Multiobjective Dynamic Optimization of Cooperative Difference Games in Infinite Horizon

This article derives necessary and sufficient conditions for Pareto optimal solutions in infinite horizon cooperative difference games of autonomous systems with exponentially discounted performances. First, the \mathcal {N} constrained optimal control problems are converted into an unconstrained characterization with mixed endpoint constraints by introducing appropriate auxiliary states. Second, the infinite horizon cooperative difference games are transformed equivalently into an augmented and truncated finite horizon optimization problem by defining two real-valued functions and the necessary conditions are derived based on the maximum principle (MP) of discrete-time type. Moreover, we present sufficient conditions for general nonautonomous systems. Finally, the results developed are employed to address the linear quadratic (LQ) cooperative difference games for fixed as well as arbitrary initial states.