This paper is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems . Our proposal involves decomposition of interconnected systems intosmaller subsystems and leverages the notion of control sub-barrier certificates of subsystems . The main goal is to synthesize hybrid controllers enforcing complex logicproperties including the ones represented by the accepting language of DFA . We provide two systematic approaches based on sum-of-squares (SOS)optimization program and counter-example guided inductive synthesis (CEGIS) framework . We finally apply our proposed techniques to two physical casestudies . We propose a systematic approach to first decompose high-level specifications into simple reachability tasks by utilizing automata corresponding to thecomplement of specifications . We then construct control sub . and synthesize local controllers for those simpler tasks and combine them to obtain a hybrid controller that ensures satisfaction of the

Author(s) : Mahathi Anand, Abolfazl Lavaei, Majid Zamani

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Keywords : control - barrier - certificates - systems - synthesize -

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