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Abstract. This paper is devoted to the study of noise effects on blow-up solutions to stochastic nonlinear Schrödinger equations. It is a continuation of our recent work [2], where the (local) well-posedness is established in H 1 , also in the non-conservative critical case. Here we prove that in the non-conservative focusing mass-(super)critical case, by adding a large multiplicative Gaussian noise, with high probability one can prevent the blow-up on any given bounded time interval [0, T ], 0 < T < ∞. Moreover, in the case of spatially independent noise, the explosion even can be prevented with high probability on the whole time interval [0, ∞). The noise effects obtained here are completely different from those in the conservative case studied in [5].

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Contact mechanics plays an important role in the design, performance analysis, simulation, and control of legged robots. The Hunt-Crossley model and the Coulomb friction model are often used as black-box models with limited consideration of the properties of the terrain and the feet. This paper analyzes the foot-terrain interaction based on the knowledge of terramechanics and reveals the relationship between the parameters of the conventional models and the terramechanics models. The proposed models are derived in three categories: deformable foot on hard terrain, hard foot on deformable terrain, and deformable foot on deformable terrain. A novel model of tangential forces as the function of displacement is proposed on the basis of an in-depth understanding of the terrain properties. Methods for identifying the model parameters are also developed. Extensive foot-soil interaction experiments have been carried out, and the experimental results validate the high fidelity of the derived models.

Here is investigated the bilinear optimal control problem of quantum mechanical systems with final observation governed by a stochastic nonlinear Schrödinger equation perturbed by a linear multiplicative Wiener process. The existence of an open loop optimal control and first order Lagrange optimality conditions are derived, via Skorohod's representation theorem, Ekeland's variational principle and the existence for the linearized dual backward stochastic equation. Moreover, our approach in particular applies to the deterministic case.

In order to investigate wheel slip-sinkage problem, which is important for the design, control and simulation of lunar rovers, experiments were carried out with a wheel-soil interaction test system to measure the sinkage of three types of wheels in dimension with wheel lugs of different heights and numbers under a series of slip ratios (0−0.6). The curves of wheel sinkage versus slip ratio were obtained and it was found that the sinkage with slip ratio of 0.6 is 3−7 times of the static sinkage. Based on the experimental results, the slip-sinkage principle of lunar's rover lugged wheels (including the sinkage caused by longitudinal flow and side flow of soil, and soil digging of wheel lugs) was analyzed, and corresponding calculation equations were derived. All the factors that can cause slip sinkage were considered to improve the conventional wheel-soil interaction model, and a formula of changing the sinkage exponent with the slip ratio was established. Mathematical model for calculating the sinkage of wheel according to vertical load and slip ratio was developed. Calculation results show that this model can predict the slip-sinkage of wheel with high precision, making up the deficiency of Wong-Reece model that mainly reflects longitudinal slip-sinkage.