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An algorithm is described to solve multiple-phase optimal control problems using a recently developed numerical method called the Gauss pseudospectral method . The algorithm is well suited for use in modern vectorized programming languages such as FORTRAN 95 and MATLAB. The algorithm discretizes the cost functional and the differential-algebraic equations in each phase of the optimal control problem. The phases are then connected using linkage conditions on the state and time. A large-scale nonlinear programming problem (NLP) arises from the discretization and the significant features of the NLP are described in detail. A particular reusable MATLAB implementation of the algorithm, called GPOPS , is applied to three classical optimal control problems to demonstrate its utility. The algorithm described in this article will provide researchers and engineers a useful software tool and a reference when it is desired to implement the Gauss pseudospectral method in other programming languages.
Rao et al. (Thu,) studied this question.
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