Robust data-driven state-feedback design (1909.04314v3)

Abstract: We consider the problem of designing robust state-feedback controllers for discrete-time linear time-invariant systems, based directly on measured data. The proposed design procedures require no model knowledge, but only a single open-loop data trajectory, which may be affected by noise. First, a data-driven characterization of the uncertain class of closed-loop matrices under state-feedback is derived. By considering this parametrization in the robust control framework, we design data-driven state-feedback gains with guarantees on stability and performance, containing, e.g., the $\mathcal{H}_\infty$-control problem as a special case. Further, we show how the proposed framework can be extended to take partial model knowledge into account. The validity of the proposed approach is illustrated via a numerical example.

• The paper proposes a novel framework to design robust state-feedback controllers directly from noisy measurement data without requiring explicit system identification.
• It establishes robust stability and quadratic performance guarantees using linear matrix inequalities (LMIs), demonstrating computational tractability.
• This data-driven approach is particularly valuable for control applications with partial or noisy data, enabling adaptable real-time system management.

Robust Data-Driven State-Feedback Design: A Formal Overview

The paper "Robust data-driven state-feedback design" investigates the construction of robust state-feedback controllers directly derived from measured data, specifically for discrete-time linear time-invariant (LTI) systems. This innovative approach utilizes open-loop data trajectories without relying on traditional model identification methods, an attribute that provides significant practical value in scenarios where complete knowledge of system dynamics is unavailable or unreliable. Employing a single data trajectory affected by noise, the authors propose a novel framework that integrates robust control techniques with data-driven system representation.

Data-Driven System Characterization

At the core of this research is the data-driven characterization of uncertain closed-loop matrices under state-feedback. This process begins with a unique parametrization based on a single trajectory of measured data. The proposed method effectively circumvents the necessity for full system identification by leveraging a data-driven representation inspired by behavioral systems theory, notably drawing from Willems' fundamental results on systems' trajectory space. The authors extend these ideas to encapsulate uncertain system classes that arise when data is contaminated by noise, thereby allowing the derivation of control solutions with predefined stability and performance guarantees.

Stability and Performance Guarantees

A significant contribution of the paper is the establishment of robust state-feedback gains guaranteeing system stability. Through strategic application of known robust control methodologies, the authors demonstrate how controllers can be tailored directly from noisy data. Furthermore, they provide conditions under which these controllers can ensure the desired quadratic performance benchmarks for systems with uncertainties. This approach includes the consideration of $\mathcal{H}_\infty$ and strict passivity criteria, showcasing the versatility of the framework in handling various control specifications.

The solution to these robust design problems is facilitated by linear matrix inequalities (LMIs), providing computational tractability. The feasibility of these LMIs, however, is sensitive to the richness and length of the available data. The authors note that persistence of excitation enhances the robustness of the solution, though robust guarantees can still be attained under less ideal conditions where state data are not persistently exciting.

Practical Implications and Applications

The practical implications of this methodology are considerable. By removing the dependency on precise model identification, the design process ameliorates challenges faced in environments with partial or noisy data representations. This advancement is particularly relevant in fields where rapid adaptability to new data is crucial, such as adaptive control systems, automated process adjustments, and real-time system management. The application in control scenarios with mixed data-driven and model-based components further highlights the potential for integrating existing model knowledge with freshly acquired data to refine control strategies.

Future Directions

The authors acknowledge the need for extension into output-feedback scenarios, suggesting that the propagation of data-driven techniques into broader control structures could open new avenues for system management without exhaustive model elucidation. Additionally, incorporating stochastic data considerations could refine the application of their framework in even more uncertain environments. Insights garnered here might streamline real-time optimization and adaptive learning in autonomous systems, especially where sensor data must be interpreted on-the-fly.

The paper contributes meaningfully to the literature by presenting a coherent and rigorous approach to leveraging measured data for robust control design. This work lays a foundation for subsequent exploration and methodological refinement, potentially harmonizing data-driven control with traditional model-based strategies to yield flexible, resilient control designs adaptable to practical uncertainties.