3, pp. 449–454, 1973; Navigation 20(2):144–152, 1973; Tarnopolskaya and Fulton in J. Optim. Theory Appl. 140(2):355–375, 2009) is a degenerate case of this more general solution. The results of this paper are useful for benchmarking and validating automated proximity management and collision avoidance systems.

Keywords: Collision avoidance; Cooperative maneuvers; Optimal control; Mayer problem; Pontryagin maximum principle; Unequal turn rates; Close proximity (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10957-009-9597-1

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