This aliasing phenomenon in optimal control was first discovered by Ross et al.[2] Rather than use signal processing techniques to anti-alias the solution, Ross et al. proposed that Bellman's principle of optimality can be applied to the converged solution to extract information between the nodes.
Because the Gauss–Lobatto nodes cluster at the boundary points, Ross et al. suggested that if the node density around the initial conditions satisfy the Nyquist–Shannon sampling theorem, then the complete solution can be recovered by solving the optimal control problem in a recursive fashion over piecewise segments known as Bellman segments.
In this version, one can apply the Bellman pseudospectral method at even lower number of nodes even under the knowledge that the solution may not have converged to the optimal one.
[2][3] One of the computational advantages of the Bellman pseudospectral method is that it allows one to escape Gaussian rules in the distribution of node points.
The Bellman pseudospectral method was first applied by Ross et al.[2] to solve the challenging problem of very low thrust trajectory optimization.