A multi-level algorithm for the finite horizon LQ optimal control problem with assigned final state: additive and multiplicative procedures

A multi-level computational framework which overcomes the dimensionality constraint intrinsic in the solution by pseudoinversion of the discrete-time finite horizon LQ optimal control problem with assigned final state is presented. Depending on design priorities, the algorithm can be based on either of two different nesting procedures: an additive procedure or a multiplicative procedure. In both cases, the solution of the infinite horizon problem can be retrieved if some rather extensive conditions are met. The algorithmic framework holds independently of the control weighting matrix being regular, singular, or zero. Moreover, the devised algorithm differs from those available in the literature in that it handles non-left-invertible systems with no further complications.