This paper deals with the robust stabilization of infinite dimensional systems subjected to stochastic and deterministic perturbations. First, we give conditions providing the stability of the parameterized system. Then, we investigate the maximization of the stability radius by state feedback. We establish conditions for the existence of suboptimal controllers. Using these conditions we characterize the supreme achievable stability radius via an infinite dimensional Riccati equation.

Soil-structure interaction is the key to study the behavior of the structure under static or dynamic loading. The pile foundation is adopted to transfer the load from the structure to the soil when the structure is embedded in a weak soil stratum. Soil-pile system has a nonlinear behavior, thus, it is more complicated to understand. This study focuses on the numerical investigations of interaction soil–pile–structure system (ISPS) and interaction soil–pile system (ISP) under lateral loads. The nonlinear static analysis is carried out considering the lateral capacity of ISPS and ISP system under lateral loading using the pushover analysis, with a parametric study. The results show that in most cases, the lateral capacity of the fixed system is low compared to lateral capacity in ISPS system when increasing the axial load, pile diameter and length of the pile in all types of sand.

One of the main data-driven challenges when assessing bearing health is that training and test samples must be drawn from the same probability distribution. Indeed, it is difficult and almost rare to witness such a phenomenon in practical applications due to the constantly changing working conditions of rotating machines. In addition, collecting sufficient deterioration samples from the bearing life cycle is not possible due to the huge memory requirements and processing costs. As a result, accelerated life tests are believed to be the primary alternatives to such a situation. However, and unfortunately, the recorded samples always are subject to lack of real patterns. Therefore, in this paper, a transfer learning approach is performed to solve such kind of problem where PRONOSTICO dataset is used to assess the current procedures.

The issue of robustness of stability has been prominent in the literature on control theory over the last two decades. An important state-space approach to robustness analysis is the stability radii theory. The robust stability problems of infinite dimensional systems subjected to stochastic bounded structured perturbations have been studied using the stability radius approach. In the applications it is important to study these problems in the case where the perturbations operator structure are unbounded, because it covers the case of partial differential equations with boundary and ...

A wave equation in a bounded and smooth domain of Rnℝ with a delay term in the nonlinear boundary feedback is considered. Under suitable assumptions, global existence and uniform decay rates for the solutions are established. The proof of existence of solutions relies on a construction of suitable approximating problems for which the existence of the unique solution will be established using nonlinear semigroup theory and then passage to the limit gives the existence of solutions to the original problem. The uniform decay rates for the solutions are obtained by proving certain integral inequalities for the energy function and by establishing a comparison theorem which relates the asymptotic behavior of the energy and of the solutions to an appropriate dissipative ordinary differential equation.