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This paper develops decentralized team strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The system considered is linear and the cost criterion is quadratic. First, a multimodel solution is obtained when the decision makers make different noisy linear observations of the random initial state only. Then the solution to this static team problem is utilized to obtain a multimodel solution to the dynamic team problem with sampled observations under the one-step-delay observation sharing pattern. In both cases, the well-posedness of the multimodel solution is demonstrated.

This paper considers Markovian Stackelberg problems with one leader and N followers. Firstly, an algorithm is proposed to compute optimal affine incentive strategy for the leader and Nash reactions of the followers, for general finite state Markov cahins, under the average-cost-per-stage criteria. Next, this algorithm is analyzed in the context of weakly-coupled Markov chains to compute near-optimal strategies from a reduced-order aggregate model. The robustness of the near-optimal solution is established, and the multimodel feature of the computational algorithm is highlighted.

Recent progress in the use of singular perturbation and two-time-scale methods of modeling and design for control systems is reviewed. Over 350 references are organized into major problem areas. Representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application. The survey is aimed at engineers and applied mathematicians interested in model-order reduction, separation of time scales and allied simplified methods of control system analysis and design. The exposition does not assume prior knowledge of singular perturbation methods.

A decentralized filtering and control scheme is presented for obtaining low-order Nash equilibrium strategies for decision makers using different models of the same large-scale system. Multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables. The small parameters are appropriately scaled so that the variables in both time scales are well defined. The decision makers have decentralized information structures and are constrained to use only finite dimensional compensators of a specified dimension. It is shown that the proposed scheme is in fact the asymptotic limit of the exact solution as the small parameters go to zero.