Decoupled nonsingular terminal sliding mode control for affine nonlinear systems

A decoupled nonsingular terminal sliding mode control（DNTSMC） approach is proposed to address the tracking control problem of affine nonlinear systems.A nonsingular terminal sliding mode control（NTSMC） method is presented,in which the nonsingular terminal sliding surface is defined as a special nonsingular terminal function and the convergence time of the system states can be specified.The affine nonlinear system is firstly decoupled into linear subsystems via feedback linearization.Then,a nonsingular terminal sliding surface is defined and the NTSMC method is applied to each subsystem separately to ensure the finite time convergence of the closed-loop system.The verification example is given to demonstrate the effectiveness and robustness of the proposed approach.The proposed approach exhibits a considerable advantage in terms of faster tracking error convergence and less chattering compared with the conventional sliding mode control（CSMC）.

Optimal control of quadratic functionals for affine nonlinear systems

In this paper we analyze the optimal control problem for a class of afflne nonlinear systems under the assumption that the associated Lie algebra is nilpotent. The Lie brackets generated by the vector fields which define the nonlinear system represent a remarkable mathematical instrument for the control of affine systems. We determine the optimal control which corresponds to the nilpotent operator of the first order. In particular, we obtain the control that minimizes the energy of the given nonlinear system. Applications of this control to bilinear systems with first order nilpotent operator are considered.

Fixed-Time Antidisturbance Consensus Tracking for Nonlinear Multiagent Systems With Matching and Mismatching Disturbances

In this paper,fixed-time consensus tracking for mul-tiagent systems(MASs)with dynamics in the form of strict feed-back affine nonlinearity is addressed.A fixed-time antidistur-bance consensus tracking protocol is proposed,which consists of a distributed fixed-time observer,a fixed-time disturbance observer,a nonsmooth antidisturbance backstepping controller,and the fixed-time stability analysis is conducted by using the Lyapunov theory correspondingly.This paper includes three main improvements.First,a distributed fixed-time observer is developed for each follower to obtain an estimate of the leader’s output by utilizing the topology of the communication network.Second,a fixed-time disturbance observer is given to estimate the lumped disturbances for feedforward compensation.Finally,a nonsmooth antidisturbance backstepping tracking controller with feedforward compensation for lumped disturbances is designed.In order to mitigate the“explosion of complexity”in the tradi-tional backstepping approach,we have implemented a modified nonsmooth command filter to enhance the performance of the closed-loop system.The simulation results show that the pro-posed method is effective.

On global asymptotic controllability of planar affine nonlinear systems

In this paper, we present a necessary and sufficient condition for globally asymptotic controllability of the general planar affine nonlinear systems with single-input. This result is obtained by introducing a new method in the analysis, which is based on the use of some basic results in planar topology and in the geometric theory of ordinary differential equations.

On global controllability of affine nonlinear systems with a triangular-like structure

In this paper, we investigate a class of affine nonlinear systems with a triangular-like structure and present its necessary and sufficient condition for global controllability, by using the techniques developed by Sun Yimin and Guo Lei recently. Furthermore, we will give two examples to illustrate its application.

NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL CONTROLLABILITY OF A CLASS OF AFFINE NONLINEAR SYSTEMS

In this paper, we investigate the global controllability of a class of n-dimensional affine nonlinear systems with n- 1 controls and constant control matrix. A necessary and sufficient condition for its global controllability has been obtained by using the methods recently developed. Furthermore, we generalize the above result to a class of affine nonlinear systems with a block-triangular-like structure. Finally, we will give three examples to show the applications of our results.

EXACT LINEARIZATION BASED MULTIPLE-SUBSPACE ITERATIVE RESOLUTION TO AFFINE NONLINEAR CONTROL SYSTEM

To the optimal control problem of affine nonlinear system, based on differential geometry theory, feedback precise linearization was used. Then starting from the simulative relationship between computational structural mechanics and optimal control, multiple-substructure method was inducted to solve the optimal control problem which was linearized. And finally the solution to the original nonlinear system was found. Compared with the classical linearizational method of Taylor expansion, this one diminishes the abuse of error expansion with the enlargement of used region.

APPROXIMATE OUTPUT REGULATION FOR AFFINE NONLINEAR SYSTEMS

Output regulation for affine nonlinear systems driven by an exogenous signal is investigated in this paper. In the absence of the standard exosystem hypothesis, we assume availability of the instantaneous values of the exogenous signal and its first time-derivative for use in the control law. For affine nonlinear systems, the necessary and sufficient conditions of the solvability of approximate output regulation problem are obtained. The precise form of the control law is presented under some suitable assumptions.

On global controllability for a class of polynomial affine nonlinear systems

In this paper, a necessary and sufficient condition of the global controllability for a class of low dimensional polynomial affine nonlinear systems with special structure is obtained. The condition is imposed on the coefficients of the system only and the methods are based on Green＇s formula and the trajectory analysis of planar linear system. Furthermore, I point out that the global controllability does not hold for the corresponding high dimensional polynomial system.

Evaluation of fault diagnosability for nonlinear uncertain systems with multiple faults occurring simultaneously

Up to present,the problem of the evaluation of fault diagnosability for nonlinear systems has been investigated by many researchers.However,no attempt has been done to evaluate the diagnosability of multiple faults occurring simultaneously for nonlinear systems.This paper proposes a method based on differential geometry theories to solve this problem.Then the evaluation of fault diagnosability for affine nonlinear systems with multiple faults occurring simultaneously is achieved.To deal with the effect of control laws on the evaluation results of fault diagnosability,a design scheme of the evaluation of fault diagnosability is proposed.Then the influence of uncertainties on the evaluation results of fault diagnosability for affine nonlinear systems with multiple faults occurring simultaneously is analyzed.The numerical simulation results are obtained to show the effectiveness of the proposed evaluation scheme of fault diagnosability.

An Iterative Relaxation Approach to the Solution of the Hamilton-Jacobi-Bellman-Isaacs Equation in Nonlinear Optimal Control

In this paper, we propose an iterative relaxation method for solving the Hamilton-Jacobi-Bellman-Isaacs equation(HJBIE) arising in deterministic optimal control of affine nonlinear systems. Local convergence of the method is established under fairly mild assumptions, and examples are solved to demonstrate the effectiveness of the method. An extension of the approach to Lyapunov equations is also discussed. The preliminary results presented are promising, and it is hoped that the approach will ultimately develop into an efficient computational tool for solving the HJBIEs.

A sliding-mode variable-structure controller based on exact feedback linearization for automatic navigation system

In order to improve the path tracking accuracy and robustness of the agricultural machinery navigation system,a sliding-mode variable-structure controller based on exact feedback linearization was presented.Firstly,based on the differential geometry theory and the affine nonlinear kinematics model,the corresponding nonlinear coordinate change matrix and nonlinear state variable feedback equations were deduced,and an exact feedback linearization model was then established.Secondly,based on the exact feedback linearization model,a sliding-mode variable-structure controller was designed by selecting suitable linear switching function and exponential reaching law.Finally,the comparative experiments were carried out.And the experimental results indicated that the proposed method had a high tracking accuracy and robustness.The maximum lateral error of the straight line tracking was less than 0.06 m,and maximum lateral error of the curve path tracking was less than 0.09 m.Experimental results show that the transplanter based on this automatic navigation system can effectively track the predefined path.

AIG Based Nonlinear Anisotropic Smoothing Strategy for Vector-Valued Images

The effects of the Rician noise on the calculated tensors are analyzed and an affine invariant gradient (AIG) based nonlinear anisotropic smoothing strategy is presented.The AIG based smoothing strategy is a development of the affine invariant nonlinear anisotropic diffusion(AINAD) restoration model,introduced by Guillermo Sapiro,and adopted to restore vector-valued data.To evaluate the efficiency of the presented AINAD model in accounting for the Rician noise introduced into the vector-valued data,the peak-to-peak signal-to-noise ratio(PSNR),signal-to-mean squared error ratio(SMSE) and Beta(parameter that stands for edge preservation) metrics are used.The experiment results acquired from the synthetic and real data prove the good performance of the presented filter.