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This paper investigates the dynamic positioning (DP) control problem of marine surface vessels (MSVs) suffering from external perturbations and input saturation. The linear Matrix Inequalities (LMI) based guaranteed cost control scheme is designed to obtain the satisfaction of the preset performance indicators. Aiming towards this purpose, the mathematical model of the MSV is first translated into a novel state-and-parameter-dependent (SPD) structure under small yaw angle variation. Furthermore, the performance indicator of the control scheme is derived for robustness against disturbances. With the application of LMI analysis method, the performance function will be transformed to a matrix inequality. Then, input saturation constraints are imposed to the control input, which will also be treated as a matrix inequality. Eventually, theoretical analysis shows that asymptotic stability will be endowed to the closed-loop system and input saturation constraints are also satisfied. Numerical simulation results are presented to demonstrate the advantage and validity of the proposed controller.

The complexity of near surface intensifies the diversity of seismic wave fields, which makes study on near surface wavefields important in many aspects. The strong absorption of low velocity layer can affect the resolution of seismic data, and free boundary can cause surface wave. Considering the above problems, we focus on the Rayleigh wavefields simulation using finite-difference wave equation of higher-order staggered grids and PML boundary conditions. Free boundary, buried source and overlying low velocity layer are taken into consideration and point explosion source is adopted. Through some numerical simulation with different parameters, we quantitatively analyze relationship between wave intensity and source depth, as well as the energy variation with propagation and obtain some practical knowledge and conclusions.

The stability problem is a very important aspect in seismic wave numerical modeling. Based on the theory of seismic waves and constitutive equations of viscoelastic models, the stability problems of finite difference scheme for Kelvin-Voigt and Maxwell models with rectangular grids are analyzed. Expressions of stability conditions with arbitrary spatial accuracies for two viscoelastic models are derived. With approximation of quality factor Q≥5, simplified expressions are developed and some numerical models are given to verify the validity of the corresponding theoretical results. Then this paper summarizes the influences of seismic wave velocity, frequency, size of grid and difference coefficients, as well as quality factor on stability condition. Finally the prerequisite conditions of the simplified stability equations are given with error analysis.