Closed-Loop Nash Games for Interconnected Positive Nonlinear Systems with \(H_\infty \) Constraint
In this paper, infinite horizon closed-loop Nash games for interconnected positive nonlinear systems with \(H_\infty \) constraint are investigated. The systems considered here are cooperative systems defined by Abara, Ticozzi, Altafini (IEEE Trans Autom Control, 63:402–417, (2018), ) and the \(H_\infty \) control recovers the influence of modeling error caused by linearization. For this class of positive systems, we provide conditions that guarantee the existence of Nash equilibrium via state feedback strategy. These conditions can be formulated in terms of cross-coupled algebraic Riccati equations (CCAREs) and a linear matrix inequality (LMI).
KeywordsNash games Interconnected positive nonlinear systems \(H_\infty \) control Multiple players
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