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.

Tracking control for strict-feedback nonlinear systems with time-varying full state constraints

2018 ◽  
Vol 40 (14) ◽  
pp. 3964-3977 ◽  
Author(s):  
Chunxiao Wang ◽  
Yuqiang Wu ◽  
Zhongcai Zhang
Keyword(s):  
Nonlinear Systems ◽  
Tracking Control ◽  
State Constraints ◽  
Tracking Error ◽  
Input Saturation ◽  
Constrained Systems ◽  
Time Varying ◽  
Full State ◽  
Full State Constraints ◽  
Strict Feedback

This paper focuses on the tracking control problem for strict-feedback nonlinear systems subject to asymmetric time-varying full state constraints. Time-varying asymmetric barrier Lyapunov functions are employed to ensure time-varying constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. High-order coupling terms caused by backstepping are cancelled through a novel variable substitution for the first time. Besides the normal case, where the full knowledge of the system is available, we also handle scenarios of parametric uncertainties. Asymptotic tracking is achieved without violation of any constraints, and all signals in the closed-loop system are ultimately bounded. State-constrained systems with input saturation and bounded disturbances are also considered; the tracking error converges to a bounded set around zero. The performance of the asymmetric-barrier-Lyapunov-function-based control is illustrated through a numerical example.

Finite-time tracking control for nonstrict-feedback nonlinear systems with unknown time delays and input saturation

2021 ◽  
pp. 014233122110583
Author(s):  
Xiaojing Qi ◽  
Wenhui Liu
Keyword(s):  
Finite Time ◽  
State Constraints ◽  
Tracking Error ◽  
Input Saturation ◽  
Small Neighborhood ◽  
Delay Systems ◽  
Fuzzy Logic Systems ◽  
Time Control ◽  
Full State ◽  
Full State Constraints

In this article, the problem of adaptive finite-time control is studied for a category of nonstrict-feedback nonlinear time-delay systems with input saturation and full state constraints. The fuzzy logic systems are applied to model the unknown nonlinear terms in the systems. Then, a novel tan-type barrier Lyapunov function is adopted to overcome the problem of full state constraints. By utilizing the finite-time control theory and the backstepping technique, a finite-time fuzzy adaptive controller is designed. The controller can guarantee that the tracking error is adjusted around zero with a small neighborhood in a finite time and all the signals in the closed-loop system are bounded. Finally, two simulation examples are included to verify the validity and feasibility of the control scheme.

scholarly journals Prescribed Performance Control of Marine Surface Vessel Trajectory Tracking in Finite-Time with Full-State Constraints and Input Saturation

2021 ◽  
Vol 9 (8) ◽  
pp. 866
Author(s):  
Xiyun Jiang ◽  
Yuanhui Wang
Keyword(s):  
Finite Time ◽  
State Constraints ◽  
Tracking Error ◽  
Input Saturation ◽  
Prescribed Performance ◽  
Full State ◽  
Marine Surface ◽  
Surface Vessel ◽  
Full State Constraints ◽  
Function Matrix

This manuscript mainly solves a fully actuated marine surface vessel prescribed performance trajectory tracking control problem with full-state constraints and input saturation. The entire control design process is based on a backstepping technique. The prescribed performance control is introduced to embody the analytical relationship between the transient performance and steady-state performance of the system and the parameters. Meanwhile, a new finite time performance function is introduced to ensure that the performance of the system tracking error is constrained within the preset constraints in finite time, and the full-state constraints problem of the system can be solved simultaneously in the entire control design, at the same time without introducing additional theory and parameters. To solve the non-smooth input saturation function matrix is not differentiable, the smooth function matrix is introduced to replace the non-smooth characteristics. Combining the Moore-Penrose generalized inverse matrix to design the virtual control law, the dynamic surface control is introduced to avoid the complicated virtual control derivation process, and finally the actual control law is designed using the properties of Nussbaum function. In addition, in view of the uncertainties in the system, a fractional disturbance observer is designed to estimate it. With the proposed control, the full-state will never be violated constraints, and the system tracking error satisfies transient and steady-state performance. Compared with other methods, the simulation results show the effectiveness and advantages of the proposed method.

scholarly journals Finite-Time Tracking Control for Nonstrict-Feedback State-Delayed Nonlinear Systems with Full-State Constraints and Unmodeled Dynamics

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Yangang Yao ◽  
Jieqing Tan ◽  
Jian Wu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Tracking Control ◽  
State Constraints ◽  
Unmodeled Dynamics ◽  
Time Varying ◽  
Cubic Form ◽  
Time Control ◽  
Full State ◽  
Full State Constraints

The problem of finite-time tracking control is discussed for a class of uncertain nonstrict-feedback time-varying state delay nonlinear systems with full-state constraints and unmodeled dynamics. Different from traditional finite-control methods, a C 1 smooth finite-time adaptive control framework is introduced by employing a smooth switch between the fractional and cubic form state feedback, so that the desired fast finite-time control performance can be guaranteed. By constructing appropriate Lyapunov-Krasovskii functionals, the uncertain terms produced by time-varying state delays are compensated for and unmodeled dynamics is coped with by introducing a dynamical signal. In order to avoid the inherent problem of “complexity of explosion” in the backstepping-design process, the DSC technology with a novel nonlinear filter is introduced to simplify the structure of the controller. Furthermore, the results show that all the internal error signals are driven to converge into small regions in a finite time, and the full-state constraints are not violated. Simulation results verify the effectiveness of the proposed method.

Command filtered adaptive neural tracking control of uncertain nonlinear time-delay systems with asymmetric time-varying full state constraints and actuator saturation

2020 ◽  
pp. 095965182097526
Author(s):  
Yuxiang Wu ◽  
Tian Xu ◽  
Haoran Fang
Keyword(s):  
Time Delay ◽  
Tracking Control ◽  
State Constraints ◽  
Actuator Saturation ◽  
Small Neighborhood ◽  
Delay Systems ◽  
Time Varying ◽  
Time Delay Systems ◽  
Full State ◽  
Full State Constraints

This article investigates the command filtered adaptive neural tracking control for uncertain nonlinear time-delay systems subject to asymmetric time-varying full state constraints and actuator saturation. To stabilize such a class of systems, the radial basis function neural networks and the backstepping technique are used to structure an adaptive controller. The command filter is utilized to overcome the complexity explosion problem in backstepping. By employing the Lyapunov–Krasovskii functionals, the effect of time-delay is eliminated. The asymmetric time-varying barrier Lyapunov functions are designed to ensure full state constraint satisfaction. Moreover, the hyperbolic tangent function and an instrumental variable are introduced to deal with actuator saturation. All signals in the closed-loop system are proved to be bounded and the tracking error converges to a small neighborhood of the origin. Finally, two examples are provided to illustrate the effectiveness of the proposed method.

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 Fixed-Time Bounded H Infinity Tracking Control of a Single-Joint Manipulator System with Input Saturation

2021 ◽  
Author(s):  
ming chen
Keyword(s):  
Tracking Control ◽  
Initial Conditions ◽  
Tracking Error ◽  
Input Saturation ◽  
Small Neighborhood ◽  
Fixed Time ◽  
H Infinity ◽  
Finite Time Stability ◽  
Control Objective ◽  
H Infinity Control

Abstract Based on Lyapunov finite-time stability theory and backstepping strategy, we put forward a novel fixed-time bounded H infinity tracking control scheme for a single-joint manipulator system with input saturation. The main control objective is to maintain that the system output variable tracks the desired signal at fixed time. The advantages of this paper are the settling time of the tracking error converging to the origin is independent of the initial conditions, and its convergence speed is more faster. Meanwhile, bounded H infinity control is adopted to suppress the influence of the external disturbances on the controlled system. At the same time, the problem of input saturation control is considered, which effectively reduce the input energy consumption. Theoretical analysis shows that the tracking error of the closed-loop system converges to a small neighborhood of the origin within fixed time. In the end, a simulation example is presented to demonstrate the effectiveness of the proposed scheme.

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