In this paper we investigate a class of combined discrete-continuous mechanical systems consisting of a continuous elastic structure and a finite number of concentrated masses, elastic supports, and linear oscillators of arbitrary dimension. After the motion equations for such combined systems are derived, they are formulated as an abstract evolution equation on an appropriately defined Hilbert space. Our main objective is to ascertain conditions under which the combined systems have classical normal modes. Using the sesquilinear form approach, we show that unless some matching conditions are satisfied, the combined systems cannot have normal modes even if Kelvin-Voigt damping is considered.

In order to build an accurate and effective model, simulation of driver behavior is absolutely essential for the development of advanced driver assistance systems and the current assessment of vehicle handling stability. The purpose of the proposed active steering control is to assist the driver to follow the desired path, especially in situations of the vehicle under strong external disturbance, distracted driver, or other unforeseen circumstances that can cause deviations. Based on the preview optimal simple artificial neural network driver model, an active steering system using general predictive control method is established. In order to improve the path-following capability of vehicles under disturbances, a general predictive controller, with the deviation between the vehicles’ actual and desired lateral positons as inputs and with the corrective steering wheel angle as outputs, is developed to follow the desired path. Meanwhile, adapting recursion least square method with the forgetting factor to estimate the parameters of the controlled auto-regressive and integrated moving average model of the vehicle is designed. The proposed vehicle path-following control system is evaluated in some typical conditions (e.g. under strong crosswind condition in standard double-lane-change, etc.). Simulation results and analysis have verified that this new vehicle path-following strategy, given by general predictive controller, is capable of capturing driver’s steering behavior and the amended driver steering angle can improve the dynamic performance of vehicle under some external disturbances.

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We propose a navigation system for transcatheter aortic valve implantation that employs a magnetic tracking system (MTS) along with a dynamic aortic model and intra-operative ultrasound (US) images. This work is motivated by the desire of our cardiology and cardiac surgical colleagues to minimize or eliminate the use of radiation in the interventional suite or operating room. The dynamic 3-D aortic model is constructed from a preoperative 4-D computed tomography dataset that is animated in synchrony with the real time electrocardiograph input of patient, and then preoperative planning is performed to determine the target position of the aortic valve prosthesis. The contours of the aortic root are extracted automatically from short axis US images in real-time for registering the 2-D intra-operative US image to the preoperative dynamic aortic model. The augmented MTS guides the interventionist during positioning and deployment of the aortic valve prosthesis to the target. The results of the aortic root segmentation algorithm demonstrate an error of 0.92±0.85 mm with a computational time of 36.13±6.26 ms. The navigation approach was validated in porcine studies, yielding fiducial localization errors, target registration errors, deployment distance, and tilting errors of 3.02±0.39 mm, 3.31±1.55 mm, 3.23±0.94 mm, and 5.85±3.06(°) , respectively.