Stochastic differential games with weak spatial and strong informational coupling
We formulate a parameterized family of linear quadratic two-person nonzero-sum stochastic differential games where the players are weakly coupled through the state equation and strongly coupled through the measurements. A positive parameter {epsilon} characterizes this family, in terms of which the subsystems are coupled (weakly). With {epsilon} = 0 the problem admits a unique Nash equilibrium solution, while {epsilon} > 0, no matter how small, no general method is available to obtain the Nash equilibrium solution and even to prove existence and uniqueness. In this paper, we develop an iterative technique whereby Nash solutions of all orders (in terms of {epsilon}) are obtained by starting the iteration with the unique (strong team) solution determined for {epsilon} = 0. The Nash solutions turnout to be linear, requiring only finite-dimensional controllers, in spite of the fact that a separation (of estimation and control) result does not hold.
- Research Organization:
- Illinois Univ., Urbana, IL (USA). Coordinated Science Lab.
- Sponsoring Organization:
- DOE/ER
- DOE Contract Number:
- FG02-88ER13939
- OSTI ID:
- 7184737
- Report Number(s):
- CONF-9006183-1; ON: DE90011925
- Country of Publication:
- United States
- Language:
- English
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