This paper focuses on the adaptive control problem for a class of nonlinear single-input single-output lower triangular systems with partial state constraints and unknown backlash-like hysteresis. To prevent the partial states from transgressing the predefined constrained region, a barrier Lyapunov function is presented, whose values will increase to infinity when any of its parameters grows to a given boundary value. To counteract the effect caused by the backlash-like hysteresis, an auxiliary variable with its adaptive mechanism is introduced in the backstepping technique. At the same time, the output of the considered systems can track the reference signal, and all the variables in the design procedure are uniformly ultimate boundedness. In the end, a numerical example is employed to validate the efficiency of the developed theoretical method.

In this paper, the fault detection problem for a class of switched nonlinear systems with unknown functions is solved. First, the unknown internal dynamics are approximated by the radial basis function neural networks due to their powerful approximation capabilities. Then, a switched nonlinear observer is developed. Based on the observer, a fault detection scheme is set up with a switched fault detection threshold instead of a common threshold. At the same time, the boundedness of all the signals in the closed-loop system can be guaranteed by using the average dwell time method. Moreover, the fault detection threshold is dependent on the average dwell time, which implies that the fault sensibility can be improved to a certain extent by selecting the average dwell time. Finally, a simulation example on the Chua's circuit system are employed to show the effectiveness of the proposed scheme.

Here, an adaptive neural control problem for a switched non‐linear system with multiple tracking error constraints is studied by using the dwell‐time method. The unknown functions are approximated by radial basis function neural networks. In order to avoid the difficulty caused by the adoption of different coordinate transformations, a common transition function is selected. Moreover, different update laws are designed for both active time‐interval and inactive time‐interval of each subsystem. The proposed controllers and switching signals guarantee the stability of the closed‐loop system and the boundedness of all signals. Furthermore, both transient‐state and steady‐state performances of the tracking errors are ensured. Finally, a simulation example is used to clarify the effectiveness of the proposed method.

In this paper, a class of flexible riser systems modeled by partial differential equations (PDEs) with the backlash is considered. The backlash is formulated as the addition of a linear input and a interference-like term, then an new auxiliary item is introduced to compensate for the impact of this backlash. In addition, the constraint problem for the position and the velocity is also taken into consideration. To solve this constrain problem, the logarithmic barrier Lyapunov function is employed. For the flexible riser system, two kinds of adaptive controllers are proposed under the following two cases. One controller is designed when only the parameter of backlash is unknown. On the basis of this result, the other controller is presented when some system parameters cannot be measured through actual measurement. Then, combing the theory of Lyapunov stability, the two controllers can guarantee the boundedness of all signals in the closed-loop flexible riser system. Further, both the position and the velocity satisfy their corresponding constraint condition. Finally, the simulation example verifies that the proposed control method is effective.

The active fault-tolerant control (FTC) problem for a class of switched nonlinear systems is investigated by using average dwell time method. First, an observer-based fault detection scheme is established. Because only the system output is assumed to be available, the threshold of fault detection only depends on the output error. Moreover, all the signals in the closed-loop system are bounded in fault-free case. After a fault has been detected, the fault estimation and FTC schemes are activated. Due to the existence of faults, unstable subsystems are allowed to exist. The fault-tolerant controllers of subsystems and a class of switching signals with average dwell time are designed such that all the signals in the closed-loop system remain bounded, and the system states can be estimated by the observer. Finally, in order to illustrate the effectiveness of the proposed method, we apply it to the switched RCL circuit system.