Geometric characterization on the solvability of regulator equations

The solvability of the regulator equation for a general nonlinear system is discussed in this paper by using geometric method. The `feedback' part of the regulator equation, that is, the feasible controllers for the regulator equation, is studied thoroughly. The concepts of minimal output zeroing control invariant submanifold and left invertibility are introduced to find all the possible controllers for the regulator equation under the condition of left invertibility. Useful results, such as a necessary condition for the output regulation problem and some properties of friend sets of controlled invariant manifolds, are also obtained. 2007 Elsevier Ltd. All rights reserved.

• Type: Journal
• Year: 2008
• Where: AUTOMATICA
• Authors: Xiaohua Xia, Jiangfeng Zhang
• Keywords: AUTOMATICA 2007, AUTOMATICA 2008, Control Invariant Submanifold, Feasible Controllers, Regulator Equation