Synthesizing Safety Controllers for Uncertain Linear Systems: A Direct Data-driven Approach

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.

Data-Driven Computation of Robust Invariant Sets and Gain-Scheduled Controllers for Linear Parameter-Varying Systems

“…We now enforce the invariance condition x i,j + ∈ S(q) in ( 14) for all w ∈ W and for all feasible models in the set M ∈ M T . Recall that condition ( 14) is enforced at each vertex {x i , u i , i ∈ I vs 1 } and {p j , j ∈ I vp 1 } of the set P. Note that from (22), the vertices of S(q) are {x i V i q, i ∈ I vs 1 }, under the constraints in (21). Then, the successor state from x i,j + for parameter p j , input u i , and disturbance w is given in terms of q as follows…”

“…manas.mejari@supsi.ch S. K. Mulagaleti and A. Bemporad are with the IMT School for Advanced Studies Lucca, Italy. {s.mulagaleti, alberto.bemporad}@imtlucca.it [22], which synthesize RCI sets and controllers directly from open-loop data, without the need of model identification. The algorithm presented in [3], computes a state-feedback controller from open-loop data to induce robust invariance in a given polyhedral set, while methods proposed in [2], [11], [22] simultaneously compute invariance-inducing controllers along with RCI sets having zonotopic [2], polytopic [11] or ellipsoidal [22] representations.…”