A Legendre technique for solving time-varying linear quadratic optimal control problems (Q1338567)

The authors consider the time-varying linear-quadratic optimal control problem without constraints. They approximate the state, the control and the state and control matrices by shifted Legendre polynomials obtaining a finite-dimensional quadratic program with equality constraints. There are no assumptions concerning the continuity properties in time of the matrices defining the problem. There is no error analysis and no comparison to other methods. The two one-dimensional examples presented are not convincing.