Multilevel dynamic programming for general multiple linear-quadratic control in discrete-time systems

AbstractThis paper extends the reach of dynamic programming to general multiple linear-quadratic control problems in discrete-time systems, where the overall objective is a nonlinear function of multiple quadratic performance indices. A multilevel dynamic programming solution procedure is proposed to obtain an analytical linear control law for this nonseparable control problem. At the lower level the formulated auxiliary Lagrangian problem is of a parametric linear-quadratic structure and is solved by dynamic programming. The weighting vector in the auxiliary Lagrangian problem is adjusted by the upper level iteratively. This two-level process repeats until an optimal condition is satisfied