Utilizing the Algorithmic Differentiation Package ADiGator for Solving Optimal Control Problems Using Direct Collocation

Abstract

ADiGator is a newly developed free MATLAB algorithmic differentiation package. In this paper, we study the use of the ADiGator algorithmic differentiation tool in order to supply the first and second derivatives of the NLP arising from direct collocation of optimal control problems. While the methods of this paper may be applied to multiple direct collocation schemes, we focus on an hp-adaptive Legendre-Gauss-Radau scheme which has been coded in the MATLAB optimal control software GPOPS-II. The methods required to indirectly compute the first and second derivatives of the NLP using ADiGator are presented and three test cases are given. In the test cases, the method of supplying derivatives via ADiGator is shown to be highly efficient when compared to the classical method of finite-differencing.

Battery Aging-Aware Online Optimal Control: An Energy Management System for Hybrid Electric Vehicles Supported by a Bio-Inspired Velocity Prediction

“…The exact Hessian of the Lagrangian can be optionally supplied, otherwise Ipopt will numerically approximate it. The required analytical derivatives are computed using ADiGator [86], an alghorithmic differentiator, which can run on Matlab. We solve both the offline and the online optimal control problems on Matlab 2019b running on a MacBook Pro equipped with a 2.7 GHz Intel i7 processor with 16 GB of memory.…”

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“…13: Equality between Jacobians of two-point boundary condition functions in normalized and unnormalized coordinates.…”

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