Multi-stage Neural Networks: Function Approximator of Machine Precision

Deep learning techniques are increasingly applied to scientific problems, where the precision of networks is crucial. Despite being deemed as universal function approximators, neural networks, in practice, struggle to reduce the prediction errors below $O(10^{-5})$ even with large network size and extended training iterations. To address this issue, we developed the multi-stage neural networks that divides the training process into different stages, with each stage using a new network that is optimized to fit the residue from the previous stage. Across successive stages, the residue magnitudes decreases substantially and follows an inverse power-law relationship with the residue frequencies. The multi-stage neural networks effectively mitigate the spectral biases associated with regular neural networks, enabling them to capture the high frequency feature of target functions. We demonstrate that the prediction error from the multi-stage training for both regression problems and physics-informed neural networks can nearly reach the machine-precision $O(10^{-16})$ of double-floating point within a finite number of iterations. Such levels of accuracy are rarely attainable using single neural networks alone.Comment: 38 pages, 17 page

Fault Diagnosis System Based on Multiagent Technique for Ship Power System

Fault diagnosis system of ship power system can assist the crew to deal with faults, shorten the processing time, and prevent faults expanding. Multiagent technique is adopted for the fault diagnosis system. Ship power system is divided into several feeder units. Each one is abstracted as a regional feeder agent (FED-Agent). A multiagent fault diagnosis system is established with FED-Agent and other functional agents. Considering of the characteristics of agent, the multiagent system processes both autonomy and interactivity. It can solve fault diagnosis problem of ship power system effectively

Design of a discrete tracking controller for a magnetic levitation system: A nonlinear rational model approach

This work proposes a discrete-time nonlinear rational approximate model for the unstable magnetic levitation system. Based on this model and as an application of the input-output linearization technique, a discrete-time tracking control design will be derived using the corresponding classical state space representation of the model. A simulation example illustrates the efficiency of the proposed methodology

A Three-Dimensional Cooperative Guidance Law of Multimissile System

In order to conduct saturation attacks on a static target, the cooperative guidance problem of multimissile system is researched. A three-dimensional guidance model is built using vector calculation and the classic proportional navigation guidance (PNG) law is extended to three dimensions. Based on this guidance law, a distributed cooperative guidance strategy is proposed and a consensus protocol is designed to coordinate the time-to-go commands of all missiles. Then an expert system, which contains two extreme learning machines (ELM), is developed to regulate the local proportional coefficient of each missile according to the command. All missiles can arrive at the target simultaneously under the assumption that the multimissile network is connected. A simulation scenario is given to demonstrate the validity of the proposed method

Prescribed Time Time-varying Output Formation Tracking for Uncertain Heterogeneous Multi-agent Systems

The time-varying output formation tracking for the heterogeneous multi-agent systems (MAS) is investigated in this paper. First, a distributed observer is constructed for followers to estimate the states of the leader, which can ensure that the estimation error converges to the origin in the prescribed time. Then, the local formation controller is designed for each follower based on the estimation of the observer, under which, the formation errors converge to the origin in the prescribed time as well. That is, the settling time of the whole system can be predefined in advance. It's noted that not only the uncertainties in the state matrix but also the uncertainties in the input matrix are considered, which makes the problem more practical. Last, a simulation is performed to show the effectiveness of the proposed approach

Design of a networked control system with random transmission delay and uncertain process parameters

This paper discusses the compensation of the transmission delay in a networked control system (NCS) with a state feedback, which possesses a randomly varying transmission delay and uncertain process parameters. The compensation is implemented by using a buffer in the actuator node and a state estimator in the controller node. A Linear Matrix Inequality (LMI) based sufficient condition for the stability of the NCS under the designed compensation is proposed. The simulation results illustrate the efficiency of the compensation method