PS optimal control theory has been used in ground and flight systems[1] in military and industrial applications.
[8][9][10] In a pseudospectral method, the continuous functions are approximated at a set of carefully selected quadrature nodes.
For example, with just N nodes, a Legendre-Gauss quadrature integration achieves zero error for any polynomial integrand of degree less than or equal to
In the PS discretization of the ODE involved in optimal control problems, a simple but highly accurate differentiation matrix is used for the derivatives.
Because a PS method enforces the system at the selected nodes, the state-control constraints can be discretized straightforwardly.
All these mathematical advantages make pseudospectral methods a straightforward discretization tool for continuous optimal control problems.