Summary
This paper addresses the peculiar treatment that time receives when studying control systems. For example, why is the ability to perfectly observe time assumed implicitly in virtually all control formulations? What happens if this implicit assumption is violated? It turns out that some basic control results fall apart when time cannot be perfectly measured. To make this explicit, we introduce information space concepts that permit imperfect time information to be considered in the same way as imperfect state information. We then argue that classical open-loop control should be reconsidered as perfect time-feedback control. Following this, we introduce a notion of strongly open-loop control, which does not require perfect time observations. We provide some examples of these concepts and argue that many fascinating directions for future controls research emerge.
The authors thank Roger Brockett and Dan Koditschek for helpful comments and discussions. LaValle is supported in part by the DARPA SToMP program (DSO HR0011-07-1-0002). Egerstedt is supported in part by the National Science Foundation through NSF-CAREER award (grant # 0237971).
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LaValle, S.M., Egerstedt, M. (2009). An Information Space View of “Time”: From Clocks to Open-Loop Control. In: Ghosh, B.K., Martin, C.F., Zhou, Y. (eds) Emergent Problems in Nonlinear Systems and Control. Lecture Notes in Control and Information Sciences, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03627-9_6
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DOI: https://doi.org/10.1007/978-3-642-03627-9_6
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