Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

This paper presents a novel fixed-time stabilization control(FSC)method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics.The key feature of the proposed method is the design of two dynamic parameters.Specifically,a set of auxiliary variables is first introduced through state transformation.These variables combine the original system states and the two introduced dynamic parameters,facilitating the closed-loop system stability analyses.Then,the two dynamic parameters are delicately designed by utilizing the Lyapunov method,ensuring that all the closed-loop system states are globally fixed-time stable.Compared with existing results,the“explosion of complexity”problem of backstepping control is avoided.Moreover,the two designed dynamic parameters are dependent on system states rather than a time-varying function,thus the proposed controller is still valid beyond the given fixedtime convergence instant.The effectiveness of the proposed method is demonstrated through two practical systems.

A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation equations.Firstly,to reduce the complexity of solving the meanfield game,a limiting control problem is introduced.By virtue of the decomposition approach,an admissible control set is proposed.Applying a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also addressed.Secondly,we discuss an approximate Nash equilibrium property of the decentralized control strategy.Finally,we work out a financial problem with some numerical simulations.

Deterministic Learning-Based Neural PID Control for Nonlinear Robotic Systems

Traditional proportional-integral-derivative(PID)controllers have achieved widespread success in industrial applications.However,the nonlinearity and uncertainty of practical systems cannot be ignored,even though most of the existing research on PID controllers is focused on linear systems.Therefore,developing a PID controller with learning ability is of great significance for complex nonlinear systems.This article proposes a deterministic learning-based advanced PID controller for robot manipulator systems with uncertainties.The introduction of neural networks(NNs)overcomes the upper limit of the traditional PID feedback mechanism’s capability.The proposed control scheme not only guarantees system stability and tracking error convergence but also provides a simple way to choose the three parameters of PID by setting the proportional coefficients.Under the partial persistent excitation(PE)condition,the closed-loop system unknown dynamics of robot manipulator systems are accurately approximated by NNs.Based on the acquired knowledge from the stable control process,a learning PID controller is developed to further improve overall control performance,while overcoming the problem of repeated online weight updates.Simulation studies and physical experiments demonstrate the validity and practicality of the proposed strategy discussed in this article.

Intelligent Fault Diagnosis Method of Rolling Bearings Based on Transfer Residual Swin Transformer with Shifted Windows

Due to their robust learning and expression ability for complex features,the deep learning(DL)model plays a vital role in bearing fault diagnosis.However,since there are fewer labeled samples in fault diagnosis,the depth of DL models in fault diagnosis is generally shallower than that of DL models in other fields,which limits the diagnostic performance.To solve this problem,a novel transfer residual Swin Transformer(RST)is proposed for rolling bearings in this paper.RST has 24 residual self-attention layers,which use the hierarchical design and the shifted window-based residual self-attention.Combined with transfer learning techniques,the transfer RST model uses pre-trained parameters from ImageNet.A new end-to-end method for fault diagnosis based on deep transfer RST is proposed.Firstly,wavelet transform transforms the vibration signal into a wavelet time-frequency diagram.The signal’s time-frequency domain representation can be represented simultaneously.Secondly,the wavelet time-frequency diagram is the input of the RST model to obtain the fault type.Finally,our method is verified on public and self-built datasets.Experimental results show the superior performance of our method by comparing it with a shallow neural network.

Adaptive Attitude Control for a Coaxial Tilt-Rotor UAV via Immersion and Invariance Methodology

Dear Editor,This letter is concerned with the attitude control for a novel tiltrotor unmanned aerial vehicle with two pairs of tiltable coaxial rotors and one rear rotor.An immersion and invariance-based adaptive attitude controller for the tilt-rotor unmanned aerial vehicle is proposed.In the proposed control strategy,an adaptive update law is specially designed to compensate for the uncertainties of damping coefficients.The stability of the resulting closed-loop coaxial tiltrotor unmanned aerial vehicle(CTRUAV)system is proved by the Lyapunov methodology and LaSalle’s invariance theory.Finally。

Dust Distribution Study at the Blast Furnace Top Based on k-Sε-u_(p)Model

The dust distribution law acting at the top of a blast fumace(BF)is of great significance for understanding gas flow distribution and mitigating the negative influence of dust particles on the accuracy and service life of detection equipment.The harsh environment inside a BF makes it difficult to describe the dust disthibution.This paper adresses this problem by proposing a dust distribution k-Sε-u_(p)model based on interphase(gas-powder)coupling.The proposed model is coupled with a k-Sεmodel(which describes gas flow movement)and a u_(p)model(which depicts dust movement).First,the kinetic energy equation and turbulent dissipation rate equation in the k-Sεmodel are established based on the modeling theory and single Green-function two scale direct interaction approximation(SGF-TSDIA)theory.Second,a dust particle mnovement u_(p)model is built based on a force analysis of the dust and Newton's laws of motion.Finally,a coupling factor that descibes the interphase interaction is proposed,and the k-Sε-u_(p)model,with clear physical meaning.ligorous mathematical logic,and adequate generality,is dleveloped.Siumulation results and o-site verification show that the k-Sε-u_(p)model not only has high precision,but also reveals the aggregate distribution features of the dust,which are helpful in optimizing the installation position of the detection equipment and imnproving its accuracy and service life.

Variational Inference Based Kernel Dynamic Bayesian Networks for Construction of Prediction Intervals for Industrial Time Series With Incomplete Input

Prediction intervals(PIs)for industrial time series can provide useful guidance for workers.Given that the failure of industrial sensors may cause the missing point in inputs,the existing kernel dynamic Bayesian networks(KDBN),serving as an effective method for PIs construction,suffer from high computational load using the stochastic algorithm for inference.This study proposes a variational inference method for the KDBN for the purpose of fast inference,which avoids the timeconsuming stochastic sampling.The proposed algorithm contains two stages.The first stage involves the inference of the missing inputs by using a local linearization based variational inference,and based on the computed posterior distributions over the missing inputs the second stage sees a Gaussian approximation for probability over the nodes in future time slices.To verify the effectiveness of the proposed method,a synthetic dataset and a practical dataset of generation flow of blast furnace gas(BFG)are employed with different ratios of missing inputs.The experimental results indicate that the proposed method can provide reliable PIs for the generation flow of BFG and it exhibits shorter computing time than the stochastic based one.

Knowledge-Guided Data-Driven Model With Transfer Concept for Battery Calendar Ageing Trajectory Prediction

Dear Editor, Lithium-ion(Li-ion) battery has become a promising source to supply and absorb energy/power for many energy-transportation applications. However, Li-ion battery capacity would inevitably degrade over time, making its related ageing prediction necessary.

Distributed Cooperative Learning for Discrete-Time Strict-Feedback Multi Agent Systems Over Directed Graphs

This paper focuses on the distributed cooperative learning(DCL)problem for a class of discrete-time strict-feedback multi-agent systems under directed graphs.Compared with the previous DCL works based on undirected graphs,two main challenges lie in that the Laplacian matrix of directed graphs is nonsymmetric,and the derived weight error systems exist n-step delays.Two novel lemmas are developed in this paper to show the exponential convergence for two kinds of linear time-varying(LTV)systems with different phenomena including the nonsymmetric Laplacian matrix and time delays.Subsequently,an adaptive neural network(NN)control scheme is proposed by establishing a directed communication graph along with n-step delays weight updating law.Then,by using two novel lemmas on the extended exponential convergence of LTV systems,estimated NN weights of all agents are verified to exponentially converge to small neighbourhoods of their common optimal values if directed communication graphs are strongly connected and balanced.The stored NN weights are reused to structure learning controllers for the improved control performance of similar control tasks by the“mod”function and proper time series.A simulation comparison is shown to demonstrate the validity of the proposed DCL method.

Barrier Lyapunov Function-Based Finite-Time Dynamic Surface Control for Output-Constrained Nonstrict-Feedback Systems

This paper investigates a finite-time tracking problem for the uncertainty nonlinear systems in nonstrict-feedback form,in which the output signal is restricted in a region.Based on the barrier Lyapunov function and dynamic surface control scheme,a novel adaptive neural controller is proposed by using the finite-time Lyapunov technology.Unlike the aforementioned literature on finite time tracking control,the violation of system output constraint is avoided by combining the barrier Lyapunov function method with finite-time theory.The structural characteristics of neural network is introduced to expand the adaptive neural finite-time backstepping method to the uncertainty nonlinear systems in the non-strict form.Correspondingly,the dynamic surface control is introduced to cope with the problem of“explosion of complexity”inherent in conventional backstepping scheme.It is shown that the designed controller can achieve finite-time tracking control and all the variables in the closed-loop system are bounded with output constraint guaranteed form stability analysis and simulation results.

A Feasible Zone Analysis Method with Global Partial Load Scanning for Solving Power Flow Coupling Models of CCHP Systems

Heat exchanger systems(HXSs)or heat recovery steam generators(HRSGs)are commonly used in 100 kW to 50 MW combined cooling,heating,and power(CCHP)systems.Power flow coupling(PFC)is found in HXSs and is complex for researchers to quantify.This could possibly mislead the dispatch schedule and result in the inaccurate dispatch.PFC is caused by the inlet and outlet temperatures of each component,gas flow pressure variation,conductive medium flow rate,and atmosphere condition variation.In this paper,the expression of PFC is built by using quadratic functions to fit the non!inearit>of thermal dynamics.While fitting the model,the environmental condition needs prediction,which is calculated using phase space reconstruction(PSR)Kalman filter.In order to solve the complex quadratic dispatch model,a hybrid following electricity load(FEL)and following thermal load(FTL)mode for reducing the dimension of dispatch model,and a feasible zone analysis(FZA)method are proposed.As a result,the PFC problem of CCHP system is solved,and the dispatch cost,investment cost,and the maximum power requirements are optimized.In this paper,a case in Jinan,China is studied.The PFC model is proven to be more precise and accurate compared with traditional models.