TOPS is a general-purpose pseudospectral optimal control software developed by the author as part of their research in the Aero-Astro Computational and Experimental (ACE) Lab.
Special attention is given to the Legendre-Gauss-Radau (LGR) method, which is the primary transcription employed by the MATLAB-based Tiger Optimization Software (TOPS). Several types of pseudospectral methods are presented, including the Legendre-Gauss and Chebyshev-Gauss methods.
The theoretical groundwork of pseudospectral methods is laid, leading to a pseudospec-tral formulation and software for solving general optimal control problems. The focus of this study then shifts to pseudospectral direct methods, which belong to the class of collocation methods. The indirect necessary conditions and Pontryagin's Minimum Principle are reviewed, and the approaches taken by direct methods are presented. This study provides a basic overview of the direct and indirect methods. Indirect methods seek to satisfy the first-order necessary conditions of optimality, while direct methods discretize the problem and transcribe it into a large-scale nonlinear programming (NLP) problem. Practical trajectory optimization techniques are built on the indirect and direct methods for solving optimal control problems. The fields of trajectory optimization and optimal control are closely connected.
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