Finite-time stabilization of uncertain non-autonomous chaoticgyroscopes with nonlinear inputs

Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos. In this paper, the problem of robust stabilization of the nonlinear non-autonomous gyroscopes in a given finite time is studied. It is assumed that the gyroscope system is perturbed by model uncertainties, external disturbances, and unknown parameters. Besides, the effects of input nonlinearities are taken into account. Appropriate adaptive laws are proposed to tackle the unknown parameters. Based on the adaptive laws and the finite-time control theory, discontinuous finite-time control laws are proposed to ensure the finite-time stability of the system. The finite-time stability and convergence of the closed-loop system are analytically proved. Some numerical simulations are presented to show the efficiency of the proposed finite-time control scheme and to validate the theoretical results.

Control for the synchronization of Chen system via a single nonlinear input

This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.

Finite-time control of chaotic systems with nonlinear inputs

A finite-time controller is designed for a class of nonlinear systems subject to sector nonlinear inputs. A novel and simple approach is suggested based on the finite-time control principle. The designed sliding-mode controller can drive a chaotic system to track a smooth target signal in a finite time. The chaotic Duffing-Holmes oscillator is used for verification and demonstration.

A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs

In this paper, the problem of the finite-time synchronization of two uncertain chaotic gyros is discussed. The parameters of both the master and the slave gyros are assumed to be unknown in advance. The effects of model uncertainties and input nonlinearities are also taken into account. An appropriate adaptation law is proposed to tackle the gyros＇ unknown parameters. Based on the adaptation law and the finite-time control technique, proper control laws are introduced to ensure that the trajectories of the slave gyro converge to the trajectories of the master gyro in a given finite time. Simulation results show the applicability and the efficiency of the proposed finite-time controller.

Nonsingular terminal sliding mode approach applied to synchronize chaotic systems with unknown parameters and nonlinear inputs

This paper deals with the design of a novel nonsingular terminal sliding mode controller for finite-time synchro-nization of two different chaotic systems with fully unknown parameters and nonlinear inputs. We propose a novel nonsingular terminal sliding surface and prove its finite-time convergence to zero. We assume that both the master＇s and the slave＇s system parameters are unknown in advance. Proper adaptation laws are derived to tackle the unknown parameters. An adaptive sliding mode control law is designed to ensure the existence of the sliding mode in finite time. We prove that both reaching and sliding mode phases are stable in finite time. An estimation of convergence time is given. Two illustrative examples show the effectiveness and usefulness of the proposed technique. It is worthwhile noticing that the introduced nonsingular terminal sliding mode can be applied to a wide variety of nonlinear control problems.

Sliding mode identifier for parameter uncertain nonlinear dynamic systems with nonlinear input

This paper presents a sliding mode(SM) based identifier to deal with the parameter idenfification problem for a class of parameter uncertain nonlinear dynamic systems with input nonlinearity. A sliding mode controller (SMC) is used to ensure the global reaching condition of the sliding mode for the nonlinear system;an identifier is designed to identify the uncertain parameter of the nonlinear system. A numerical example is studied to show the feasibility of the SM controller and the asymptotical convergence of the identifier.

Robust Dissipative Control for Nonlinear System with Sector Input

Based on the quadratic supply rate, the problem of robust dissipative control for a class of uncertain nonlinear system with sector nonlinear input is discussed. The uncertainty is described by bounded norm. It is shown that the robust dissipative control problem can be resolved for all admissible uncertainty, if there exists a storage function such that Hamilton Jacobi inequality holds. When the uncertainties of the system satisfy the matching condition, and input function within the boundedness of the sector, the closed loop system will be stronger dissipativeness, and the controller which we obtained in the paper is more flexible, because it contains an adjustable parameter for some certain range.

Adaptive Backstepping Sliding Mode Control for Nonlinear Systems with Input Saturation

An adaptive backstepping sliding mode control is proposed for a class of uncertain nonlinear systems with input saturation.A command filtered approach is used to prevent input saturation from destroying the adaptive capabilities of neural networks (NNs).The control law and adaptive updating laws of NNs are derived in the sense of Lyapunov function,so the stability can be guaranteed even under the input saturation.The proposed control law is robust against the disturbance,and it can also eliminate the impact of input saturation.Simulation results indicate that the proposed controller has a good performance.

Quantifying the thermal damping effect in underground vertical shafts using the nonlinear autoregressive with external input(NARX) algorithm

As air descends the intake shaft, its infrastructure, lining and the strata will emit heat during the night when the intake air is cool and, on the contrary, will absorb heat during the day when the temperature of the air becomes greater than that of the strata. This cyclic phenomenon, also known as the "thermal damping effect" will continue throughout the year reducing the effect of surface air temperature variation. The objective of this paper is to quantify the thermal damping effect in vertical underground airways. A nonlinear autoregressive time series with external input(NARX) algorithm was used as a novel method to predict the dry-bulb temperature(Td) at the bottom of intake shafts as a function of surface air temperature. Analyses demonstrated that the artificial neural network(ANN) model could accurately predict the temperature at the bottom of a shaft. Furthermore, an attempt was made to quantify typical "damping coefficient" for both production and ventilation shafts through simple linear regression models. Comparisons between the collected climatic data and the regression-based predictions show that a simple linear regression model provides an acceptable accuracy when predicting the Tdat the bottom of intake shafts.

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchro- nization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.

Constrained sliding mode control of nonlinear fractional order input affine systems

Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time.To eliminate the chattering in the sliding mode and make the input controller bounded,hyperbolic tangent is used for designing the proposed fractional order sliding surface.Finally,the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory.A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case.Finally,simulation results are provided to show the effectiveness of the designed controller.

A Nonlinear Control Strategy for Vienna Rectifier Under Unbalanced Input Voltage

The Vienna rectifier with unbalanced input voltage and load transient is analyzed.A nonlinear control strategy for Vienna rectifier under unbalanced input is proposed.From the view of positive and negative sequence components,the proposed nonlinear control strategy suppresses the twice frequency ripple and guarantees the dynamic response characteristic at the same time.Thanks to the proposed nonlinear control strategy,the DC bus capacitor can be reduced a lot since the voltage ripple and drop can be suppressed.A 10 kW Vienna rectifier is built to verify the proposed control strategy.After applying the proposed nonlinear control strategy,the voltage ripple is only7 V and decreases over 75%over the traditional PI control when the unbalanced degree is 20%.The voltage drop can be reduced about 80%than former control strategy which is helpful to reduce the DC bus capacitor and achieve higher power density.The volume of the capacitor can be reduced by 83.3%with the new control method.

Robust Output Feedback Control for a Class of Nonlinear Systems with Input Unmodeled Dynamics

The robust global stabilization problem of a class of uncertain nonlinear systems with input unmodeled dynamics is considered using output feedback, where the uncertain nonlinear terms satisfy a far more relaxed condition than the existing triangulartype condition. Under the assumption that the input unmodeled dynamics is minimum-phase and of relative degree zero, a dynamic output compensator is explicitly constructed based on the nonseparation principle. An example illustrates the usefulness of the proposed method.

Soft Sensor for Inputs and Parameters Using Nonlinear Singular State Observer in Chemical Processes

Chemical processes are usually nonlinear singular systems.In this study,a soft sensor using nonlinear singular state observer is established for unknown inputs and uncertain model parameters in chemical processes,which are augmented as state variables.Based on the observability of the singular system,this paper presents a simplified observability criterion under certain conditions for unknown inputs and uncertain model parameters.When the observability is satisfied,the unknown inputs and the uncertain model parameters are estimated online by the soft sensor using augmented nonlinear singular state observer.The riser reactor of fluid catalytic cracking unit is used as an example for analysis and simulation.With the catalyst circulation rate as the only unknown input without model error,one temperature sensor at the riser reactor outlet will ensure the correct estimation for the catalyst circulation rate.However,when uncertain model parameters also exist,additional temperature sensors must be used to ensure correct estimation for unknown inputs and uncertain model parameters of chemical processes.

Tracking Control of Uncertain Nonlinear Systems With Unknown Constant Input Delay

A robust delay compensator has been developed for a class of uncertain nonlinear systems with an unknown constant input delay.The control law consists of feedback terms based on the integral of past control values and a novel filtered tracking error,capable of compensating for input delays.Suitable Lyapunov-Krasovskii functionals are used to prove global uniformly ultimately bounded(GUUB)tracking,provided certain sufficient gain conditions,dependent on the bound of the delay,are satisfied.Simulation results illustrate the performance and robustness of the controller for different values of input delay.

Terminal Angular Constraint Integrated Guidance and Control for Flexible Hypersonic Vehicle with Dead-Zone Input Nonlinearity

This paper presents an integrated guidance and control model for a flexible hypersonic vehicle with terminal angular constraints.The integrated guidance and control model is bounded and the dead-zone input nonlinearity is considered in the system dynamics.The line of sight angle,line of sight angle rate,attack angle and pitch rate are involved in the integrated guidance and control system.The controller is designed with a backstepping method,in which a first order filter is employed to avoid the differential explosion.The full tuned radial basis function(RBF)neural network(NN)is used to approximate the system dynamics with robust item coping with the reconstruction errors,the exactitude model requirement is reduced in the controller design.In the last step of backstepping method design,the adaptive control with Nussbaum function is used for the unknown dynamics with a time-varying control gain function.The uniform ultimate boundedness stability of the control system is proved.The simulation results validate the effectiveness of the controller design.

Neural Network Based Adaptive Tracking Control for a Class of Pure Feedback Nonlinear Systems With Input Saturation

In this paper, an adaptive neural networks(NNs)tracking controller is proposed for a class of single-input/singleoutput(SISO) non-affine pure-feedback non-linear systems with input saturation. In the proposed approach, the original input saturated nonlinear system is augmented by a low pass filter.Then, new system states are introduced to implement states transformation of the augmented model. The resulting new model in affine Brunovsky form permits direct and simpler controller design by avoiding back-stepping technique and its complexity growing as done in existing methods in the literature.In controller design of the proposed approach, a state observer,based on the strictly positive real(SPR) theory, is introduced and designed to estimate the new system states, and only two neural networks are used to approximate the uncertain nonlinearities and compensate for the saturation nonlinearity of actuator. The proposed approach can not only provide a simple and effective way for construction of the controller in adaptive neural networks control of non-affine systems with input saturation, but also guarantee the tracking performance and the boundedness of all the signals in the closed-loop system. The stability of the control system is investigated by using the Lyapunov theory. Simulation examples are presented to show the effectiveness of the proposed controller.

Optimal Neuro-Control Strategy for Nonlinear Systems With Asymmetric Input Constraints

In this paper,we present an optimal neuro-control scheme for continuous-time(CT)nonlinear systems with asymmetric input constraints.Initially,we introduce a discounted cost function for the CT nonlinear systems in order to handle the asymmetric input constraints.Then,we develop a Hamilton-Jacobi-Bellman equation(HJBE),which arises in the discounted cost optimal control problem.To obtain the optimal neurocontroller,we utilize a critic neural network(CNN)to solve the HJBE under the framework of reinforcement learning.The CNN's weight vector is tuned via the gradient descent approach.Based on the Lyapunov method,we prove that uniform ultimate boundedness of the CNN's weight vector and the closed-loop system is guaranteed.Finally,we verify the effectiveness of the present optimal neuro-control strategy through performing simulations of two examples.