State-based supervisory control with restrictions on the supervisor realization
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State-based supervisory control with restrictions on the supervisor realization Pedro A. C. F. Leite1 · Fabio L. Baldissera1 · Jose´ E. R. Cury1 Received: 15 August 2018 / Accepted: 12 April 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we formalize and solve a state-based Supervisory Control problem with restrictions on the supervisor realization that have not been tackled by the Supervisory Control Theory (SCT) community so far. This problem was derived from the application of SCT to intervene in the dynamics of gene regulatory networks, a relevant problem in the fields of Systems and Synthetic Biology. In our framework, a plant, whose states x are represented by Boolean strings, must be driven from an initial state to a target one, by means of m state-feedback control laws ui = hi (x). The Boolean functions hi , though, cannot be freely chosen, but must rather belong to a (possibly strict) subset R of all the Boolean functions on x. Keywords Supervisory control theory · Realization restrictions · Gene regulatory networks
1 Introduction 1.1 Background and Motivation Works in Supervisory Control Theory (SCT) often assume that a supervisor is implemented in electronic digital computers. Restrictions can only arise if the computational device does not have enough memory to store the automaton associated with the supervisor, and if there is not enough processing power to deliver an output at the correct time. In recent years, though, some application domains have raised new challenges in the synthesis of controllers. This is due to the need to implement control strategies (totally or partially) on media other than traditional computational devices. For example, to intervene in the behavior of biological systems at the cellular level, one may resort to using synthetic biomolecules to realize the controller (Vecchio et al. 2016; Hsiao et al. 2018; Cury and
Fabio L. Baldissera
[email protected] Jos´e E. R. Cury [email protected] 1
Universidade Federal de Santa Catarina, Florian´opolis, SC 88040-970, Brazil
Discrete Event Dynamic Systems
Baldissera 2013). The realization of a control strategy as sets of molecules, however, is much more demanding and restrictive than its realization as a C code to be embedded in an automotive electronic control unit, or as a ladder logic that runs in a programmable logic controller in industrial applications (Cox et al. 2007; Buchler et al. 2003). In some situations, even a simple ‘if − then − else’ structure might be difficult to obtain with molecules. It is not only in biological applications that the need to compute with unconventional media appears. Research on smart materials and related fields (McEvoy and Correll 2015; Hawkes et al. 2010) also raises similar challenges for control engineers. These materials couple sensing, computation, actuation and communication in a way similar to that found in living beings (the interested reader may refer to (El-Samad 2010) for an example of multifunctional molecules in intra
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