Data-Driven Output Feedback Control for Unknown Piecewise Affine Systems

No prior work had resolved how to stabilize unknown piecewise affine systems without explicit subsystem models. Researchers often struggle to maintain stability when system dynamics switch unexpectedly between different operating regimes. Traditional control strategies frequently rely on precise mathematical descriptions that are difficult to obtain for complex industrial processes. This gap motivated the development of techniques that utilize raw operational data instead of structural equations. Prior research has shown that data-driven methods offer a flexible alternative for managing uncertain dynamical environments. That uncertainty drove the need for robust frameworks capable of handling switching behaviors directly from observations. Existing literature highlights the difficulty of ensuring stability across multiple modes using limited information. This study addresses these limitations by proposing a framework that operates directly on input and output measurements.

The aim of this study is to design controllers that exponentially stabilize unknown piecewise affine systems using data-driven techniques. Researchers seek to overcome the reliance on explicit subsystem models that often hinder control implementation. The project addresses the challenge of managing systems that switch between different operational modes based on state or input conditions. By leveraging input-state-output or input-output data, the authors develop a representation that facilitates controller synthesis. The work specifically targets the reduction of conservativeness through the integration of partition information. Furthermore, the study explores how to accommodate switching dynamics without requiring a single long persistently exciting trajectory. The authors also investigate the necessity of a left coprime condition for ensuring controllability in input-output scenarios. This research provides a systematic approach to stabilizing complex systems through direct observation.

The authors utilize a data-dependent representation to model the unknown dynamics. Their review approach involves synthesizing controllers based on either input-state-output or input-output measurements. The design process integrates partition information to refine the operational boundaries of the system. Multiple datasets are processed to capture the switching behavior inherent in the target dynamics. The researchers apply multiple Lyapunov functions to verify the stability of the resulting control laws. A left coprime condition is introduced to ensure controllability when state measurements are missing. Three numerical examples serve to validate the performance of the proposed synthesis technique. This methodology provides a structured framework for managing uncertainty through observed system responses.

The proposed method successfully achieves exponential stabilization for piecewise affine systems without relying on explicit subsystem models. The synthesis process effectively incorporates partition information to lower the level of conservativeness in the controller. By utilizing multiple datasets, the researchers avoid the necessity for a single long persistently exciting trajectory. The left coprime condition ensures controllability when the system relies solely on input and output data. Three distinct examples demonstrate the practical effectiveness of this data-driven approach. The results confirm that the controller maintains stability across different switching modes. The framework performs reliably regardless of whether state measurements are fully available or restricted. These findings indicate that the approach is robust for unknown dynamical systems.

The researchers demonstrate that piecewise output feedback controllers successfully stabilize unknown systems using only measured data. Their synthesis relies on multiple Lyapunov functions to ensure exponential stability across all operational modes. By incorporating partition information, the design reduces the inherent conservativeness found in previous control approaches. The authors show that using multiple datasets effectively manages the switching nature of these systems. This strategy avoids the requirement for a single long trajectory of persistently exciting data. The left coprime condition provides a necessary guarantee for controllability when only input and output observations are available. These findings suggest that data-driven techniques are viable for complex systems lacking explicit models. The proposed method offers a practical pathway for implementing stable control in uncertain environments.