Viable immersion and invariance control for a class of nonlinear systems and its application to aero-engines

This paper presents a novel approach to stabilize a class of nonlinear systems with state constraints. The motivation behind this study is the need to develop a stabilizing state feedback controller that does not require the knowledge of Lyapunov function and can regulate the states to the equilibri...

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Bibliographic Details
Published inJournal of the Franklin Institute Vol. 356; no. 1; pp. 42 - 57
Main Authors Lou, Zhi-E, Zhao, Jun
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.01.2019
Elsevier Science Ltd
Subjects
Aerospace engines
Computer simulation
Constraint modelling
Control systems
Controllers
Feedback control
Feedback control systems
Invariance
Liapunov functions
Nonlinear systems
Simulation
State feedback
Submerging
Systems stability
Theory of constraints
Viability
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Summary:This paper presents a novel approach to stabilize a class of nonlinear systems with state constraints. The motivation behind this study is the need to develop a stabilizing state feedback controller that does not require the knowledge of Lyapunov function and can regulate the states to the equilibrium while meeting the constraints. By using an integration of two relatively new tools: immersion and invariance (I&I) theory and viability theory, a sufficient condition for stability and stabilizability of a general nonlinear affine system with state constraints is derived; Then, the related results are exploited to stabilize a class of nonlinear system in feedback form and with state constraints represented by inequalities and the viable I&I stabilizing state feedback controller is obtained constructively. Further, an application to a nonlinear aero-engine model with the temperature constraint is given to illustrate the applicability and the effectiveness of the proposed method. Finally, a comparative simulation is presented, highlighting the advantages of the viable I&I controller.
ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2018.10.002