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Motivated by some landslide models, and related estimation challenges, this paper presents an optimal estimation method for state and parameter in a special class of so-called ODE–PDE system based on the adjoint method for discrete-time asynchronous measurements. This system is described by a pair of coupled Ordinary Differential Equation (ODE) and Partial Differential Equation (PDE), with a mixed boundary condition for the PDE. The coupling appears both in the ODE and in the Neuman boundary condition of the PDE. For this system, initial conditions or state variables and some empirical parameters are assumed to be unknown and need to be estimated. The Lagrangian multiplier method is used to connect the dynamics of the system and the cost function defined as the least square error between the simulation values and the available measurements. The adjoint state method is applied to the objective functional to get the adjoint system and the gradients with respect to parameters and initial state. The cost functional is optimised, employing the steepest descent method to estimate parameters and initial state. This general approach is illustrated by two application examples corresponding to two different landslide models that validate the presented optimal estimation approach. The first one is about state and parameter estimation in an extended sliding-consolidation landslide model, and the second one is in the viscoplastic sliding-consolidation landslide model. [ABSTRACT FROM AUTHOR]

In this paper, the global sliding mode control technique is designed for anti-sway control of offshore crane mounted on surface vessel. The offshore cranes are responsible for moving containers from mega container ships to a smaller vessel. In this regard, after introducing the dynamics of the crane mounted on the surface vessel, the sliding surfaces and control laws are designed to maintain the stability of the system against external disturbances such as sea waves and wind induced movements. Furthermore, using the Lyapunov's stability analysis, it is proven that the position/velocity errors are converged to the origin. Finally, to determine the effectiveness of the proposed method, the simulation results of the global sliding mode control technique are compared to those of the continuous integral sliding mode control and proportional-integral-derivative approaches. The development of this procedure due to its high productivity and economic feasibility can be used as a new tool in the modern maritime industry. [ABSTRACT FROM AUTHOR]