Cgpops

Abstract

A general-purpose C++ software program called CGP OP S is described for solving multiple-phase optimal control problems using adaptive direct orthogonal collocation methods. The software employs a Legendre-Gauss-Radau direct orthogonal collocation method to transcribe the continuous optimal control problem into a large sparse nonlinear programming problem (NLP). A class of hp mesh refinement methods are implemented that determine the number of mesh intervals and the degree of the approximating polynomial within each mesh interval to achieve a specified accuracy tolerance. The software is interfaced with the open source Newton NLP solver IPOPT. All derivatives required by the NLP solver are computed via central finite differencing, bicomplex-step derivative approximations, hyper-dual derivative approximations, or automatic differentiation. The key components of the software are described in detail, and the utility of the software is demonstrated on five optimal control problems of varying complexity. The software described in this article provides researchers a transitional platform to solve a wide variety of complex constrained optimal control problems.

Trajectory Optimization for High-Speed and Long-Range Interceptor Based on Improved Adaptive hp Pseudospectral Method

“…hp method adaptively adopts h method or p method in mesh refinement through a preset criterion, so that the advantages of both methods can be fully brought into play [20][21][22]. In recent years, many scholars [23][24][25][26][27][28][29][30] have further enriched and developed adaptive mesh refinement method along the research ideas of Ref. [20][21][22].…”

“…In addition, Ref. [26] introduces a C++ software program for solving the multiplephase optimal control problems, which is called CGPOPS. Ref.…”

“…(2) When pseudospectral method is used to optimize interceptor trajectory, most studies [23][24][25][26][27][28][29][30] do not pay attention to the sudden changes of optimization control in the process of mesh refinement, which will cause a large number of collocation points to be configured near the control sudden change points, thus increasing the number of mesh iterations and affecting optimization efficiency…”

“…(3) In the process of trajectory optimization, the existing researches [23][24][25][26][27][28][29][30] basically insert new mesh points at equal intervals during the piecewise iteration of the mesh, which will cause the waste of collocation points resources and reduce the solving efficiency…”

Application of Generalized (Hyper-) Dual Numbers in Equation of State Modeling

“…However, aside from the availability of complex numbers in many programming languages, there is no advantage whatsoever to use complex step differentiation above dual numbers: complex step differentiation can be seen as an improved numerical derivative that alleviates the problems at small step sizes, whereas dual number differentiation always results in exact derivatives within machine precision. Automatic differentiation using (hyper-) dual numbers has been used in various fields of engineering and science such as solving optimal control problems (Agamawi and Rao, 2020) or formulating equations of motion for rigid-and multi-body systems (Cohen and Shoham, 2015;Cohen and Shoham, 2017). Yet, the concept of automatic differentiation with dual numbers is rarely used in chemical engineering and thermodynamics in particular, with the exception of the work of Diewald et al (2018) and Rehner et al (2019).…”