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The paper contains procedures for obtaining Nash strategies from simplified models for singularly perturbed systems which are non-linear in the slow variables, and linear in the fast variables and controls. Two classes of problems are considered. The first is a Nash problem on single parameter systems where both the decision makers interact at the slow and fast subsystem levels. The second is a Nash problem on multi-parameter systems where the fast subsystems are individually controlled by each decision maker, and the interaction between the decision makers is only through the slow ‘ core ’. This problem is studied within the framework of multimodelling. The solution procedures for these two problems are compared to reveal the interaction between the slow and fast subsystem designs in the two cases. The simplified Nash solutions of both the problems are shown to be robust, in the sense that there is little incentive for either decision-maker to deviate from the proposed strategy.

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.

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.

This paper presents a unified approach to reduced-order modelling and control of large-scale systems with multiple decision makers. The ‘core’ of a large game problem is identified through the information structure and the class of structure preserving strategies. The induced decomposition results in a low-order game problem and two decentralized optimal control problems. An example of a two-area power system demonstrates the computational attractiveness of the proposed design methodology.

This document analyzes the interaction between model simplification and strategy design in a multimodel context and for multiple agent stochastic decision problems with decentralized information. Under quasi-classical information patterns, and using singular perturbations approach, the authors establish asymptotic optimality of different multimodels which involve continuous and two types of sampled measurements. Our general analysis and discussion serve to enhance our understanding of the interrelationships between structural features of stochastic large scale systems, like time-scales and weak coupling, and strategy design.