Optimization of Communication Network Topology in Distributed Control Systems Subject to Prescribed Decay Rate

• Published in: IEEE transactions on cybernetics Vol. 51; no. 8; pp. 4277 - 4285
• Main Authors: Gaeini, Nozhatalzaman, Moradi Amani, Ali, Jalili, Mahdi, Yu, Xinghuo
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Combinatorial analysis; Control systems; Cost function; Decay rate; Decentralized control; distributed control; Distributed control systems; eigenvalue optimization problem; Eigenvalues; Eigenvalues and eigenfunctions; Equivalence; large-scale systems; Network topologies; Optimal control; Optimization; sparsity-promoting optimal control; Transient response
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2019.2926386

In this paper, we propose a simple cohesive framework to find an optimal directed control network topology with minimum number of links while a prescribed decay rate is satisfied in the transient response of a distributed control system. In order to guarantee the system's decay rate to be faster than a prespecified value, a constraint on the dominant eigenvalue of the system is required to be considered. This results in a nonconvex optimization problem as eigenvalue of a parametric nonsymmetric matrix is a nonconvex, nonsmooth, and even non-Lipschitz function. Here, we present a convex equivalent optimization problem whose minimizer also solves this eigenvalue optimization problem. This optimization problem proposes a state-feedback matrix which results in a decay rate faster than a given value while input signal costs are considered. The equivalent optimization problem in combination with sparsity-promoting optimal control constitutes a combinatorial optimization problem. Using alternating direction method of multipliers, the problem is decomposed into a chain of analytically solvable subproblems which are differentiable and separable. The proposed optimization framework includes relative preference between the topology of the control network and the decay rate of the system. The simulation results show the effectiveness of the proposed framework.