Multiplier (economics)

Physics

Norm (philosophy)

Computer science

Matrix norm

Mathematical optimization

Macroeconomics

Political science

Quantum mechanics

Mathematics

Eigenvalues and eigenvectors

Economics

IEEE Transactions on Automatic Control

A globally convergent algorithm for synthesis of sparse optimal state feedback (SOSF) control of linear time-invariant (LTI) systems is proposed. This problem is known to be NP-hard due to its combinatorial nature. A structured H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm controller design problem is intrinsically non-convex, even if a fixed structure is known in advance. The proposed algorithm minimizes the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> norm performance index, and simultaneously regularizes the sparsity of the control structure using the 11 norm. It guarantees that the solution converges to a stationary point of the original problem. The algorithm is implemented using Linear Matrix Inequalities (LMIs) which are efficient, reliable and extendable to other control problems. The performance of the proposed algorithm is illustrated with application to several examples. The r...

Sparsity Promotion in State Feedback Controller Design