direct transcription approach to dynamic optimization problems in engineering

The direct transcription method that employs global collocation at legendre-gauss-radau points is addressed and applied to infinite-dimensional dynamic optimization problems in engineering. the formulation of these latter is considered referring to a bolza-type performance index. a reduced unconstrained form of it is particularly studied in the pseudospectral domain and the continuous-to-discrete conversion is thoroughly discussed. an equivalent finite-dimension nonlinear programming problem is therefore obtained and hints on its numerical implementation are given. eventually, a few benchmark historical problems in engineering are revisited, stated, numerically solved and compared to literature.