Paper Info
Title
Control for a Class of Second-Order Systems via a State-Dependent Riccati Equation Approach.
Abstract
This study investigates the state-dependent Riccati equation (SDRE) controller for a class of second-order nonlinear systems. By fully exploiting the design degree of freedom (DOF) arising from the nonunique state-dependent coefficient (SDC) matrices, we explicitly calculate the ranges of control input via the SDRE scheme. Moreover, when a permissible control input is determined, we also explicitly parameterize the SDC matrices that result in the designated control value, in terms of system states and parameters, so the engineer can easily implement the scheme. Notably, this is the first analytical result that explores the range of control input using the design DOF of SDC matrices. In addition, by applying the analytical results, it is shown that the second order systems are always globally stabilizable, without any supplementary assumptions on weighting matrices (as extended from existing SDRE global results), and the corresponding stabilizing SDC matrices are also explicitly presented. Finally, illustrative examples clearly demonstrate the benefits of the analytical results.
Year
DOI
Venue
2018
10.1137/16M1073820
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
nonlinear control system,state-dependent Riccati equation,state-dependent coefficient matrix,globally asymptotic stability
Applied mathematics,Degrees of freedom (statistics),State dependent,Weighting,Control theory,Nonlinear system,Mathematical analysis,Matrix (mathematics),Riccati equation,Mathematics
Journal
Volume
Issue
ISSN
56
1
0363-0129
Citations 
PageRank 
References 
1
0.37
9
Authors
3
Name
Order
Citations
PageRank
Li-Gang Lin110.71
Yew-Wen Liang218715.62
Li-Jen Cheng310.37