Design of Fixed-Time Neural Controller for Uncertain Nonstrict-Feedback Systems with Smooth Switching Functions

The tracking problem of uncertain nonstrict-feedback nonlinear systems(UNFNS)is examined to develop a novel adaptive neural control scheme to ensure fixed-time convergence.In particular,the challenge associated with the unknown nonlinear function can be overcome through neural network(NN)based estimation.Therefore,an NN-based adaptive fixed-time control scheme is established with only one parameter,using the property of the basis function vector to address the algebraic loop problem.Furthermore,the singularity problem can be solved by incorporating a smooth switching function.A rigorous theoretical analysis is performed to demonstrate that the output signal can track the reference signal within a fixed time and that the signals in the control systems are bounded.Finally,numerical simulations are performed to validate the feasibility of the proposed methodology.

Analysis of Higher Order System with Impulse Exciting Functions in Z-Domain

This paper deals with mathematical modelling of impulse waveforms and impulse switching functions used in electrical engineering. Impulse switching functions are later investigated using direct and inverse z-transformation. The results make possible to present those functions as infinite series expressed in pure numerical, exponential or trigonometric forms. The main advantage of used approach is the possibility to calculate investigated variables directly in any instant of time;dynamic state can be solved with the step of sequences (T/6, T/12) that means very fast. Theoretically derived waveforms are compared with simulation worked-out results as well as results of circuit emulator LT spice which are given in the paper.

DESIGN AND ANALYSIS FOR NEW DISCRETE TRACKING-DIFFERENTIATORS

In this paper,some kinds of linear and nonlinear tracking-differentiators are designed by using suitable exponent functions instead of switch functions,and the stability of these tracking-differentiators is proved.From the result of simulations,it is manifest that the tracking speeds of these kinds of linear and nonlinear tracking-differentiators are very high,and their design procedures are simple.

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular （SLS） systems for arbitrary switching laws is solved. By using the switched Lyapunov function approach, some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities （LMIs）. Based on the admissibility results, control synthesis is then to design switched state feedback and static output feedback controllers, guaranteeing that the resulting closed-loop system is admissible. The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases. Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.

Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities（LMIs）.An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms（ignored in previous methods） when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.

Sliding mode control for mobile welding robot

The sliding mode controller of mobile welding robot is established in this paper through applying the method of variable structure control with sliding mode into the control of the mobile welding robot. The traditional switching function smooth method is improved by combining the smoothed switching function with the time-varying control gain. It is shown that the proposed sliding mode controller is robust to bounded external disturbances. Experimental results demonstrate that sliding mode controller algorithm can be used into seam tracking and the tracking system is stable with bounded uncertain disturbance. In the seam tracking process, the robot moves steadily without any obvious chattering.

Self-adjusting entropy-stable scheme for compressible Euler equations

In this work,a self-adjusting entropy-stable scheme is proposed for solving compressible Euler equations.The entropy-stable scheme is constructed by combining the entropy conservative flux with a suitable diffusion operator.The entropy has to be preserved in smooth solutions and be dissipated at shocks.To achieve this,a switch function,which is based on entropy variables,is employed to make the numerical diffusion term be automatically added around discontinuities.The resulting scheme is still entropy-stable.A number of numerical experiments illustrating the robustness and accuracy of the scheme are presented.From these numerical results,we observe a remarkable gain in accuracy.

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lyapunov function （SLF） method with Finsler＇s Lemma. Based on linear matrix inequality （LMI） a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.

Non-Characteristic Harmonics Analysis of the ITER Pulsed Power Supply

The ITER pulsed power supply system will be operated in non-ideal conditions including an asymmetric firing angle, an unbalanced AC supply and an unbalanced AC side impedance of the transformer. In this study the switching functions approach is used to calcu- late non-characteristic harmonics in ITER, possibly caused by an AC-DC convertor in non-ideal conditions. A PSCAD simulation model is set up to study the non-characteristic harmonics in those non-ideal conditions. It is found that the non-characteristic harmonic does appear and the simulation result is in accordance with the calculating strategy.

On the State-dependent Switched Energy Functions of DFIG-based Wind Power Generation Systems

This paper proposes a novel state-dependent switched energy function(SdSEF)for general nonlinear autonomous systems,and constructs an SdSEF for doubly-fed induction generator(DFIG)-based wind power generation systems(WPGSs).Different from the conventional energy function,SdSEF is a piece-wise continuous function,and it satisfies the conditions of conventional energy functions on each of its continuous segments.SdSEF is designed to bridge the gap between the well-developed energy function theory and the description of system energy of complex nonlinear systems,such as power electronics converter systems.The stability criterion of nonlinear autonomous systems is investigated with SdSEF,and mathematical proof is presented.The SdSEF of a typical DFIGbased WPGS is simulated in the whole processes of a grid fault and fault recovery.Simulation results verify the negativeness of the derivative of each continuous segment of the SdSEF.

H-infinity filtering for discrete-time switched linear systems under arbitrary switching

This paper is concerned with the problem of H-infinity filtering for discrete-time switched linear systems under arbitrary switching laws.New sufficient conditions for the solvability of the problem are given via switched quadratic Lyapunov functions.Based on Finsler's lemma,two sets of slack variables with special structure are introduced to provide extra degrees of freedom in optimizing the guaranteed H-infinity performance.Compared to the existing methods,the proposed one has better performances and less conservatism.An example is given to illustrate its effectiveness.

Wavelength-selective switch based on a high fill-factor micromirror array

A novel design and fabrication approach for a high fill-factor micro-electro-mechanical system （MEMS） micromirror array-based wavelength-selective switch （WSS） is presented. The WSS is composed of a polarization-independent transmission grating and a high fill-factor micromirror array. The WSS is successfully demonstrated based on the fabricated high fill-factor micromirror array. Test results show that the polarization-dependent loss （PDL） is less than 0.3 dB and that the insertion loss （IL） of the wavelength channel is about -6 dB. The switching function between the two output ports of WSS is measured. The forward switching time is recorded to be about 0.5 ms, whereas the backward switching time is about 7 ms.

L_2-gain Analysis and Anti-windup Design of Discretetime Switched Systems with Actuator Saturation

This paper investigates L2-gain analysis and anti-windup compensation gains design for a class of discrete-time switched systems with saturating actuators and L2 bounded disturbances by using the switched Lyapunov function approach.For a given set of anti-windup compensation gains,we firstly give a sufficient condition on tolerable disturbances under which the state trajectory starting from the origin will remain inside a bounded set for the corresponding closed-loop switched system subject to L2 bounded disturbances.Then,the upper bound on the restricted L2-gain is obtained over the set of tolerable disturbances.Furthermore,the antiwindup compensation gains aiming to determine the largest disturbance tolerance level and the smallest upper bound of the restricted L2-gain are presented by solving a convex optimization problem with linear matrix inequality(LMI) constraints.A numerical example is given to illustrate the effectiveness of the proposed design method.

The dichotomous role of TGF-β in controlling liver cancer cell survival and proliferation

Hepatocellular carcinoma(HCC) is the major form of primary liver cancer and one of the most prevalent and life-threatening malignancies globally. One of the hallmarks in HCC is the sustained cell survival and proliferative signals, which are determined by the balance between oncogenes and tumor suppressors.Transforming growth factor beta(TGF-β) is an effective growth inhibitor of epithelial cells including hepatocytes, through induction of cell cycle arrest, apoptosis, cellular senescence, or autophagy. The antitumorigenic effects of TGF-β are bypassed during liver tumorigenesis via multiple mechanisms.Furthermore, along with malignant progression, TGF-β switches to promote cancer cell survival and proliferation. This dichotomous nature of TGF-β is one of the barriers to therapeutic targeting in liver cancer. Thereafter, understanding the underlying molecular mechanisms is a prerequisite for discovering novel antitumor drugs that may specifically disable the growth-promoting branch of TGF-β signaling or restore its tumor-suppressive arm. This review summarizes how TGF-β inhibits or promotes liver cancer cell survival and proliferation, highlighting the functional switch mechanisms during the process.

Stability analysis and antiwindup design of uncertain discrete-time switched linear systems subject to actuator saturation

This paper investigates the stability analysis and antiwindup design problem for a class of discrete-time switched linear systems with time-varying norm-bounded uncertainties and saturating actuators by using the switched Lyapunov function approach. Supposing that a set of linear dynamic output controllers have been designed to stabilize the switched system without considering its input saturation, we design antiwindup compensation gains in order to enlarge the domain of attraction of the closed-loop system in the presence of saturation. Then, in terms of a sector condition, the antiwindup compensation gains which aim to maximize the estimation of domain of attraction of the closed-loop system are presented by solving a convex optimization problem with linear matrix inequality （LMI） constraints. A numerical example is given to demonstrate the effectiveness of the proposed design method.

A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows

In this paper,a hybrid lattice Boltzmann flux solver(LBFS)is proposed for simulation of viscous compressible flows.In the solver,the finite volume method is applied to solve the Navier-Stokes equations.Different from conventional Navier-Stokes solvers,in this work,the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model,while the viscous flux is still approximated by conventional smooth function approximation.The present work overcomes the two major drawbacks of existing LBFS[28–31],which is used for simulation of inviscid flows.The first one is its ability to simulate viscous flows by including evaluation of viscous flux.The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux,which takes a value close to zero in the boundary layer and one around the strong shock wave.Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows.

A hybrid lattice Boltzmann flux solver for integrated hypersonic fluid-thermal-structural analysis

In this paper,a hybrid Lattice Boltzmann Flux Solver(LBFS)with an improved switch function is proposed for simulation of integrated hypersonic fluid-thermal-structural problems.In the solver,the macroscopic Navier–Stokes equations and structural heat transfer equation are discretized by the finite volume method,and the numerical fluxes at the cell interface are reconstructed by the local solution of the Boltzmann equation.To compute the numerical fluxes,two equilibrium distribution functions are introduced.One is the D1Q4 discrete velocity model for calculating the inviscid flux across the cell interface of Navier–Stokes equations,and the other is the D2Q4 model for evaluating the flux of structural energy equation.In this work,a new dual thermal resistance model is proposed to calculate the thermal properties at the fluid–solid interface.The accuracy and stability of the present hybrid solver are validated by simulating several numerical examples,including the fluid-thermal-structural problem of cylindrical leading edge.Numerical results show that the present solver can accurately predict the thermal properties of hypersonic fluid-thermalstructural problems and has the great potential for solving fluid-thermal-structural problems of long-endurance high-speed vehicles.

Switched Three-Dimensional Decoupling Stabilization of Underactuated Autonomous Underwater Vehicles

A three-dimensional stabilization problem for underactuated autonomous underwater vehicles(AUVs)is addressed in this paper.A novel coordinate transformation form consisting of state modifications and input transformations is introduced such that the whole system is divided into two decoupled one-order subsystems.Some switching functions are presented to further decouple the underactuated dynamics and to produce persistently exciting(PE)signals for those underactuated states.Based on the aforementioned results,a quite simple control law is designed to achieve global three-dimensional asymptotic convergence of all states of underactuated AUVs.Comparative simulations are carried out to validate the effectiveness and performance of the proposed control scheme.

New Delay-Dependent Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delays

This paper deals with the issues of robust stability for uncertain discrete-time switched systems with mode-dependent time delays.Based on a novel difference inequality and a switched Lyapunov function,new delay-dependent stability criteria are formulated in terms of linear matrix inequalities （LMIs） which are not contained in known literature.A numerical example is given to demonstrate that the proposed criteria improves some existing results significantly with much less computational effort.