2018 conference paper
Sparsity-Constrained Mixed $H_{2}/H_{\infty}$ Control
2018 Annual American Control Conference (ACC), 6253β6258,
We propose an algorithm for designing sparsity-constrained controllers for linear time-invariant systems with model uncertainties using a mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</sub> objective. We first improve a previously proposed descent algorithm for mixed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</sub> control using a modified Zoutendijk's method. Thereafter, we impose a sparsity constraint on this design by combining it with a greedy gradient support pursuit (GraSP) method. The proposed algorithm guarantees a predetermined level of sparsity while maintaining acceptable H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> performance as well as H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</sub> robustness to uncertainties in the open-loop model. The effectiveness of the proposed method is illustrated through simulations.