scholarly journals Tracking Control Strategy Using Filter-Based Approximation for the Unknown Control Direction Problem of Uncertain Pure-Feedback Nonlinear Systems

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1341
Author(s):  
Yun Ho Choi ◽  
Sung Jin Yoo
Keyword(s):  
Controller Design ◽  
Tracking Error ◽  
Design Procedure ◽  
Control Input ◽  
State Variables ◽  
Feedback Systems ◽  
Unknown Control Directions ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction

A filter-based recursive tracker design approach is presented for the problem of unknown control directions of pure-feedback systems with completely unknown non-affine nonlinearities. In the controller design procedure, the first-order filters for error surfaces, a control input, and state variables are employed to design nonadaptive virtual and actual control laws independent of adaptive function approximators. In addition, for the unknown control direction problem, the filtering signals are incorporated with Nussbaum functions. Different from existing adaptive approximation-based control schemes in the presence of unknown control directions, the proposed approach does not require any adaptive technique regardless of completely unknown nonlinear functions. Therefore, a simplified tracking structure can be constructed. Using the Lyapunov stability analysis, it is shown that the tracking error is reduced within an adjustable neighborhood of the origin while ensuring all the closed-loop signals are bounded.

ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEAR TIME-VARYING DELAYS SYSTEMS WITH UNKNOWN CONTROL DIRECTION

2013 ◽  
Vol 21 (04) ◽  
pp. 497-531 ◽  
Author(s):  
HONGYUN YUE ◽  
JUNMIN LI
Keyword(s):  
Controller Design ◽  
Adaptive Fuzzy Control ◽  
Small Neighborhood ◽  
Design Procedure ◽  
Time Varying ◽  
Adaptive Fuzzy ◽  
Control Scheme ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction

An adaptive fuzzy control scheme with only one adjusted parameter is developed for a class of nonlinear time-varying delays systems. Three kinds of uncertainties: time-varying delays, control directions, and nonlinear functions are all assumed to be completely unknown, which is different from the previous work. During the controller design procedure, appropriate Lyapunov-Krasovskii functionals are used to compensate the unknown time-varying delays terms and the Nussbaum-type function is used to detect the unknown control direction. It is proved that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. The two main advantages of the developed scheme are that (i) by combining the appropriate Lyapunov-Krasovskii functionals with the Nussbaum-gain technique, the control scheme is proposed for a class of nonlinear time-varying delays systems with unknown control directions, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the computational burden greatly. Finally, two examples are used to show the effectiveness of the proposed approach.

scholarly journals Observer-Based Adaptive Fuzzy Predefined Performance Control of a Class of Nonlinear Pure-Feedback Systems with Input Delay

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xin Li ◽  
Qiang Zhang ◽  
Dakuo He
Keyword(s):  
Dynamic Surface Control ◽  
Input Delay ◽  
Feedback Systems ◽  
Estimation Errors ◽  
Dynamic Surface ◽  
Performance Control ◽  
Adaptive Fuzzy ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction

This paper presents a problem of observer-based adaptive fuzzy predefined performance control of a class of nonlinear pure-feedback systems with input delay and unknown control direction. Compared with the existing research, a novel predefined performance controller is proposed, which relaxes the assumption that the initial error is known. In addition, it is difficult to design the controllers due to input delay and nonaffine properties of the pure-feedback systems, which can be simplified by Pade approximation. Moreover, dynamic surface control and Nussbaum functions are applied to overcome the calculation explosion caused by repeated differentiations and unknown control direction, respectively. Based on the above methods, an adaptive fuzzy predefined performance controller is proposed, and it is proved that all the signals of a closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). The tracking errors converge within a predefined range, while the observer estimation errors converge within a small zero region. Finally, the simulation results demonstrate the effectiveness of the proposed control system.

Output Regulation Design for a Class of Nonlinear Systems With an Unknown Control Direction

2009 ◽  
Vol 132 (1) ◽  
Author(s):  
Dabo Xu ◽  
Jie Huang
Keyword(s):  
Nonlinear Systems ◽  
Lorenz System ◽  
Output Regulation ◽  
Feedback Systems ◽  
Asymptotic Tracking ◽  
Robust Output Regulation ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction ◽  
Output Regulation Problem

This paper presents the solution of the global robust output regulation problem for a class of nonlinear systems without knowing the control direction. The class of the systems is larger than previously studied strict output feedback systems of relative degree equal to one. The result is also applied to an asymptotic tracking problem associated with the well-known Lorenz system.

scholarly journals Finite-Time Performance Guaranteed Event-Triggered Adaptive  Control for  Nonlinear Systems with Unknown Control Direction

2021 ◽  
Author(s):  
Min Wang ◽  
Lixue Wang
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Tracking Error ◽  
Tracking Performance ◽  
Performance Function ◽  
Time Performance ◽  
Unknown Control ◽  
Unknown Control Direction ◽  
Control Direction ◽  
Event Triggered

Abstract This paper studies the issue of finite-time performance guaranteed event-triggered (ET) adaptive neural tracking control for strict-feedback nonlinear systems with unknown control direction. A novel finite-time performance function is first constructed to describe the prescribed tracking performance, and then a new lemma is given to show the differentiability and boundedness for the performance function, which is important for the verification of the closed-loop stability. Furthermore, with the help of the error transformation technique, the origin constrained tracking error is transformed into an equivalent unconstrained one. By utilizing the first-order sliding mode differentiator, the issue of ``explosion of complexity'' caused by the backstepping design is adequately addressed. Subsequently, an ingenious adaptive updated law is given to co-design the controller and the ET mechanism by the combination of the Nussbaum-type function, thus effectively handling the influences of the measurement error resulted from the ET mechanism and the challenge of the controller design caused by the unknown control direction. The presented event-triggered control scheme can not only guarantee the prescribed tracking performance, but also alleviate the communication burden simultaneously. Finally, numerical and practical examples are provided to demonstrate the validity of the proposed control strategy.

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