In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary orderN∈ ℕ on a bounded 1-dimensional spatial domain (a,b). In order to achieve stabilization, we couple the system to a dynamic boundary controller, that is, a controller that acts on the system only via the boundary pointsa,bof the spatial domain. We use a nonlinear controller in order to capture the nonlinear behavior that realistic actuators often exhibit and, moreover, we allow the output of the controller to be corrupted by actuator disturbances before it is fed back into the system. What we show here is that the resulting nonlinear closed-loop system is input-to-state stable w.r.t. square-integrable disturbance inputs. In particular, we obtain uniform input-to-state stability for systems of orderN= 1 and a special class of nonlinear controllers, and weak input-to-state stability for systems of arbitrary orderN∈ ℕ and a more general class of nonlinear controllers. Also, in both cases, we obtain convergence to 0 of all solutions ast→∞. Applications are given to vibrating strings and beams.

We establish the local input-to-state stability of a large class of disturbed nonlinear reaction–diffusion equations w.r.t. the global attractor of the respective undisturbed system.

Systematic decision making in engineering requires appropriate models. In this article, we introduce a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity constraints. Incorporating such information is particularly useful when the available datasets are small or do not cover the entire input space, as is often the case in manufacturing applications. We set up the regression subject to the considered monotonicity constraints as a semi-infinite optimization problem, and propose an adaptive solution algorithm. The method is applicable in multiple dimensions and can be extended to more general shape constraints. It was tested and validated on two real-world manufacturing processes, namely, laser glass bending and press hardening of sheet metal. It was found that the resulting models both complied well with the expert’s monotonicity knowledge and predicted the training data accurately. The suggested approach led to lower root-mean-squared errors than comparative methods from the literature for the sparse datasets considered in this work.

We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee–Infante equations, for example.