Regularization for Optimal Sparse Control Structures: A Primal-Dual Framework

In this paper, the optimal trade-off between control structures and achievable closed-loop performance is addressed. Incorporation of sparsity promoting regularization terms to the primary objective function is a well-suited approach in feature selection and compressed sensing. By the evolving role of distributed and large-scale applications, modern optimal control problems have been equipped with regularization tools as well. However, the system dynamics and convex/nonconvex constraints in optimal control framework limits the effectiveness and applicability of regularization, enforce iterative or non-convex heuristics, and pose extensive exploration. In fact, available regularized feedback control problems do not enjoy the solid theoretical footing established in the feature selection framework. This paper presents a new method to efficiently construct optimal sparse control structures. The solution of the proposed approach is guaranteed to be sparse with a prescribed number of zero elements in the control structure. In contrast to the previously developed methods, exact values of regularization parameters for the detection of active feedback links can be determined a-priori, and the sparse control structures can be derived. The effectiveness of the proposed approach is evaluated by synthetic and real-life case studies.