Taira Kaminaga

Taira Kaminaga, Hampei Sasahara

Matrix ellipsoids provide a standard framework for representing bounded uncertainties in data-driven control. Since noise models for sequential observations are naturally represented as the Minkowski sum of multiple matrix ellipsoids, applying existing robust control methods, which typically assume a single ellipsoidal set, requires a tight outer approximation. While techniques based on linear matrix inequalities (LMI) are applicable, their computational cost grows quadratically with the data length, limiting their scalability. This paper investigates the optimal outer approximation problem under two criteria: the sum of squared semi-axes and the volume. We propose an LMI-free approach by introducing a parameterized family of bounding matrix ellipsoids. Specifically, we derive an exact analytical solution for the first criterion and develop an efficient majorization-minimization (MM) algorithm for the second. The proposed MM algorithm employs a first-order approximation of the log-determinant function to provide closed-form update rules, ensuring monotonic convergence to the set of stationary points. Numerical experiments demonstrate that our method offers significantly higher computational efficiency and scalability than standard interior-point solvers.

Taira Kaminaga, Hampei Sasahara

Data informativity provides a theoretical foundation for determining whether collected data are sufficiently informative to achieve specific control objectives in data-driven control frameworks. In this study, we investigate the data informativity subject to noise characterized by quadratic matrix inequalities (QMIs), which describe constraints through matrix-valued quadratic functions. We introduce a generalized noise model, referred to as data perturbation, under which we derive necessary and sufficient conditions formulated as tractable linear matrix inequalities for data informativity with respect to stabilization and performance guarantees via state feedback, as well as stabilization via output feedback. Our proposed framework encompasses and extends existing analyses that consider exogenous disturbances and measurement noise, while also relaxing several restrictive assumptions commonly made in prior work. A central challenge in the data perturbation setting arises from the non-convexity of the set of systems consistent with the data, which renders standard matrix S-procedure techniques inapplicable. To resolve this issue, we develop a novel matrix S-procedure that does not rely on convexity of the system set by exploiting geometric properties of QMI solution sets. Furthermore, we derive sufficient conditions for data informativity in the presence of multiple noise sources by approximating the combined noise effect through the QMI framework. The proposed results are broadly applicable to a wide class of noise models and subsume several existing methodologies as special cases.

Taira Kaminaga, Hampei Sasahara

Assessing data informativity, determining whether the measured data contains sufficient information for a specific control objective, is a fundamental challenge in data-driven control. In noisy scenarios, existing studies deal with system noise and measurement noise separately, using quadratic matrix inequalities. Moreover, the analysis of measurement noise requires restrictive assumptions on noise properties. To provide a unified framework without any restrictions, this study introduces data perturbation, a novel notion that encompasses both existing noise models. It is observed that the admissible system set with data perturbation does not meet preconditions necessary for applying the key lemma in the matrix S-procedure. Our analysis overcomes this limitation by developing an extended version of this lemma, making it applicable to data perturbation. Our results unify the existing analyses while eliminating the need for restrictive assumptions made in the measurement noise scenario.