TY - JOUR
T1 - Augmented lagrangian approach to design of structured optimal state feedback gains
AU - Lin, Fu
AU - Fardad, Makan
AU - Jovanovic, Mihailo R.
PY - 2011/12
Y1 - 2011/12
N2 - We consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers. These constraints are in the form of sparsity requirements for the feedback matrix, implying that each controller has access to information from only a limited number of subsystems. The minimizer of this constrained optimal control problem is sought using the augmented Lagrangian method. Notably, this approach does not require a stabilizing structured gain to initialize the optimization algorithm. Motivated by the structure of the necessary conditions for optimality of the augmented Lagrangian, we develop an alternating descent method to determine the structured optimal gain. We also utilize the sensitivity interpretation of the Lagrange multiplier to identify favorable communication architectures for structured optimal design. Examples are provided to illustrate the effectiveness of the developed method.
AB - We consider the design of optimal state feedback gains subject to structural constraints on the distributed controllers. These constraints are in the form of sparsity requirements for the feedback matrix, implying that each controller has access to information from only a limited number of subsystems. The minimizer of this constrained optimal control problem is sought using the augmented Lagrangian method. Notably, this approach does not require a stabilizing structured gain to initialize the optimization algorithm. Motivated by the structure of the necessary conditions for optimality of the augmented Lagrangian, we develop an alternating descent method to determine the structured optimal gain. We also utilize the sensitivity interpretation of the Lagrange multiplier to identify favorable communication architectures for structured optimal design. Examples are provided to illustrate the effectiveness of the developed method.
KW - Augmented Lagrangian
KW - Optimal distributed design
KW - Sparse matrices
KW - Structured feedback gains
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U2 - 10.1109/TAC.2011.2160022
DO - 10.1109/TAC.2011.2160022
M3 - Article
AN - SCOPUS:80053146759
SN - 0018-9286
VL - 56
SP - 2923
EP - 2929
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 12
M1 - 5893917
ER -