Decentralized Implementation of Centralized Controllers for Interconnected Systems

Given a centralized controller associated with a linear time-invariant interconnected system, this paper is concerned with designing a parameterized decentralized controller such that the state and input of the system under the obtained decentralized controller can become arbitrarily close to those of the system under the given centralized controller, by tuning the controller's parameters. To this end, a two-level decentralized controller is designed, where the upper level captures the dynamics of the centralized closed-loop system, and the lower level is an observed-based sub-controller designed based on the new notion of structural initial value observability. The proposed method can decentralize every generic centralized controller, provided the interconnected system satisfies very mild conditions. The efficacy of this work is elucidated by some numerical examples

System-level, Input-output and New Parameterizations of Stabilizing Controllers, and Their Numerical Computation

It is known that the set of internally stabilizing controller $\mathcal{C}_{\text{stab}}$ is non-convex, but it admits convex characterizations using certain closed-loop maps: a classical result is the {Youla parameterization}, and two recent notions are the {system-level parameterization} (SLP) and the {input-output parameterization} (IOP). In this paper, we address the existence of new convex parameterizations and discuss potential tradeoffs of each parametrization in different scenarios. Our main contributions are: 1) We first reveal that only four groups of stable closed-loop transfer matrices are equivalent to internal stability: one of them is used in the SLP, another one is used in the IOP, and the other two are new, leading to two new convex parameterizations of $\mathcal{C}_{\text{stab}}$. 2) We then investigate the properties of these parameterizations after imposing the finite impulse response (FIR) approximation, revealing that the IOP has the best ability of approximating $\mathcal{C}_{\text{stab}}$ given FIR constraints. 3) These four parameterizations require no \emph{a priori} doubly-coprime factorization of the plant, but impose a set of equality constraints. However, these equality constraints will never be satisfied exactly in numerical computation. We prove that the IOP is numerically robust for open-loop stable plants, in the sense that small mismatches in the equality constraints do not compromise the closed-loop stability. The SLP is known to enjoy numerical robustness in the state feedback case; here, we show that numerical robustness of the four-block SLP controller requires case-by-case analysis in the general output feedback case.Comment: 20 pages; 5 figures. Added extensions on numerial computation and robustness of closed-loop parameterization

Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework

As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal processing techniques is the issue of privacy in handling sensitive data. To address this privacy issue, we propose a novel yet general subspace perturbation method for privacy-preserving distributed optimization, which allows each node to obtain the desired solution while protecting its private data. In particular, we show that the dual variables introduced in each distributed optimizer will not converge in a certain subspace determined by the graph topology. Additionally, the optimization variable is ensured to converge to the desired solution, because it is orthogonal to this non-convergent subspace. We therefore propose to insert noise in the non-convergent subspace through the dual variable such that the private data are protected, and the accuracy of the desired solution is completely unaffected. Moreover, the proposed method is shown to be secure under two widely-used adversary models: passive and eavesdropping. Furthermore, we consider several distributed optimizers such as ADMM and PDMM to demonstrate the general applicability of the proposed method. Finally, we test the performance through a set of applications. Numerical tests indicate that the proposed method is superior to existing methods in terms of several parameters like estimated accuracy, privacy level, communication cost and convergence rate