A new paper published in Automatica presents a method for constructing data-driven symbolic abstractions for control systems using random exploration of finite-length trajectories. Titled 'Data-driven abstractions for control systems via random exploration,' the work is authored by Rudi Coppola, Andrea Peruffo, and Manuel Mazo from the Technical University of Delft.
The approach addresses challenges in building abstractions for systems where obtaining an accurate mathematical model is difficult or costly. By sampling trajectories from the unknown dynamics under random initial conditions, the method creates finite-state models suitable for verification and controller synthesis while providing statistical guarantees.
Understanding Symbolic Abstractions in Dynamical Systems
Symbolic abstractions simplify complex continuous or hybrid dynamical systems into discrete models that preserve key behaviors. These finite-state representations enable the application of formal methods from computer science to prove properties such as safety or reachability and to synthesize controllers that guarantee desired outcomes. Traditional abstraction techniques typically require a precise model of the system dynamics, including knowledge of functions describing state evolution. In many practical scenarios, such as robotics or process control, deriving or identifying these models demands significant resources and may not capture all uncertainties accurately.
The new research shifts the paradigm by relying solely on sampled data. Researchers collect finite sequences of inputs and outputs generated by running the system from randomly chosen starting states. This data-driven construction avoids explicit model identification while still yielding abstractions that support control design.
The Role of Random Exploration and Scenario Theory
Central to the method is the use of random sampling of initial states to generate independent trajectories. Scenario theory, a framework from statistical learning, provides Probably Approximately Correct (PAC) bounds on the quality of the resulting abstraction. These bounds quantify the probability that the abstraction correctly over-approximates the behaviors of the concrete system, with explicit dependence on the number of samples collected.
The authors introduce a probabilistic variant of alternating simulation relations. This relation ensures that controllers synthesized on the abstract model can be refined to controllers for the original system while preserving guarantees. The PAC properties hold for the horizon length corresponding to the sampled trajectories and, under additional mild assumptions such as Lipschitz continuity of the dynamics, can be extended to arbitrarily long horizons.
Key Technical Contributions and Guarantees
The paper focuses on deterministic control systems with finite input sets and unknown transition functions. By constructing Strongest Asynchronous ℓ-complete Abstractions from trajectory data, the approach captures memory-dependent behaviors through sequences of past inputs and outputs. This memory aspect proves essential for accurate control synthesis in black-box settings.
Extensive numerical benchmarks demonstrate the method on standard control examples, confirming that the generated abstractions support reach-avoid specifications with the predicted statistical confidence. The guarantees remain valid even when the underlying dynamics are nonlinear and only partially characterized.
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Implications for Formal Methods and Control Engineering
This development bridges gaps between data-driven machine learning techniques and rigorous formal verification. Engineers working on safety-critical systems can now derive certified controllers without investing in full system identification. The framework supports synthesis for specifications expressed in temporal logic or as reach-avoid problems, common in autonomous systems and cyber-physical applications.
Academic researchers in systems and control may find new avenues for extending these ideas to stochastic systems or output-feedback settings. The statistical nature of the guarantees aligns well with modern emphasis on robustness under uncertainty.
Connections to Broader Research Landscape
The work builds on prior contributions by the same authors on data-driven abstractions for verification tasks. It advances beyond one-step transition sampling by using full trajectories, thereby enabling longer-horizon properties without violating independence assumptions required by scenario optimization.
Related techniques in the literature include interval Markov decision processes and growth-rate estimation, yet the current method distinguishes itself through its focus on control synthesis and explicit PAC extension mechanisms.
Practical Considerations for Implementation
Deploying the approach involves selecting an appropriate trajectory length and sample count to achieve desired confidence levels. Computational complexity scales with the number of collected behaviors, but the finite nature of the resulting abstraction keeps subsequent controller synthesis tractable using standard graph algorithms.
Institutions with strong programs in control theory and formal methods are well positioned to incorporate these techniques into graduate curricula and research projects. The method's reliance on sampling rather than analytic models makes it particularly suitable for experimental platforms where dynamics are learned through interaction.
Future Directions and Open Questions
Extensions could address continuous input sets, partial observability, or integration with reinforcement learning for policy improvement. Combining the abstraction framework with online adaptation mechanisms represents another promising direction for handling time-varying systems.
As data-driven methods mature, the boundary between model-based and model-free control continues to blur, offering hybrid strategies that leverage both data and partial knowledge when available.
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Relevance for Academic and Research Careers
PhD candidates and postdoctoral researchers specializing in control systems or formal verification may explore this area for thesis topics or publications. Faculty positions in electrical engineering, mechanical engineering, and computer science departments increasingly value expertise at the intersection of data science and rigorous systems analysis.
Universities seeking to strengthen their research portfolios in cyber-physical systems or autonomous technologies can reference such advances when recruiting talent or forming interdisciplinary teams.
Access the original publication through the ScienceDirect abstract page or the open arXiv preprint. The authors' affiliation with TU Delft provides additional context on the institutional research environment supporting this line of inquiry.
