H_∞-PID distributed control for output leader-tracking and containment of heterogeneous MASs with external disturbances

ABSTRACT

This paper addresses both the output leader-tracking and output containment control problems for heterogeneous linear high-order Multi-Agent Systems (MASs) sharing information over a directed communication topology and subject to external unknown disturbances. To solve these control problems, we propose a robust fully distributed Proportional-Integral-Derivative (PID) control strategy, equipped with a filter on the derivative action that allows obtaining both a simpler closed-loop formulation, without the need of the descriptor transformation, and good tracking performances in the case of fast reference signal behaviours. The stability analysis is analytically proven via the Lyapunov theory and the $H_{\mathrm{\infty }}$ approach. The derived robust stability conditions are expressed as a set Linear Matrix Inequalities (LMIs) whose solution provides the proper tuning of the robust PID control gains. Numerical simulations confirm the effectiveness and robustness of the proposed approach in solving both the output leader-tracking and output containment control problems.

KEYWORDS:

• Heterogeneous multi-agent systems
• distributed PID control
• output containment
• output leader-tracking
• robust control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Dario Giuseppe Lui

Dario Giuseppe Lui received the Ph.D. degree in Information Technology at the University of Sannio, Benevento, Italy in 2020. He is currently a research fellow at the University of Naples Federico II. His work focuses on the distributed control of multi-agent systems in the presence of communication impairments, with application to automotive field.

Alberto Petrillo

Alberto Petrillo received the Ph.D. degree in control systems engineering from the University of Naples Federico II in 2019. He is currently a research fellow at the University of Naples Federico II. His work mainly focuses on the distributed, synchronisation-based, control of networked control systems in the presence of communication impairments and security vulnerabilities, with application to automotive field and energy systems.

Stefania Santini

Stefania Santini received the M.Sc. degree in electronic engineering and the Ph.D. degree in automatic control from the University of Naples Federico II, Naples, Italy, in 1996 and 1999, respectively. She is currently an associate professor of automatic control. She is involved in many projects with industry, including small- and medium-sized enterprises operating in the automotive field. Her research interests include the area of the analysis and control of nonlinear systems with applications to automotive engineering, transportation technologies and energy systems.