Noncooperative Model Predictive Control

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Baumann, Michael Heinrich ; Stieler, Marleen:
Noncooperative Model Predictive Control.
2018
Event: 18th International Symposium on Dynamic Games and Applications , 9.-12. Juli 2018 , Grenoble, France.
(Conference item: Conference , Speech )

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Nash strategies are a natural solution concept in noncooperative game theory because of their ’stable’ nature: If the other players stick to the Nash strategy it is never beneficial for one player to unilaterally change his or her strategy. In this sense, Nash strategies are the only reliable strategies.
The idea to perform and analyze Model Predictive Control based on Nash strategies instead of optimal control sequences is appealing because it allows for a systematic handling of noncooper- ative games, which are played in a receding horizon manner. However, existence and structure of Nash strategies heavily depend on the specific game under consideration. This is in contrast to solution concepts such as usual optimality and Pareto optimality, in which one can state very general existence results or, in the case of Pareto optima, one knows that they are to be found on the ’lower left’ boundary of the set of admissible values in the value space. Moreover, the calculation of Nash strategies is, in general, a very difficult task.
In this talk we present a class of games for which the closed-loop trajectory of the Nash-based MPC scheme converges to an equilibrium of the system. This equilibrium turns out to be a Pareto-optimal steady state, i.e. a Pareto-optimal solution to the multiobjective problem of minimizing all players’ stage costs restricted to the set of equilibria. We furthermore investigate the relation between the closed loop and open-loop Nash strategies on the infinite horizon in terms of the trajectories as well as of the performance.