Analysis & Synthesis of Distributed Control Systems with Sparse Interconnection Topologies

This dissertation is about control, identification, and analysis of systems with sparse interconnection topologies. We address two main research objectives relating to sparsity in control systems and networks. The first problem is optimal sparse controller synthesis, and the second one is the identification of sparse network. The first part of this dissertation starts with the chapter focusing on developing theoretical frameworks for the synthesis of optimal sparse output feedback controllers under pre-specified structural constraints. This is achieved by establishing a balance between the stability of the controller and the systems quadratic performance. Our approach is mainly based on converting the problem into rank constrained optimizations.We then propose a new approach in the syntheses of sparse controllers by em- ploying the concept of Hp approximations. Considering the trade-off between the controller sparsity and the performance deterioration due to the sparsification pro- cess, we propose solving methodologies in order to obtain robust sparse controllers when the system is subject to parametric uncertainties.Next, we pivot our attention to a less-studied notion of sparsity, namely row sparsity, in our optimal controller design. Combining the concepts from the majorization theory and our proposed rank constrained formulation, we propose an exact reformulation of the optimal state feedback controllers with strict row sparsity constraint, which can be sub-optimally solved by our proposed iterative optimization techniques. The second part of this dissertation focuses on developing a theoretical framework and algorithms to derive linear ordinary differential equation models of gene regulatory networks using literature curated data and micro-array data. We propose several algorithms to derive stable sparse network matrices. A thorough comparison of our algorithms with the existing methods are also presented by applying them to both synthetic and experimental data-sets.