Safety-Critical Control in Dynamical Systems

Safety-critical control occupies a central role in the design of dynamical systems that must operate reliably under stringent constraints. At its core, the discipline seeks to guarantee that the system trajectory remains within predefined safe regions of the state space, even in the presence of disturbances, model uncertainties or time delays. Techniques typically draw on invariant set theory, barrier function methods and optimisation-based controllers to enforce safety certificates while achieving performance objectives. Recent advances have fused classical Lyapunov stability analysis with data-driven and learning-based approaches, permitting real-time adaptation in complex or black-box settings where precise models are unavailable. Applications span autonomous vehicles navigating crowded environments, robotic manipulators operating alongside humans and power systems subject to fluctuating loads. The global significance of safety-critical control is evident in the pressing need to deploy autonomous systems with provable guarantees, mitigating risks in transportation, energy and healthcare. Interdisciplinary research has highlighted the complementarity of techniques: model predictive control provides foresight through finite-horizon optimisation, barrier functions enforce instantaneous safety constraints and reinforcement learning contributes adaptive capability under uncertainty. Together, these methods form a cohesive framework enabling robust operation in diverse technological contexts and laying the foundation for future certification standards in autonomous system deployment.

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Safety-Critical Control in Dynamical Systems publication trend

The graph below shows the total number of articles in safety-critical control in dynamical systems across all publications each year (not limited to Nature Index journals).

Technical terms

Dynamical system: A mathematical model describing how the state of a system evolves over time under given inputs and disturbances.

Safety-critical control: A control paradigm that ensures the system trajectory remains within predefined safe regions while fulfilling performance goals.

Control barrier function: A scalar function whose superlevel set defines a safe region; enforcing non-negativity of its derivative guarantees forward invariance.

Forward invariance: The property that once the system state lies within a safe set, it cannot exit that set under the prescribed control law.

Model Predictive Control: An optimisation-based strategy that computes control actions by solving a finite-horizon problem at each sampling instant, respecting state and input constraints.

Lyapunov stability: A concept indicating that small perturbations from an equilibrium point diminish over time, ensuring bounded and predictable system behaviour.

References

1. Sablas: Learning Safe Control for Black-Box Dynamical Systems. IEEE Robotics and Automation Letters (2022).
2. Control barrier functionals: Safety‐critical control for time delay systems. International Journal of Robust and Nonlinear Control (2023).
3. On the undesired equilibria induced by control barrier function based quadratic programs. Automatica (2024).