On-Line Optimization Using Dual Decomposition and a Quasilinear Subsystem Expansion

Abstract

The problem of on-line optimal control of large scale interconnected nonlinear dynamic systems is considered using duality. A well-known goal coordination algorithm is used involving two levels of computation: at level 1 a decomposed Lagrangian function is minimized with respect to its subsystem states and controls for a given multiplier value obtained by maximizing the dual with respect to the coordinating constraints at level 2. The level 1 computation is carried out for nonlinear problems using a quasilinear expansion from which the resulting two point boundary value problems are solved using a procedure due to Pereyra. The level 2 computation is carried out using conjugate gradients. A numerical example is given and some potential application areas in process and factory automation are mentioned.