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A general-purpose C++ software program called $\mathbb{CGPOPS}$ is describedfor solving multiple-phase optimal control problems using adaptive Gaussianquadrature collocation. The software employs a Legendre-Gauss-Radau directorthogonal collocation method to transcribe the continuous-time optimal controlproblem into a large sparse nonlinear programming problem. A class of $hp$ meshrefinement methods are implemented which determine the number of mesh intervalsand the degree of the approximating polynomial within each mesh interval toachieve a specified accuracy tolerance. The software is interfaced with theopen source Newton NLP solver IPOPT. All derivatives required by the NLP solverare computed using either central finite differencing, bicomplex-stepderivative approximation, hyper-dual derivative approximation, or automaticdifferentiation. The key components of the software are described in detail andthe utility of the software is demonstrated on five optimal control problems ofvarying complexity. The software described in this article provides acomputationally efficient and accurate approach for solving a wide variety ofcomplex constrained optimal control problems.

CGPOPS: A C++ Software for Solving Multiple-Phase Optimal Control  Problems Using Adaptive Gaussian Quadrature Collocation and Sparse Nonlinear  Programming