Three Problems in the Control and Identification of Structured Linear Systems

We study three problems in the control and identification of structured linear systems. Thestructure is first manifested as sparsity pattern constraints on the system or control matrices, which complicate the feasible set of the optimal decentralized control problem. We find that the feasible set can be not only disconnected but also have a large number of connected components, which greatly limits the application of local search optimization algorithms. The issue of connectivity is addressed in the second problem, where we design homotopy paths that reduce the number of local minima of the optimal decentralized control problem. Finally, we study an identification scheme based on L-1 optimization, where the system states are subject to attacks which propagate over time. The structural constraint, which appears as inequalities involving the states and control inputs, will lead to sufficient conditions for the recovery of system matrices