Second order collocation

Cita com:
hdl:2117/366522
Document typeResearch report
Defense date2021
Rights accessOpen Access
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is licensed under a Creative Commons license
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Attribution-NonCommercial-NoDerivs 3.0 Spain
Abstract
Collocation methods for optimal control commonly assume that the system dynamics is expressed as a first order ODE of the form dx/dt = f(x, u, t), where x is the state and u the control vector. However, in many cases, the dynamics involve the second order derivatives of the coordinates: d^2q/t^2 = g(q, dq/dt, u, t), so that, to preserve the first order form, the usual procedure is to introduce one velocity variable for each coordinate and define the state as x = [q,v]T, where q and v are treated as independent variables. As a consequence, the resulting trajectories do not fulfill the mandatory relationship v = dq/dt except at the collocation points, where it is explicitly imposed.
We propose a formulation for Trapezoidal and Hermite-Simpson collocation methods adapted to deal directly with second order dynamics without the need to introduce v as independent from q, and granting the consistency of the trajectories for q and v.
Description
Technical report
CitationCelaya, E. Second order collocation. 2021.
Is part ofIRI-TR-21-02
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