Symbolic Control of Nonlinear Dynamical Systems
Summary
Symbolic control of nonlinear dynamical systems is an approach that translates complex continuous‐state behaviour into a finite, discrete representation amenable to formal analysis and automated synthesis. By partitioning the state space into regions and abstracting the original system to a symbolic model, one can apply algorithmic techniques from computer science—such as model checking, game solving and formal languages—to guarantee that closed‐loop trajectories satisfy high‐level specifications. These specifications are often expressed in temporal logics, which allow concise statements about safety (“always avoid unsafe regions”), reachability (“eventually reach a target”) and more elaborate sequential tasks. Central to the methodology are notions of simulation or bisimulation, which ensure that controllers designed on the symbolic model can be refined back to the concrete system without losing correctness. Recent advances have extended symbolic control to systems with uncertain or partially unknown dynamics through data‐driven abstraction, to large‐scale or networked systems via compositional schemes, and to disturbed environments by robustifying the abstraction relations. The global significance lies in providing formal guarantees for safety‐critical applications—from autonomous vehicles and robotics to power networks—bridging the gap between rigorous mathematical control theory and executable algorithms for real‐world nonlinear systems.
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Symbolic Control of Nonlinear Dynamical Systems publication trend
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Technical terms
Symbolic abstraction: A finite-state model representing continuous dynamical behaviour through partitioned regions.
Linear Temporal Logic (LTL): A formal language for specifying temporal properties over system trajectories.
Bisimulation: An equivalence relation linking two systems so that each can match the other's observable behaviours.
Robust stutter bisimulation: A relation allowing for disturbances by equating sequences of states that may include repeated (stutter) steps while preserving reachability under control.
Growth bound: A function that estimates how trajectories diverge over time, used to construct sound symbolic abstractions.
References
- Data-driven abstraction-based control synthesis. Nonlinear Analysis Hybrid Systems (2024).
- Robust stutter bisimulation for abstraction and controller synthesis with disturbance. Automatica (2024).
- Compositional construction of abstractions for infinite networks of discrete-time switched systems. Nonlinear Analysis Hybrid Systems (2022).
- Context-Triggered Abstraction-Based Control Design. IEEE Open Journal of Control Systems (2023).
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