Distributed H_∞ PID Feedback for Improving Consensus Performance of Arbitrary-delayed Multi-agent System

• Published in: International journal of automation and computing Vol. 11; no. 2; pp. 189 - 196
• Main Authors: Ou, Lin-Lin, Chen, Jun-Jie, Zhang, Dong-Mei, Zhang, Lin, Zhang, Wei-Dong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.04.2014; Springer Nature B.V
• Subjects: CAE) and Design; Closed loops; Communication; Computer Applications; Computer-Aided Engineering (CAD; consensus; Control; controller; Controllers; Dynamical systems; Eigenvalues; Engineering; Feedback; H-infinity control; index; Matrix theory; Mechatronics; Methods; Multi-agent; Multiagent systems; parametric; Proportional integral derivative; proportional-integral-differential(PID); Robotics; SISO (control systems); space; Subsystems; system; System theory; Vehicles; proportional-integral-differential (PID) controller; consensus; parametric space; performance index; Multi-agent system
• ISSN: 1476-8186; 2153-182X; 1751-8520; 2153-1838
• DOI: 10.1007/s11633-014-0780-y

The H∞ proportional-integral-differential(PID) feedback for arbitrary-order delayed multi-agent system is investigated to improve the system performance. The closed-loop multi-input multi-output(MIMO) control framework with the distributed PID controller is firstly described for the multi-agent system in a unified way. Then, by using the matrix theory, the prescribed H∞performance criterion of the multi-agent system is shown to be equivalent to several independent H∞ performance constraints of the single-input single-output(SISO) subsystem with respect to the eigenvalues of the Laplacian matrix. Subsequently, for each subsystem,the set of the PID controllers satisfying the required H∞ performance constraint is analytically characterized based on the extended Hermite-Biehler theorem. Finally, the three-dimensional set of the decentralized H∞ PID control parameters is derived by finding the intersection of the H∞ PID regions for all the decomposed subsystems. The simulation results reveal the effectiveness of the proposed method.