Augmented Lagrangian Approach to Design of Structured Optimal State Feedback Gains

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 subsystem...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2011-12, Vol.56 (12), p.2923-2929
Main Authors: Fu Lin, Fardad, M., Jovanovic, M. R.
Format: Article
Language:English
Subjects:
Access control
Algorithms
Applied sciences
Augmented Lagrangian
Computer science
control theory
systems
Control systems
Control theory. Systems
Controllers
Distributed control
Exact sciences and technology
Gain
Interconnected systems
Lagrange multiplier
Lagrange multipliers
Lagrangian functions
Optimal control
optimal distributed design
Optimization
Sparse matrices
State feedback
structured feedback gains
Studies
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2160022