Robust topology optimization of graphene platelets reinforced functionally graded materials considering hybrid bounded uncertainties

An efficient scheme for the robust topology optimization considering hybrid bounded uncertainties (RTOHBU) is proposed for the graphene platelets (GPLs) reinforced functionally graded materials (FGMs). By introducing the concept of the layer-wise FGMs, the properties of the GPLs reinforced FGMs are calculated based on the Halpin-Tsai micromechanics model. The practical boundedness of probabilistic variables is naturally ensured by utilizing a generalized Beta distribution in constructing the robust topology optimization model. To address the issue of lacking the information of critical loads in existing topology optimization approaches considering hybrid uncertainties, a gradient-attributed search is carried out at first based on the hypothesis of linear elasticity to determine the critical loads leading to the worst structural performance. Subsequently, the statistical characteristics of the objective structural performance under such critical loads are efficiently evaluated by integrating the univariate dimension reduction method and the Gauss-Laguerre quadrature, the accuracy of which is verified by the comparison analysis utilizing the results of Monte Carlo simulation as references. Furthermore, a novel realization vector set is constructed for the bounded probabilistic uncertainties to parallelize the sensitivity analysis and accelerate the optimization process. All the proposed innovations are integrated into the robust topology optimization scheme, the effectiveness and efficiency of which are verified by three illustrative examples.

Design of distributed functional interval observers for large-scale networks impulsive systems

In this paper, we consider the problem of designing distributed functional interval observers (IOs) for a class of large-scale networks impulsive systems with bounded uncertainties. We first design IOs for linear functions of the state vector of each system of the considered system. We then provide conditions for the existence of such IOs and an effective algorithm for computing unknown observer matrices. Finally, two examples and simulation results are given to illustrate the effectiveness of the proposed design method.

Prospects on Solving an Optimal Control Problem with Bounded Uncertainties on Parameters using Interval Arithmetics

An interval method based on the Pontryagin Minimum Principle is proposed to enclose the solutions of an optimal control problem with embedded bounded uncertainties. This method is used to compute an enclosure of all optimal trajectories of the problem, as well as open loop and closed loop enclosures meant to enclose a concrete system using an optimal control regulator with inaccurate knowledge of the parameters. The differences in geometry of these enclosures are exposed, as well as some applications. For instance guaranteeing that the given optimal control problem will yield a satisfactory trajectory for any realization of the uncertainties or on the contrary that the problem is unsuitable and needs to be adjusted.

Autonomous navigation in unknown environment using sliding mode SLAM and genetic algorithm

In this paper, sliding mode control is combined with the classical simultaneous localization and mapping (SLAM) method. This combination can overcome the problem of bounded uncertainties in SLAM. With the help of genetic algorithm, our novel path planning method shows many advantages compared with other popular methods.