Fast Implementation Algorithm for Multivariable Algebraic Loops

Abstract

An important class of nonlinear control systems can be represented as the feedback interconnection of two parts: a linear time-invariant system and a block of decentralized nonlinearities. When the linear time-invariant part has a nontrivial feedthrough term, control computation involves the online implementation of a multivariable algebraic loop which must be resolved at each sampling instant. This work considers a fast algorithm based on the Projected Gauss-Seidel algorithm for the implementation of algebraic loops that arise in constrained control. The Projected Gauss-Seidel algorithm shows promise for real-time and embedded control applications where a fast but approximate solution is of the essence.