Infinite horizon forward–backward stochastic differential equations

AbstractA class of systems of infinite horizon forward–backward stochastic differential equations is investigated. Under some monotonicity assumptions, the existence and uniqueness results are established by means of a homotopy method. The global exponential asymptotical stability is also obtained. A comparison theorem is given

Physical configuration-based feedforward active noise control using adaptive second-order truncated Volterra filter

This paper presents a physical configuration-based feedforward active noise control scheme with an adaptive second-order truncated Volterra filter for point source cancellation in three-dimensional free-field acoustic environment. The inertial particle swarm optimization (PSO) algorithm is used as the parameter adjustment mechanism for tuning the coefficients of the adaptive Volterra filter. The first motivation of this paper is to provide a precise description of the relationship between the degree of cancellation and the physical distances between system components. The second motivation is to improve the cancellation performance in the presence of nonlinearities with the adaptive Volterra filter in light of the characteristics of sensing microphone and actuating loudspeaker. The reason for choosing the inertial PSO algorithm is that it can avoid the trap of local optima. The work thus presented makes two main contributions. The first is using the degree of cancellation as a function of the physical distances between system components to provide a quantitative analysis of system performance. The second is the application of the adaptive Volterra filter, which achieves improvements in the cancellation performance of the system under different physical configurations with a reasonable compromise with complexity. For consistency with the numerical analysis, several simulation experiments are conducted using MATLAB/Simulink

Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications

The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short). And as an example of the SMP, we solve a kind of forward-backward doubly stochastic linear quadratic optimal control problems as well. In the last section, we use the solution of FBDSDEs to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and open-loop Nash equilibrium point for nonzero sum differential games problem

Performance characteristics of a conceptual ring-shaped spar-type VLFS with double-layered perforated-wall breakwater

A ring-shaped spar-type Very Large Floating Structure (VLFS) is proposed as an intermediate base for supporting deepwater resource exploitation far away from the coast line. The proposed VLFS is composed of eight rigidly connected deep-draft spar-type modules and an inside harbor. A double-layered perforated-wall breakwater is vertically attached to the VLFS and pierces through the water surface to attenuate the wave energy in the inside harbor. The hydrodynamic performance characteristics of the ring-shaped VLFS was experimentally evaluated in the present study, focusing on the motion responses, wave elevations, and wave run-ups. The natural periods of the motions in vertical plane were determined to be larger than 40s, which is much larger than common wave periods. This enhanced the motion performance in vertical plane and afforded favorable habitation and operation condition on the VLFS. A large surge damping was induced by the vertical breakwater, which tended to significantly affect the surge and pitch motions, but had a negligible effect on the heave motion. The component frequencies of the wave elevations in the inside harbor and the wave run-ups were identical with those of the incident waves. The wave attenuation was frequency-dependent and effective for the common wave frequencies, with a smaller loss coefficient observed in higher sea state. The wave attenuation and wave run-ups tended to improve in the absence of the leeward walls

Arena: A Learning-based Synchronization Scheme for Hierarchical Federated Learning--Technical Report

Federated learning (FL) enables collaborative model training among distributed devices without data sharing, but existing FL suffers from poor scalability because of global model synchronization. To address this issue, hierarchical federated learning (HFL) has been recently proposed to let edge servers aggregate models of devices in proximity, while synchronizing via the cloud periodically. However, a critical open challenge about how to make a good synchronization scheme (when devices and edges should be synchronized) is still unsolved. Devices are heterogeneous in computing and communication capability, and their data could be non-IID. No existing work can well synchronize various roles (\textit{e.g.}, devices and edges) in HFL to guarantee high learning efficiency and accuracy. In this paper, we propose a learning-based synchronization scheme for HFL systems. By collecting data such as edge models, CPU usage, communication time, \textit{etc}., we design a deep reinforcement learning-based approach to decide the frequencies of cloud aggregation and edge aggregation, respectively. The proposed scheme well considers device heterogeneity, non-IID data and device mobility, to maximize the training model accuracy while minimizing the energy overhead. Meanwhile, the convergence bound of the proposed synchronization scheme has been analyzed. And we build an HFL testbed and conduct the experiments with real data obtained from Raspberry Pi and Alibaba Cloud. Extensive experiments under various settings are conducted to confirm the effectiveness of \textit{Arena}