Compositional Model~basedDesign of Physical systems Prasanta Bose Shankar A. Rajamoney Computer Science Department University of Southern California Los Angeles, CA 90089-0781 Email: pbose, rajamone©pollux.usc,edu Abstract Model-based design constructs physical systems in two stages. First, a causal rela- tion network (CRN) of quantities that entails the desired behavior is constructed from a domain model. Second, a physical system is designed by assembling components such that all the causal relations specified by the CRN are imposed. The Compositional Model-based Design method, CMD, simplifies the design of complex physical systems by decomposing the specified behavior into logical portions, building CRNs for each portion, and incrementafly composing the CRNs until the entire desired behavior is achieved. Importantly, the method detects potential interactions between individual CRNs that may nullify the portions of behavior already designed for by detecting vi- olations of the closure assumptions under which each CRN was formed. 1~heCRN is revised using operators derived from axioms that specify the conditions for a change to hold in the presence of such interference. While this paper illustrates the method in the context of a boiler control system, the approach applies to regulatory physical systems with multiple operating regions. 1 Introduction In model-based design [11, 9], a physical system that meets input behavioral specifications is designed in two steps: 1) a network of causal relations, causal relation network (CRN), which entails the desired behavior, is constructed from a domain model describing components and their interactions, and 2) a design of the physical system, consisting of the components and their structural relations, is obtained from the design constraints that were instantiated in order to impose the causal relations in the constructed CRN representation. The interme- diate CRN plays a pivotal role by explicating the causal paths that show how the designed physical system achieves the desired behavior, By bridging the specified behavior and the desired physical system, the causal relation network considerably simplifies the search for candidate design hypothesis. However, the design of complex physical systems using this model-based approach is im- practical since the construction of the CRN becomes computationally expensive due to the large number of components and interactions that must be considered. In this paper, we describe compositional model-based design (CMD), an approach for the model-based design of complex physical systems. This method adopts a divide-and-conquer strategy. It de- composes the specified behavior into logical portions, and separately constructs CRNs and 56