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We consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents. The strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, quantized team policies are asymptotically optimal. This result is then applied to Witsenhausen's celebrated counterexample and the Gaussian relay channel problem. For Witsenhausen's counterexample, our approximation approach provides, to our knowledge, the first rigorously established result that one can construct an $\varepsilon$-optimal strategy for any $\varepsilon > 0$ through a solution of a simpler problem. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the following problem: what passivity properties can be inferred for a system by studying only an approximate mathematical model for it. Our results show that an excess of passivity (whether in the form of input strictly passive, output strictly passive or very strictly passive) in the approximate model guarantees a certain passivity index for the system, provided that the norm of the error between the approximate and the true models is sufficiently small in a suitably defined sense. Further, we consider $(Q,S,R)$-dissipative systems and show that $(Q,S,R)$- dissipativity has a similar robustness property, even though the supply rates for the system and its approximation may be different. These results may be particularly useful if either the approximate model is much easier to analyze, or if the precise system model is unknown. We illustrate the results by considering particular approximation methods, e.g., model reduction, discretization, quantization, and linearization around an equilibrium point. [ABSTRACT FROM PUBLISHER]

We consider the discrete approximation of stationary policies for a discrete-time Markov decision process with Polish state and action spaces under total, discounted, and average cost criteria. Deterministic stationary quantizer policies are introduced and shown to be able to approximate optimal deterministic stationary policies with arbitrary precision under mild technical conditions, thus demonstrating that one can search for $\varepsilon$-optimal policies within the class of quantized control policies. We also derive explicit bounds on the approximation error in terms of the quantization rate. [ABSTRACT FROM AUTHOR]