Augmented Lagrangian Approach to Design of Structured Optimal State Feedback Gains

• Published in: IEEE transactions on automatic control Vol. 56; no. 12; pp. 2923 - 2929
• Main Authors: Fu Lin, Fardad, M., Jovanovic, M. R.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.12.2011; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• 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; State feedback; Lagrangian; Feedback regulation; Information access; optimal distributed design; structured feedback gains; Constrained optimization; Control constraint; Lagrange multiplier; Optimal control; Descent method; Augmented Lagrangian; Optimality condition; Optimality criterion; Lagrangian method; sparse matrices
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2160022

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.