Safety and invariance

Safety-critical systems, such as autonomous vehicles, robots and power systems must stay within safe limits despite uncertainties and disturbances, which makes ensuring reliable operation challenging. Robust controlled invariant sets are used to formalize this notion of safety by identifying all states from which the system can be kept safe indefinitely through admissible control actions, regardless of disturbances. 

Our lab focuses on developing scalable methods for synthesizing safety controllers for high-dimensional and complex dynamical systems, with a particular emphasis on monotone systems, controlled invariants, and robust safety guarantees. Our research lies at the intersection of rigorous theoretical foundations, including monotonicity theory, invariant set characterization and barrier functions, and computational techniques that enable deployment in realistic applications.

• Trajectory-Based Characterization of Robust Controlled Invariant Sets

We develop characterization methods that rely only on system trajectories and hold under mild assumptions, enabling scalable computation of controlled invariant sets.

• Symbolic control-based safety controller synthesis

Our work uses symbolic control methods to design formally correct controllers that ensure safety even in high-dimensional and uncertain environments.

• A. Saoud and M. Arcak, “Characterization, verification and computation of robust controlled invariants for monotone dynamical systems,” Mathematics of Control, Signals, and Systems, 2024. 

• G. Masoumeh, M. Maghenem and A. Saoud, “Sufficient conditions for robust safety in differential inclusions using barrier functions,” Automatica, 2025 Jan 1, vol. 171, p. 111938. 

• S. W. Smith, A. Saoud and M. Arcak, “Monotonicity-Based Symbolic Control for Safety in Driving Scenarios ,” IEEE Control Systems Letters (L-CSS), vol. 6, no. 3, pp. 830–835, 2022.

• O. Reynaud, M. Maghenem, A. Saoud, S. B. Alaoui, A. Hably, “Nagumo-Type Characterization of Forward Invariance for Constrained Systems,” IEEE Conference on Decision and Control (CDC), 2025.

• E.W. Wembe Junior, A. Saoud, “On Robust Controlled Invariants for Continuous-time Monotone Systems,” IFAC Analysis and Design of Hybrid Systems (IFAC ADHS), IFAC-PapersOnLine. 2024 Jan 1. vol. 58, no. 11, pp. 135-40.  Best repeatability award.

• A. Saoud and R. G. Sanfelice, “Computation of Controlled Invariants for Nonlinear Systems: Application to Safe Neural Networks Approximation and Control,”  IFAC Analysis and Design of Hybrid Systems (IFAC ADHS), IFAC-PapersOnLine, 2021 Jan. vol. 54, no. 5, pp.91-96.