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Anand, Mahathi; Lavaei, Abolfazl; Zamani, Majid (2020): Compositional Construction of Control Barrier Certificates for Large-Scale Interconnected Stochastic Systems. In: Ifac Papersonline, Vol. 53, No. 2: pp. 1862-1867
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This paper proposes a compositional approach for constructing control barrier certificates of large-scale interconnected discrete-time stochastic control systems. The proposed compositional methodology is based on a notion of control sub-barrier certificates enabling one to construct control barrier certificates of interconnected systems by leveraging some small-gain type conditions. The main goal is to synthesize control policies satisfying safety properties for interconnected systems utilizing those control sub-barrier certificates of subsystems while providing upper bounds on the probability that interconnected systems reach unsafe regions in finite-time horizons. A sum-of-squares optimization problem is formulated for searching control sub-barrier certificates and corresponding local control policies satisfying safety specifications. The proposed compositional approaches are illustrated on a temperature regulation in a circular building containing 1000 rooms by compositionally synthesizing safety controllers to maintain the temperature of each room in a comfort zone in a bounded-time horizon. Copyright (C) 2020 The Authors.