A Computational Method for Optimal L-Q Regulation with Simultaneous Disturbance Decoupling

The disturbance decoupling problem using state feedback (DDP), with simultaneous infinite-time horizon optimal L-Q regulation (LQR), for continuous time-invariant linear systems, is formulated as a parameter optimization problem in L-Q regulators subjected to control constraints imposed by the solution of DDP. For computational solution of DDP it is proposed an efficient numerical procedure, which gives the solution directly in the form of constraints on some parameters of the control matrix. For computational solution of the optimization problem, it is proposed a specialized hybrid descent method, suitable for problems with severe control structural constraints, composed by a sequence of steps of the following methods: Modified Newton, Newton´s and Quasi-Newton. The results are illustrated by a numerical example.