Pareto optimality in infinite horizon linear quadratic differential games

In this article we derive conditions for the existence of Pareto optimal solutions for linear quadratic infinite horizon cooperative differential games. First, we present a necessary and sufficient characterization for Pareto optimality which translates to solving a set of constrained optimal control problems with a special structure. Next, we show that if the dynamical system is controllable, certain transversality conditions hold true, and as a result all the Pareto candidates can be obtained by solving a weighted sum optimal control problem. Further, exploiting the linear structure we investigate the relationship between Pareto optimality and weighted sum minimization. Finally, for the scalar case, we present an algorithm to find all the Pareto optimal solutions assuming mild conditions on the control space.