Resilient Sparse Controller Design with Guaranteed Disturbance Attenuation
For control system designers, it provides the first framework offering performance guarantees for sparse feedback gain design, addressing the need for controllers that are both sparse and robust to perturbations.
The paper designs resilient sparse state-feedback controllers for LTI systems with guaranteed H∞ performance, using non-fragile control theory and sparsification techniques (greedy and re-weighted ℓ1 norm), highlighting tradeoffs between sparsity, performance, and fragility.
We design resilient sparse state-feedback controllers for a linear time-invariant (LTI) control system while attaining a pre-specified guarantee on ${\mathcal{H}}_\infty$ performance measure. We leverage a technique from non-fragile control theory to identify a region of resilient state-feedback controllers. Afterward, we explore the region to identify a sparse controller. To this end, we use two different techniques: the greedy method of sparsification, as well as the re-weighted $\ell_1$ norm minimization. Our approach highlights a tradeoff between the sparsity of the feedback gain, performance measure, and fragility of the design. To best of our knowledge, this work is the first framework providing performance guarantees for sparse feedback gain design.