Open-Loop Dymanic Games for Interconnected Positive Nonlinear Systems with H∞ Constraint

This paper investigates the problem of infinite horizon open-loop dynamic games for interconnected positive nonlinear systems with H
_∞
constraint. Both Nash equilibrium as a non-cooperative game and Pareto optimality as a cooperative game are discussed. The systems considered here are cooperative systems and the H
_∞
control recovers the influence of modeling error caused by linearization. For this class of positive systems, the conditions that guarantee the existence of Nash equilibrium and Pareto optimality are derived. It is shown that these conditions can be formulated in terms of cross-coupled algebraic Riccati equations (CCAREs) and a linear matrix inequality (LMI). Finally, in order to show the effectiveness of the proposed strategy, a simple example is demonstrated.