Secure-by-Construction Synthesis for Control Systems

Abstract: In this paper, we present the synthesis of secure-by-construction controllers that address safety and security properties simultaneously in cyber-physical systems. Our focus is on studying a specific security property called opacity, which characterizes the system's ability to maintain plausible deniability of its secret behavior in the presence of an intruder. These controllers are synthesized based on a concept of so-called (augmented) control barrier functions, which we introduce and discuss in detail. We propose conditions that facilitate the construction of the desired (augmented) control barrier functions and their corresponding secure-by-construction controllers. To compute these functions, we propose an iterative scheme that leverages iterative sum-of-square programming techniques. This approach enables efficient computation of these functions, particularly for polynomial systems. Moreover, we demonstrate the flexibility of our approach by incorporating user-defined cost functions into the construction of secure-by-construction controllers. Finally, we validate the effectiveness of our results through two case studies, illustrating the practical applicability and benefits of our proposed approach.