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    This study introduces a data-driven safe tracking control for stochastic systems, ensuring high-probability safety and stability. The novel approach uses probabilistic set-based contractivity and a reference governor for reliable performance.

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    Area of Science:

    • Control Systems Engineering
    • Stochastic Systems Analysis
    • Data-Driven Control

    Background:

    • Stochastic linear discrete-time systems require robust control for safe operation.
    • Ensuring safety and stability in tracking control is a significant challenge.
    • Existing methods may not adequately handle system uncertainties and safety constraints.

    Purpose of the Study:

    • To design a high-confidence, data-driven safe tracking control for stochastic linear discrete-time systems.
    • To formalize safe reference tracking using probabilistic set-based $\lambda $-contractivity.
    • To develop a controller that guarantees safety and stability with high probability.

    Main Methods:

    • Formalization of safe tracking using probabilistic set-based $\lambda $-contractivity.
    • Design of a data-driven controller with learned feedback and feedforward gains.
    • Implementation of a data-driven reference governor for dynamic reference signal manipulation.
    • Optimization of a decision variable for feedback gain learning, even with limited data.

    Main Results:

    • The developed controller enforces $\lambda $-contractivity of the safe set.
    • High-probability safety and stability are guaranteed under specific equilibrium conditions.
    • The reference governor ensures safety by adjusting reference signals based on data quality.
    • The system output converges to goal states while maintaining safety.

    Conclusions:

    • The data-driven safe tracking control effectively ensures system safety and stability with high confidence.
    • The approach outperforms certainty-equivalent safe control methods, as shown in simulations.
    • This method offers a robust solution for safe tracking in stochastic systems using data-driven techniques.