Decentralized linear feedback optimal control of large-scale nonlinear systems

Decentralized optimal control for large-scale nonlinear systems with respect to local performance criteria is considered. A decoupled linear Two-Point Boundary Value (TPBV) problem sequence is constructed to approximate the nonlinear coupling large-scale TPBV problem, which is the necessary condition of the nonlinear optimal control problem. We prove that the constructed linear TPBV problem sequence uniformly converges to the nonlinear TPBV problem. By iteratively solving this linear TPBV problem sequence, a decentralized linear feedback optimal control law is obtained. An algorithm is presented to design some qualified approximate optimal control law by using a finite iteration result. An illustrative example shows the validity of the algorithm.