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Al Khatib, Mohammad; Zamani, Majid (2020): Controller synthesis for interconnected systems using parametric assume-guarantee contracts. 2020 American Control Conference (ACC), 1-3 July 2020, Denver, CO, USA.
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In this paper we synthesize controllers for interconnected systems to enforce parametric assume-guarantee contracts (AGC), which encode behaviors of the systems in some parameter domains. In our approach to solve the design problem, we synthesize a controller for each component of the system so that it satisfies its own parametric AGC separately, and then define a mapping that generates the sequence of parameters for which the corresponding contracts are satisfied after interconnecting the components. Then if a small-gain like condition on the sequence of parameters hold, a parametric AGC is declared for the interconnected system. The classical small-gain theorem on bounded input bounded output (BIBO) stability is recovered by the obtained results showing the relation between the assume-guarantee reasoning and the small-gain approach. We also provide an example of a large-scale transportation system to illustrate our results.