Nonnegative Consensus Tracking of Networked Systems With Convergence Rate Optimization

Abstract

This article investigates the nonnegative consensus tracking problem for networked systems with a distributed static output-feedback (SOF) control protocol. The distributed SOF controller design for networked systems presents a more challenging issue compared with the distributed state-feedback controller design. The agents are described by multi-input multi-output (MIMO) positive dynamic systems which may contain uncertain parameters, and the interconnection among the followers is modeled using an undirected connected communication graph. By employing positive systems theory, a series of necessary and sufficient conditions governing the consensus of the nominal, as well as uncertain, networked positive systems, is developed. Semidefinite programming consensus design approaches are proposed for the convergence rate optimization of MIMO agents. In addition, by exploiting the positivity characteristic of the systems, a linear-programming-based design approach is also proposed for the convergence rate optimization of single-input multi-output (SIMO) agents. The proposed approaches and the corresponding theoretical results are validated by case studies.

Proportional‐derivative controller design of continuous‐time positive linear systems

“…25,26 Distributed observer-based output-feedback controllers were employed for consensus of networked control systems with positivity constraint. [27][28][29] Positive stabilization of linear singular systems through PD control was discussed recently. 20 The PI controller design for positive systems was also discussed.…”

“…Static output‐feedback (SOF) controllers were designed for continuous‐time and discrete‐time positive linear systems 25,26 . Distributed observer‐based output‐feedback controllers were employed for consensus of networked control systems with positivity constraint 27‐29 . Positive stabilization of linear singular systems through PD control was discussed recently 20 .…”

Heavy-duty diesel vehicle formation with transient integrated control of fuel consumption and emission in an intelligent network environment

“…Luo et al 15 adopt centralized controller and unknown input proportional multiple integral (PMI) observer technology, so that the state and disturbance can be estimated and compensated effectively at the same time. Liu et al 16 describe networked multi-agent as a multiple input multiple output (MIMO) positive dynamic system with uncertain parameters, and propose a semi-definite programming consistency design method to optimize the convergence speed of MIMO agents. Xu et al 17 propose a dynamic output feedback controller for online speed tracking to solve the problem of speed synchronization control of connected vehicles under replay attack, considering the uncertainty caused by attack delay.…”