Sparsity-Promoting Optimal Controller Design

Considering the class of linear time-invariant (LTI) systems and utilizing the various mathematical tools, for diverse scenarios, we design sparsity-promoting feedback controllers while attaining a reasonable performance loss. Diverse scenarios can be classified as follows: (i) feedback controller sparsification subject to attain a similar frequency behavior for the case without/with parametric uncertainty (Chapters 2 and 4) (ii) improvement on sparsity in time domain in addition to sparsity promotion in feedback controller (Chapters 3 and 8) (iii) sparse feedback controller design for uncertain time-delay systems (Chapter 5) (iv) row-column (r, c)-sparse feedback controller design (Chapter 6) (v) feedback controller sparsification for large-scale systems (Chapters 7 and 9). Sparsity promotion in feedback controller is done via several techniques including l1-relaxation, a notion of non-fragility, and quasi-norms. Sparsity improvement in time domain is obtained via periodic time-triggered and self-triggered control. In Chapters 2, 3, 4, 5, and 6, the non-convexity arisen by Lyapunov stability condition is handled utilizing the bi-linear rank penalty technique. In Chapters 7 and 9, stability is provided by means of continuity of maximum real part of eigenvalue of the closed-loop system. In Chapter 8, stability is imposed by a performance-based condition which consists of a quadratic cost-to-go and a Lyapunov function.