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A numerical algorithm for the solution of DAIs — Differential systems subject to Algebraic Inequality constraints

Abstract:

This paper describes a numerical algorithm for the solution of a Differential system subject to Algebraic Inequality constraints (DAI). The algorithm consists of a dynamic integration of the equations of motion coupled with invocation of a control mechanism. After describing various applications and solution approaches to DAIs, we concentrate on one approach based on the principle of Least Constraint. This is achieved by minimization of a barrier function defined using buffer zones near the constraint boundaries. Determination of the buffer zones is done dynamically, corresponding to a local planning strategy. The control is chosen in a way resembling interior-point methods m optimization. This ensures that the solution trajectory is ‘centred) in some sense within the feasible region.

Author: Raymond J. Spiteri

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