scholarly journals Finite-Time Tracking Control for a Class of MIMO Nonlinear Systems with Unknown Asymmetric Saturations

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Fu Mingyu ◽  
Xu Yujie
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Tracking Control ◽  
Sliding Mode ◽  
External Disturbance ◽  
Tracking Error ◽  
Input Saturation ◽  
Approximation Error ◽  
Time Interval ◽  
Mimo Nonlinear Systems

This paper addresses the problem of finite-time tracking control for multiple-input and multiple-output (MIMO) nonlinear systems with asymmetric saturations. A systematic approach is proposed to eliminate the effects of unmeasured external disturbances and unknown asymmetric saturations. In the proposed control strategy, a terminal sliding mode disturbance observer is provided to estimate the augmented disturbance (which contains the unknown asymmetric input saturation and external disturbance). The approximation error of the augmented disturbance can converge to zero in a fixed finite-time interval. Furthermore, a novel finite-time tracking control algorithm is developed to guarantee fast convergence of the tracking error. Compared with the existing results on finite-time tracking control, the chattering problem and the input saturation problem can be solved in a unified framework. Several simulations are given to demonstrate the effectiveness of the proposed approach.

Adaptive neural finite-time trajectory tracking control of hydraulic excavators

2018 ◽  
Vol 232 (7) ◽  
pp. 909-925 ◽  
Author(s):  
Yong Li ◽  
Qingfeng Wang
Keyword(s):  
Trajectory Tracking ◽  
Finite Time ◽  
Tracking Control ◽  
Sliding Mode ◽  
Tracking Error ◽  
Approximation Error ◽  
Superior Performance ◽  
Observation Error ◽  
Trajectory Tracking Control ◽  
Terminal Sliding Mode

This article is focused on the high-performance trajectory tracking control of single actuator of a hydraulic excavator. A novel adaptive neural finite-time controller without tedious offline parameter identification and the complex backstepping scheme is put forward. By employing a coordinate transform, the original system can be represented in a canonical form. Consequently, the control objective is retained by controlling the transformed system, which allows a simple controller design without using backstepping. To estimate the immeasurable states of the transformed system, a high-order sliding mode observer is employed, of which observation error is guaranteed to be bounded in finite time. To guarantee finite-time trajectory tracking performance, an adaptive neural finite-time controller based on neural network approximation and terminal sliding mode theory is synthesized. During its synthesis, an echo state network is used to approximate the lumped uncertain system functions, and it guarantees an improved approximation with online-updated output weights. Besides, to handle the lumped uncertain nonlinearities resulting from observation error and neural approximation error, a robust term is employed. The influences of the uncertain nonlinearities are restrained with a novel parameter adaption law, which estimates and updates the upper bound of the lumped uncertain nonlinearities online. With this novel controller, the finite-time trajectory tracking error convergence is proved theoretically. The superior performance and the practical applicability of the proposed method are verified by comparative simulations and experiments.

Robust spacecraft attitude tracking control with integral terminal sliding mode surface considering input saturation

2018 ◽  
Vol 41 (2) ◽  
pp. 405-416 ◽  
Author(s):  
Haitao Chen ◽  
Shenmin Song ◽  
Xuehui Li
Keyword(s):  
Finite Time ◽  
Sliding Mode ◽  
External Disturbance ◽  
Input Saturation ◽  
External Disturbances ◽  
Terminal Sliding Mode ◽  
Modeling Uncertainty ◽  
Finite Time Convergence ◽  
Attitude Tracking ◽  
Attitude Tracking Control

This paper studies the finite time spacecraft attitude tracking control problem, while considering modeling uncertainty, external disturbances and control input saturation. A novel integral terminal sliding mode surface (ITSMS) is designed by combining the fast terminal sliding mode surface (FTSMS) with a low pass filter to achieve a fast finite time convergence rate for the control system, without input singularity. An auxiliary signal is used to compensate for the effects of actuator saturation. The basic controller is first formulated based on the ITSMS, fast-TSM-type reaching law and auxiliary system, in the presence of an external disturbance and input saturation. Then, an adaptive control procedure is introduced, which simultaneously handles modeling uncertainty and external disturbance, thereby creating an adaptive attitude tracking controller. The proposed controller provides a fast finite time convergence rate for the control system, based on the newly designed ITSMS, while simultaneously compensating for modeling uncertainty, external disturbances and input saturation, without restricting the parameter selection process nor requiring repeated differentiation of nonlinear functions. Finally, digital simulation results are presented and demonstrate the effectiveness of the proposed controllers.

scholarly journals Design of Adaptive Sliding Mode Controllers for Perturbed Nonlinear Systems with Partial Unmeasurable States and State Constraints

2021 ◽  
Author(s):  
Chih-Chiang Cheng ◽  
Ting-Yu Lin ◽  
Yu-Kuo Li
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
State Constraints ◽  
Sliding Mode ◽  
Tracking Error ◽  
Estimation Errors ◽  
Adaptive Sliding Mode ◽  
Adaptive Mechanisms ◽  
Approach Zero ◽  
Perturbation Estimation

Abstract A sliding mode control (SMC) strategy is proposed in this paper for a class of perturbed nonlinear systems with unmeasurable states and state constraints to deal with the state tracking problems. First of all, a partial states observer is designed for solving the problems due to unmeasurable states. The estimation errors will approach zero in a finite time. Secondly, based on a designed barrier Lyapunov function, one designs the sliding surface function and an adaptive sliding mode tracking controller to ensure that the states have the ability to track the desired signals. Moreover, the tracking error is capable of converging to zero in a finite time without violating the given state's constraints. Perturbation estimator and adaptive mechanisms are also utilized so that there is no need to know the upper bounds of perturbations and perturbation estimation errors. Finally, a numerical example is provided to demonstrate the feasibility of the proposed control strategy.

Robust adaptive finite-time tracking control of uncertain mechanical systems with input saturation and deadzone

2018 ◽  
Vol 41 (2) ◽  
pp. 560-572 ◽  
Author(s):  
Baofang Wang ◽  
Sheng Li ◽  
Qingwei Chen
Keyword(s):  
Finite Time ◽  
Tracking Control ◽  
Design Method ◽  
Tracking Error ◽  
Input Saturation ◽  
Mechanical Systems ◽  
Lyapunov Stability Theory ◽  
Continuous Functions ◽  
Model Uncertainties ◽  
Robust Adaptive

This paper addresses the problem of robust adaptive finite-time tracking control for a class of mechanical systems in the presence of model uncertainties, unknown external disturbances, and input nonlinearities containing saturation and deadzone. Without imposing any conditions on the model uncertainties, radial basis function neural networks are used to approximate unknown nonlinear continuous functions, and an adaptive tracking control scheme is proposed by exploiting the recursive design method. It is shown that the input saturation and deadzone model can be expressed as a simple linear system with a time-varying gain and bounded disturbance. An adaptive compensation term for the upper bound of the lumped disturbance is introduced. The semi-global finite-time uniform ultimate boundedness of the corresponding closed-loop tracking error system is proved with the help of the finite-time Lyapunov stability theory. Finally, an example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Approximation-Based Quantized State Feedback Tracking of Uncertain Input-Saturated MIMO Nonlinear Systems with Application to 2-DOF Helicopter

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1062
Author(s):  
Byung Mo Kim ◽  
Sung Jin Yoo
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Tracking Error ◽  
Multiple Input Multiple Output ◽  
Input Saturation ◽  
Lyapunov Theory ◽  
Experimental Results ◽  
State Variables ◽  
Mimo Nonlinear Systems ◽  
Feedback Tracking

This paper addresses an approximation-based quantized state feedback tracking problem of multiple-input multiple-output (MIMO) nonlinear systems with quantized input saturation. A uniform quantizer is adopted to quantize state variables and control inputs of MIMO nonlinear systems. The primary features in the current development are that (i) an adaptive neural network tracker using quantized states is developed for MIMO nonlinear systems and (ii) a compensation mechanism of quantized input saturation is designed by constructing an auxiliary system. An adaptive neural tracker design with the compensation of quantized input saturation is developed by deriving an augmented error surface using quantized states. It is shown that closed-loop stability analysis and tracking error convergence are conducted based on Lyapunov theory. Finally, we give simulation and experimental results of the 2-degrees-of-freedom (2-DOF) helicopter system for verifying to the validity of the proposed methodology where the tracking performance of pitch and yaw angles is measured with the mean squared errors of 0.1044 and 0.0435 for simulation results, and those of 0.0656 and 0.0523 for experimental results.

Adaptive finite-time tracking control for full state constrained nonlinear systems with time-varying delays and input saturation

2021 ◽  
pp. 014233122110658
Author(s):  
Tian Xu ◽  
Yuxiang Wu ◽  
Haoran Fang ◽  
Fuxi Wan
Keyword(s):  
Finite Time ◽  
Tracking Control ◽  
Tracking Error ◽  
Input Saturation ◽  
Time Derivative ◽  
Small Neighborhood ◽  
Constrained Systems ◽  
Design System ◽  
Time Varying ◽  
Full State

This paper investigates the adaptive finite-time tracking control problem for a class of nonlinear full state constrained systems with time-varying delays and input saturation. Compared with the previously published work, the considered system involves unknown time-varying delays, asymmetric input saturation, and time-varying asymmetric full state constraints. To ensure the state constraint satisfaction, the appropriate time-varying asymmetric Barrier Lyapunov Functions and the backstepping technique are utilized. Meanwhile, the finite covering lemma and the radial basis function neural networks are employed to solve the unknown time-varying delays. The assumption that the time derivative of time-varying delay functions is required to be less than one in traditional Lyapunov–Krasovskii functionals is removed by the proposed method. Moreover, the asymmetric input saturation is handled by an auxiliary design system. Taking the norm of the neural network weight vector as an adaptive parameter, a novel adaptive finite-time tracking controller with minimal learning parameters is constructed. It is proved that the proposed controller can guarantee that all signals in the closed-loop system are bounded, all states are constrained within the predefined sets, and the tracking error converges to a small neighborhood of the origin in a finite time. Finally, a comparison study simulation is given to demonstrate the effectiveness of our proposed strategy. The simulation results show that our proposed strategy has good advantages of high tracking precision and disturbance rejection.

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