Numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers

AbstractIn this paper we study different algorithms for reflected backward stochastic differential equations (BSDE in short) with two continuous barriers based on the framework of using a binomial tree to simulate 1-d Brownian motion. We introduce numerical algorithms by the penalization method and the reflected method, respectively. In the end simulation results are also presented

Bioinspired Coordinated Path Following for Vessels with Speed Saturation Based on Virtual Leader

This paper investigates the coordinated path following of multiple marine vessels with speed saturation. Based on virtual leader strategy, the authors show how the neural dynamic model and passivity-based techniques are brought together to yield a distributed control strategy. The desired path following is achieved by means of a virtual dynamic leader, whose controller is designed based on the biological neural shunting model. Utilizing the characteristic of bounded and smooth output of neural dynamic model, the tracking error jump is avoided and speed saturation problem is solved in straight path. Meanwhile, the coordinated path following of multiple vessels with a desired spatial formation is achieved through defining the formation reference point. The consensus of formation reference point is realized by using the synchronization controller based on passivity. Finally, simulation results validate the effectiveness of the proposed coordinated algorithm