Input-Output Data-Driven Safe Control of Unknown Discrete-Time Linear Systems

This paper presents a data-driven quadratically constrained quadratic program for designing safe and stable controllers using only input-output measurements. Input-output-based control Lyapunov functions (CLFs) and control barrier functions (CBFs) are integrated to derive safe and stable control inputs for discrete-time linear systems with unknown system dynamics. An augmented system is formed using historical input-output measurements and is leveraged to formalize learning of data-driven CLFs and CBFs. In sharp contrast to existing data-driven results in the literature, the presented approach does not require the restrictive assumption of availability of the full system’s state for measurement, which broadens its applicability. Conditions under which the resulting CBF-CLF optimization is convex are outlined, and an interior-point method is presented to handle non-convexities arising from some choices of CBFs. In convex scenarios, closed-form expressions for control inputs are derived. Two special cases that lead to a convex optimization, i.e., systems with a scalar control input and systems with a compact safe set, are thoroughly analyzed. The computational complexity of the proposed interior-point method is discussed and its efficacy is validated through simulations and real-world experiments with mobile robots. Two scenarios are explored: a nonholonomic differential-drive mobile robot and a holonomic mobile robot equipped with Mecanum wheels. Simulations demonstrate the framework’s capability to handle nonlinear constraints, while experiments on the ROSbot XL with Mecanum wheels, highlight its computational efficiency, practical applicability, and effectiveness in ensuring safety and stability in real-world environments. Note to Practitioners—Ensuring safety is paramount in safety-critical systems such as robotics, autonomous vehicles, and industrial automation, where operations in uncertain environments can lead to costly delays, equipment damage, or even harm to human operators. Although designing controllers for such systems typically requires comprehensive knowledge of system dynamics, acquiring an exact model is often challenging due to inherent uncertainties and disturbances. Data-driven control offers a solution by enabling the design of controllers directly from data, circumventing the need for complete dynamic models. In many real-world applications, collecting comprehensive state data is impractical; we often have access only to a subset of the system’s states. To address this limitation, we propose designing safe and stable control inputs using only input-output measurements. Leveraging a quadratic control barrier function, our method accommodates a wide array of safety constraints, including both linear and quadratic forms. This reliance on readily available input-output data simplifies control design, allowing engineers to develop effective controllers without the laborious process of constructing detailed models. This approach not only facilitates faster deployment and easier adaptation to changes but also simplifies the implementation process. Future work will focus on extending the method to handle complex, nonlinear stochastic systems.