Looking Forward Approach in Cooperative Differential Games with Uncertain Stochastic Dynamics
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In this study, a novel approach for defining and computing a solution for a differential game is presented for a case, wherein players do not have complete information about the game structure for the full time interval. At any instant in time, players have certain information about the motion equations and payoff functions for a current subinterval, and a forecast about the game structure for the rest of the time interval. The forecast is described by stochastic differential equations. The information about the game structure updates at fixed instants of time and is completely unknown in advance. A new solution is defined as a recursive combination of sets of imputations in the combined truncated subgames that are analyzed by the Looking Forward Approach. An example with a resource extraction game is presented to demonstrate a comparison of payoff functions without a forecast and that with stochastic and deterministic forecasts.
KeywordsDifferential game Looking Forward Approach Imputation distribution procedure Time consistency Strong time consistency
Mathematics Subject Classification49N70 91A12
The first author acknowledges Saint-Petersburg State University for the research Grant No. 188.8.131.524. The work of the second author was supported by Saint-Petersburg State University, Project 6.37.349.2015 and 184.108.40.2065.
- 2.Petrosyan, L.A.: Time-consistency of solutions in multi-player differential games. Vestn. Leningr. State Univ. 4, 46–52 (1977)Google Scholar
- 4.Kwon, W.H., Han, S.H.: Receding Horizon Control: Model Predictive Control for State Models. Springer, New York (2005)Google Scholar
- 5.Wang, L.: Model Predictive Control System Design and Implementation Using MATLAB. Springer, New York (2005)Google Scholar
- 6.Rawlings, J.B., Mayne, D.Q.: Model Predictive Control: Theory and Design. Nob Hill Publishing, Madison, WI (2009)Google Scholar
- 9.Petrosian, O.L.: Looking Forward approach in cooperative differential games with infinite-horizon. Vestn. Leningr. Univ. (2016) (to be published)Google Scholar
- 10.Gromova, E.V., Petrosian, O.L.: Control of informational horizon for cooperative differential game of pollution control. IEEE (2016). doi: 10.1109/STAB.2016.7541187