Reachability Analysis in Dynamic and Hybrid Systems
Summary
Reachability analysis examines which states a dynamic or hybrid system can attain over time, given initial conditions and admissible inputs. Dynamic systems evolve continuously according to differential equations, while hybrid systems combine such continuous evolution with discrete transitions, capturing the behaviour of many modern cyber-physical systems. By computing reachable sets—collections of all possible states reachable within a time horizon—engineers can verify safety properties, design robust controllers and predict worst-case scenarios. Core methods include set-propagation techniques such as flowpipe construction, interval and zonotope enclosures, and over-approximation strategies that trade tightness for computational tractability. Recent advances have focused on improving scalability for high-dimensional systems, handling nonlinearity via linearisation or abstraction, and ensuring robustness under modelling uncertainties and perturbations. These developments underpin applications in autonomous transport, robotics, aerospace mission planning and industrial automation, where guarantees of safe operation under all allowable disturbances are paramount.
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Reachability Analysis in Dynamic and Hybrid Systems publication trend
The graph below shows the total number of articles in reachability analysis in dynamic and hybrid systems across all publications each year (not limited to Nature Index journals).
Technical terms
Dynamic system: A model describing the evolution of a system’s state over time via differential or difference equations.
Hybrid system: A mathematical representation that integrates both continuous dynamics and discrete transitions to capture mixed-mode behaviours.
Reachable set: The collection of all states a system can attain from a specified initial set within a given time horizon under all admissible inputs.
Flowpipe: A sequence of state sets over time obtained by propagating initial uncertainty through system dynamics to approximate the reachable set.
Over-approximation: A conservative bounding technique that encloses the true reachable set within a computationally tractable superset to ensure safety guarantees.
Scott continuity: A property of set-based analyses in lattice theory that ensures robustness under small perturbations by preserving directed suprema.
References
- Online hazard prediction of train operations with parametric hybrid automata based runtime verification. Reliability Engineering & System Safety (2024).
- Recent developments in theory and tool support for hybrid systems verification with HyPro. Information and Computation (2022).
- Safe & robust reachability analysis of hybrid systems. Theoretical Computer Science (2018).
- Robustness, Scott continuity, and computability. Mathematical Structures in Computer Science (2023).
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