A decomposition technique for an optimal control problem with "PQDZ" cost and bounded controls

In this note we present a solution method for a discrete-time linear optimal control problem where the controls are bounded and both the states and controls have asymmetric costs with dead zones containing the nominal values. This model generalizes the well-known optimal control model for a linear system with symmetric (quadratic) objective functional. We transform the problem into an equivalent large quadratic programming problem with equality and inequality, constraints and decompose it into simpler subproblems, each with very easily computed optimal solutions. Using a two-level approach suggested by Lasdon and Schoeffler [11] the optimal solution to the overall problem is obtained.