This report presents a theory of quantized systems in support of predictive filtering based on a process called "quantization" to reduce state update transmission. A quantized system is a system with input and output quantizers. Quantization, which generates state updates only at quantum level crossings, abstracts a sender model into a DEVS (Discrete Event System Specification) representation. This affords an alternative, efficient approach to embedding continuous models within distributed discrete event simulations. The theory of quantized systems examines the conditions under which a coupling of DEVSrepresented systems is a good representation of the original composition. This corresponds to closed loop study of predictive filtering, i.e., where both sender and receiver are exposing abstractions of each other. Previous analyses of Dead Reckoning accuracy/performance tradeoffs have assumed that open loop analysis carries over to the closed loop case. Unfortunately, experience in numerical analysis suggests that the dynamics of feedback interaction may cause errors generated to grow without bound. The theory of quantized systems provides conditions under which homomorphic (error-free) quantization-based predictive filtering is possible. It shows how error can be generated if the conditions are violated and formulates a suitable concept of approximate homomorphism. Applications of quantization to message traffic reduction are discussed. The theory has been confirmed by simulations of test cases. It will be subject to further test in actual distributed simulations using the DEVS/HLA modeling and simulation environment under construction.
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