One approach to data-driven control is proposed as a method based on Data Informativity. This approach is formulated based on the idea of Data Informativity that a system consistent with data has desirable properties. In the Data Informativity framework, one of the main problems is the analytical problem of determining the conditions of the data on which the controller is to be designed. In the analysis problem, it is assumed that the order of the dynamic characteristics (the dimension of the system) is equal to the dimension of the space in which the data is defined. Therefore, the analysis cannot be applied when the data size is different from the dimension of the model. In this report, we address the problem of finding conditions of data for the determination of modes (poles and their multiple degrees) in the Data Informativity framework, without assuming an equidimensionality condition between the order of the dynamic characteristics (dimension of the system) and the dimension of the space in which the data is defined. The method of polynomial representation, which is theoretically organized in model-based control, is incorporated into the Data Informativity framework.

This paper investigates two mathematical models of the glucose-insulin dynamics for type 1 diabetes mellitus. In particular, we propose two switched models, which are the linear switched model and the bilinear switched model. The switching parameters, which give significant effects to the resulting time responses of the switched systems, are determined by using the metabolic parameters of each subject. The time responses of the proposed switched models are evaluated by comparing with the one that is obtained from the UVA/Padova model, which is accepted by the United States Food and Drug Administration as a substitute to animal trials for the pre-clinical testing. As a validation, the metabolic parameters of ten subjects are used to evaluate the resulting glucose time responses.

In this paper, we propose a quantized stabilization method for unknown discrete-time linear systems with uncertainty. In previous studies, the coarsest logarithmic quantizer design has been given for unknown linear systems using direct data-driven control method. However, in real linear systems, the closed-loop system may become unstable due to the perturbation of the system parameters caused by changes in the environment or aging. In this paper, we extend the logarithmic quantizer design for linear systems with uncertainty to take account of such uncertainties, which may not be reflected in the original system data. We illustrate the effectiveness of the method through numerical simulations.

This paper proposes a data-driven method to approximate stable manifolds in forwarding design. A control law designed with forwarding includes functions describing stable manifolds and their partial derivatives. In order to consider the approximation of partial derivatives, the proposed method constructs neural networks that fit the training data and also satisfy certain differential equations characterizing stable manifolds. We define a loss function suitable for this purpose based on the idea of Physics-Informed Neural Networks. A computational algorithm for learning with the proposed loss function is accordingly derived. The effectiveness of the proposed method is confirmed by application to an input-constrained nonlinear control for a planar quadrotor.