Partial‐state stabilization and optimal feedback control. (21st April 2015)

• Record Type: Journal Article
• Authors: L'Afflitto, Andrea; Haddad, Wassim M.; Bakolas, Efstathios
• Is Part Of: International journal of robust and nonlinear control. Volume 26:Number 5(2016)
• Page Start: 1026
• Page End: 1050
• Publication Date: 2015-04-21
• Subjects: partial stability -- partial‐state stabilization -- optimal control -- Hamilton–Jacobi–Bellman theory -- time‐varying systems -- polynomial and multilinear performance criteria; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.3349
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: In this paper, we develop a unified framework to address the problem of optimal nonlinear analysis and feedback control for partial stability and partial‐state stabilization. Partial asymptotic stability of the closed‐loop nonlinear system is guaranteed by means of a Lyapunov function that is positive definite and decrescent with respect to part of the system state, which can clearly be seen to be the solution to the steady‐state form of the Hamilton–Jacobi–Bellman equation and hence guaranteeing both partial stability and optimality. The overall framework provides the foundation for extending optimal linear‐quadratic controller synthesis to nonlinear nonquadratic optimal partial‐state stabilization. Connections to optimal linear and nonlinear regulation for linear and nonlinear time‐varying systems with quadratic and nonlinear nonquadratic cost functionals are also provided. Finally, we also develop optimal feedback controllers for affine nonlinear systems using an inverse optimality framework tailored to the partial‐state stabilization problem and use this result to address polynomial and multilinear forms in the performance criterion. Copyright © 2015 John Wiley & Sons, Ltd.