Scenario-Based Robust Controller Design | #sciencefather #database #scientistaward #RobustControl #TrajectoryData
Data-Driven Control with Generalization Guarantees Across Probabilistic System Variations
Modern control systems often operate in uncertain and variable environments, where the system dynamics may vary due to manufacturing tolerances, environmental changes, or load variations. Traditional robust control assumes prior knowledge of these variations and builds conservative models to account for them. However, this assumption does not hold in many real-world scenarios, especially when deploying the same controller across a fleet of similar but non-identical systems, such as drones, autonomous vehicles, or wind turbines. To address this, we present a probabilistic data-driven control approach that relies on trajectory data collected from multiple system instances rather than a nominal model. The goal is to synthesize a single controller that stabilizes all such variations with high probability.
Problem Setup and Probabilistic Formulation
We consider a discrete-time linear time-invariant system with dynamics influenced by random variables representing system uncertainty. Unlike classic deterministic systems, the system matrices (A, B) are drawn from an unknown distribution, introducing aleatoric uncertainty. The control objective is to design a state-feedback controller based on finite, noisy trajectory data sampled from several i.i.d. realizations of the probabilistic system. The key challenge lies in guaranteeing closed-loop stability for new, unseen variations drawn from the same distribution, despite having no explicit knowledge of the underlying system parameters or distributions.
Scenario-Based Controller Synthesis
To tackle this challenge, we leverage the scenario approach—a powerful probabilistic tool that enables decision-making under uncertainty using finite data. Each observed trajectory from a system variant is treated as a scenario. By solving a constrained optimization problem over these scenarios, we derive a state-feedback controller that satisfies stability constraints with high probability. The main advantage is that we obtain probabilistic guarantees on controller performance without requiring a full model or distribution of the uncertainty. This framework also naturally extends existing results from robust and data-driven control, combining them in a unified setting.
Data Informatively and Controller Design
The concept of data informatively is central to ensuring that the collected trajectories contain sufficient information to synthesize a stabilizing controller. We extend the notion of informatively to a probabilistic setting and define conditions under which a dataset is informative for quadratic stabilization. These conditions are translated into linear matrix inequalities (LMIs), which can be solved efficiently to obtain a feedback gain. Unlike conventional formulations that focus on a single trajectory, our method simultaneously considers multiple trajectories from different system variants. This enables the synthesis of controllers that generalize across system realizations, ensuring broader applicability.
Robustness to System Variations
While previous direct data-driven control methods focus on robustness to noise and disturbances, they often assume a fixed, though unknown, system. In contrast, our method explicitly addresses variability in system dynamics by considering each trajectory as stemming from a distinct system instance. The robustness achieved is therefore not only to process noise but also to system variation—essential for applications where the controller is expected to work across a population of systems rather than a single instance.
Applications and Practical Implications
The proposed method is particularly relevant in settings where individual system modeling is infeasible, and large-scale deployment of identical controllers is necessary. Examples include fleets of delivery drones, satellite swarms, robotic agricultural systems, and modular power converters in renewable energy systems. By reusing trajectory data across these variants, the method reduces the cost and complexity of controller deployment. It also provides a safe and efficient way to bootstrap more sophisticated learning algorithms, such as reinforcement learning, by ensuring initial stability through a reliable baseline controller.
We have introduced a data-driven control methodology capable of synthesizing a robust state-feedback controller using data from a distribution of system variants. The use of the scenario approach offers theoretical guarantees and practical efficiency, making it suitable for real-world systems subject to stochastic variability. Future work may extend this framework to nonlinear systems, integrate adaptive learning over time, or combine it with model predictive control for improved performance and constraint handling.
#DataDrivenControl #RobustControl #LearningBasedControl #ProbabilisticSystems #TrajectoryData #ControlTheory #SystemUncertainty #ScenarioApproach #StateFeedback #StochasticSystems #Informativity #GeneralizationInControl #AIinControlSystems #AutonomousSystems #ControllerSynthesis
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