Safety Verification and Controller Synthesis for Systems with Input Constraints

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In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems.

• The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach.
• Our approach can be used to characterize the control invariance of a given set in terms of safety of a general nonlinear control system subject to input constraints.
• From the point of view of controller design, the proposed method provides an approach to synthesize a safe control law that guarantees that the trajectories of the system starting from a given initial set do not enter an unsafe set.