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In this paper, we define a class of graph grammars that can be used to model and direct concurrent robotic self-assembly and similar self-organizing processes. We give several detailed examples of the formalism and then focus on the problem of synthesizing a grammar so that it generates a given, prespecified assembly. In particular, to generate an acyclic graph we synthesize a binary grammar (rules involve at most two parts), and for a general graph we synthesize a ternary grammar (rules involve at most three parts). In both cases, we characterize the number of concurrent steps required to achieve the assembly. We also show a general result that implies that no binary grammar can generate a unique stable assembly. We conclude the paper with a discussion of how graph grammars can be used to direct the self-assembly of robotic parts. [ABSTRACT FROM AUTHOR]

The article discusses papers published in the special section of "IEEE Transactions on Automatic Control" which focuses on symbolic methods for complex control systems in the June 2006 issue. Two papers which focuses on the study of the problem of control using strings of symbolic control languages, maneuver automata, or control quanta are presented. Another study conducted by Paulo Tabuada examines the problem of producing finite models of continuous systems, by constructing models that contain only a finite number of the possible trajectories.

In this paper, we consider the synthesis of control laws for piecewise-affine hybrid systems on simplices. The construction is based on the solution to the control-to-facet problem at the continuous level, and on dynamic programming at the discrete level. The construction is given as an explicit algorithm using only linear algebra and reach-set computations for automata; no numerical integration is required. The method is conservative, in that it may fail to find a control law where one exists, but one cannot hope for a sharp algorithm for control synthesis since reachability for piece- wise-affine hybrid systems is undecidable. [ABSTRACT FROM AUTHOR]