Static Output Feedback Control for Multi-Agent Systems Using Nash Equilibrium

Abstract

This work proposes a semidefinite programming (SDP) model that synthesizes static output control feedback for networked linear time-invariant multi-agent systems (MAS). We theoretically prove that the output feedback control of MAS can be constructed using the Nash equilibrium previously derived for state-feedback control. The Nash equilibrium considers that agents seek to minimize their individual cost functions subject to the system dynamics of the MAS. The resulting control from the pro- posed SDP model ensures the stability of the closed-loop system and dissipativity when a disturbance is present in the MAS. A set of four case studies is implemented. The first three numerical cases serve to validate and compare cost effectiveness and time-domain performance of the proposed control framework with other state-of-the-art frameworks. The fourth case designs a frequency regulation scheme for a modified IEEE 24-bus power grid. Using the proposed framework, distributed controllers are synthesized for the inverters which are considered agents in the grid. Each inverter uses partial state information of the neighboring inverters. The resulting control scheme is implemented in a high-fidelity non-linear model of 261 states that describes the electromagnetic transient dynamics of the power grid. Hence, compared to prior studies that usually validate their frameworks in small-scale numerical models, this fourth case demonstrates a virtue of our pro- posed SDP: its scalability and practical utility in real-world networked MAS. We implement the proposed framework in an open-access toolbox in Python and MATLAB, enabling practitioners and researchers to readily implement it in their applications.