Pseudospectral Optimal Control and Its Convergence Theorems

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Summary. During the last decade, pseudospectral (PS) optimal control methods have emerged as demonstrable efficient methods for computational nonlinear optimal control. Some fundamental problems on the feasibility and convergence of the Legendre PS method are addressed. In the first part of this paper, we summarize the main results published separately in a series of papers on these topics. Then, a new result on the feasibility and convergence is proved. Different from existing results in the literature, in this new theorem neither the invertibility of necessary conditions nor the existence of limit points is assumed.