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

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.

Fuzzy Adaptive Control of Uncertain MIMO Chaotic Systems with Unknown Control Direction

This paper presents an adaptive controller for MIMO chaotic systems with system uncertainties and unknown control direction. In the controller design, the matrix decomposition theory is used, and we decompose the control gain matrix into a positive matrix, a diagonal matrix whose diagonal entries are +1 or −1, and a unity upper triangular matrix. To handle the unknown control direction (i.e., the unknown sign of the control gain matrix), we use the Nussbaum-type function. In addition, we propose an adaptation law named proportional integral (PI) law to update the parameters of the fuzzy system. The stability of the controlled system is proven strictly. Finally, simulation results are presented.

Adaptive Fuzzy Path Tracking Control for Mobile Robots with Unknown Control Direction

In order to synthesize controllers for wheeled mobile robots (WMRs), some design techniques are usually based on the assumption that the center of mass is at the center of the robot itself. Nevertheless, the exact position of the center of mass is not easy to measure, thus WMRs is a typical uncertain nonlinear system with unknown control direction. Based on the fast terminal sliding mode control, an adaptive fuzzy path tracking control scheme is proposed for mobile robots with unknown control direction. In this scheme, the fuzzy system is used to approximate unknown functions, and a robust controller is constructed to compensate for the approximation error. The Nussbaum-type functions are integrated into the robust controller to estimate the unknown control direction. It is proved that all the signals in the closed-loop system are bounded, and the tracking error converges to a small neighborhood of the origin in a limited time. The effectiveness of the proposed scheme is illustrated by a simulation example.

Adaptive Sliding Mode Control for a Robotic Manipulator with Unknown Friction and Unknown Control Direction

This paper is aimed at addressing the tracking control issue for an n-DOF manipulator regardless of unknown friction and unknown control direction. In order to handle the above issues, an adaptive sliding mode control (ASMC) is developed with a Nussbaum function. The sliding mode control (SMC) in the proposed control guarantees the tracking problem and fast responses for the manipulator. Additionally, there are adaptive laws for the robust gain in the SMC to deal with the unknown external disturbance and reduce the chattering effect in the system. In practice, the mistakes in the connection between actuators and drivers, named unknown control direction, cause serious damage to the manipulator. To overcome this issue, the Nussbaum function is multiplied by the ASMC law. A Lyapunov approach is investigated to analyze the stability and robustness of the whole system. Finally, several simulations are implemented on a 3-DOF manipulator and their results are compared with those of the existing controllers to validate the advantages of the proposed method.