Yaser Ghaedsharaf

Optimal state feedback controllers with strict row sparsity constraints

This paper considers the problem of optimal row sparse state feedback controller design for LTI systems, where the controller is assumed to be static with pre-specified structural constraint. Incongruous to the existing literature on the sparsity promoting control synthesis, we do not employ convex relaxation of the sparsity representing terms, such as ℓ0-norm of the controller gain, in our proposed framework. Borrowing the results from the theory of majorization, we develop an exact rank constrained reformulation of the s-sparse vector recovery from a convex set, and, then, utilized it to cast our row sparse control problem into a an optimization problem where all constraints are convex, except a single rank constraint. Furthermore, we propose a necessary and sufficient condition for the feasibility of a stabilizing row s-sparse controller, and exploited it to propose a bi-linear minimization problem, subject to convex constraints, which solve the derived equivalent rank constrained problem to deliver an optimal row sparse state feedback controller. The benefits of approach are demonstrated though several numerical simulations.

Interplay between performance and communication delay in noisy linear consensus networks

This work investigates performance of noisy time-delayed linear consensus networks from a graph topological point of view. Performance of the network is measured by the square of the H2-norm of the system. The focus of this paper is on noisy consensus networks with homogeneous time delays affecting both the agent and all its neighbors. We derive an exact expression for the performance measure of the network in terms of time delay parameter and Laplacian eigenvalues of the underlying graph of the network. It is shown that the performance measure is a convex and Schur-convex function of Laplacian eigenvalues. We characterize the network topology with optimal performance. Furthermore, we quantify a fundamental limit on the best achievable performance based on performance of the optimal topology.

Aggregate fluctuations in time-delay linear consensus networks: A systemic risk perspective

We discuss the notion of systemic risk in noisy consensus systems with delay as a measure of robustness and resilience. We propose a risk measure to characterize systemic events of the dynamic network, based on quantile functions theory. We provide explicit calculations or estimates for our consensus dynamic both in transient and steady-state dynamics. Our analysis highlights the dependence of risk on the spectral properties of the communication graph and the delay of the network. Unlike consensus networks with no delay, the risk measure exhibits a non-monotonic behavior in presence of time-delay. This non-monotonicity is the origin of potential aggregate fluctuation which is an undesirable systemic event of our network.

Performance improvement in time-delay linear consensus networks

We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. The performance is measured by the networks square of ℋ2-norm and it is shown that it is a convex function of Laplacian eigenvalues and the coupling weights of the underlying graph of the network. First, we propose a tight convex, but simple, approximation of the performance measure in order to achieve lower complexity in our design problems by eliminating the need for eigen-decomposition. Next, we present three methods to improve the performance by growing, re-weighting, or sparsifying the underlying graph of the network. It is shown that our proposed algorithms provide near-optimal solutions with lower complexity with respect to existing methods in literature.