Abstract
This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time-invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP-hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex-concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world estimated state feedback control design problem and the necessity of the augmentation for numerical stability.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1246-1260 |
| Number of pages | 15 |
| Journal | International Journal of Robust and Nonlinear Control |
| Volume | 28 |
| Issue number | 4 |
| DOIs | |
| State | Published - Mar 10 2018 |
Fingerprint
Keywords
- automotive control
- bilinear matrix inequality
- convex optimization
- nonlinear system
- output feedback
- robust control
Cite this
Sequential LMI approach for the design of a BMI-based robust observer state feedback controller with nonlinear uncertainties. / Wang, Yan; Rajamani, Rajesh; Zemouche, Ali.
In: International Journal of Robust and Nonlinear Control, Vol. 28, No. 4, 10.03.2018, p. 1246-1260.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Sequential LMI approach for the design of a BMI-based robust observer state feedback controller with nonlinear uncertainties
AU - Wang, Yan
AU - Rajamani, Rajesh
AU - Zemouche, Ali
PY - 2018/3/10
Y1 - 2018/3/10
N2 - This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time-invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP-hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex-concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world estimated state feedback control design problem and the necessity of the augmentation for numerical stability.
AB - This paper aims at developing a robust observer–based estimated state feedback control design method for an uncertain dynamical system that can be represented as a linear time-invariant system connected with an integral quadratic constraint–type nonlinear uncertainty. Traditionally, in existing design methodologies, a convex semidefinite constraint is obtained at the cost of conservatism and unrealistic assumptions. This paper avoids such assumptions and formulates, the design of the robust observer state feedback controller as the feasibility problem of a bilinear matrix inequality (BMI) constraint. Unfortunately, the search for a feasible solution of a BMI constraint is an NP-hard problem in general. The applicability of a linearization method, such as the variable change method and the congruence transformation, depends on the specific structure of the problem at hand and cannot be generalized. This paper transforms the feasibility analysis of the BMI constraint into an eigenvalue problem and applies the convex-concave–based sequential linear matrix inequality optimization method to search for a feasible solution. Furthermore, an augmentation of the sequential linear matrix inequality algorithm to improve its numerical stability is presented. In the application part, a vehicle lateral control problem is presented to demonstrate the applicability of the proposed algorithm to a real-world estimated state feedback control design problem and the necessity of the augmentation for numerical stability.
KW - automotive control
KW - bilinear matrix inequality
KW - convex optimization
KW - nonlinear system
KW - output feedback
KW - robust control
UR - http://www.scopus.com/inward/record.url?scp=85030154530&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85030154530&partnerID=8YFLogxK
U2 - 10.1002/rnc.3948
DO - 10.1002/rnc.3948
M3 - Article
AN - SCOPUS:85030154530
VL - 28
SP - 1246
EP - 1260
JO - International Journal of Robust and Nonlinear Control
JF - International Journal of Robust and Nonlinear Control
SN - 1049-8923
IS - 4
ER -