In this technical note, the problem of event-trigger based adaptive control for a class of uncertain nonlinear systems is considered. The nonlinearities of the system are not required to be globally Lipschitz. Since the system contains unknown parameters, it is a difficult task to check the assumption of the input-to-state stability (ISS) with respect to the measurement errors, which is required in most existing literature. To solve this problem, we design both the adaptive controller and the triggering event at the same time such that the ISS assumption is no longer needed. In addition to presenting new design methodologies based on the fixed threshold strategy and relative threshold strategy, we also propose a new strategy named the switching threshold strategy. It is shown that the proposed control schemes guarantee that all the closed-loop signals are globally bounded and the tracking/stabilization error exponentially converges towards a compact set which is adjustable.

In this technical note, we consider adaptive control of single input uncertain nonlinear systems in the presence of input saturation and unknown external disturbance. By using backstepping approaches, two new robust adaptive control algorithms are developed by introducing a well defined smooth function and using a Nussbaum function. The Nussbaum function is introduced to compensate for the nonlinear term arising from the input saturation. Unlike some existing control schemes for systems with input saturation, the developed controllers do not require assumptions on the uncertain parameters within a known compact set and a priori knowledge on the bound of the external disturbance. Besides showing global stability, transient performance is also established and can be adjusted by tuning certain design parameters.

In this paper, restorations for both voltage and frequency in the droop-controlled inverter-based islanded microgrid (MG) are addressed. A distributed finite-time control approach is used in the voltage restoration which enables the voltages at all the distributed generations (DGs) to converge to the reference value in finite time, and thus, the voltage and frequency control design can be separated. Then, a consensus-based distributed frequency control is proposed for frequency restoration, subject to certain control input constraints. Our control strategies are implemented on the local DGs, and thus, no central controller is required in contrast to existing control schemes proposed so far. By allowing these controllers to communicate with their neighboring controllers, the proposed control strategy can restore both voltage and frequency to their respective reference values while having accurate real power sharing, under a sufficient local stability condition established. An islanded MG test system consisting of four DGs is built in MATLAB to illustrate our design approach, and the results validate our proposed control strategy.

In this note, we consider the same class of systems as in a previous paper, i.e., a class of uncertain dynamic nonlinear systems preceded by unknown backlash-like hysteresis nonlinearities, where the hysteresis is modeled by a differential equation, in the presence of bounded external disturbances. By using backstepping technique, robust adaptive backstepping control algorithms are developed. Unlike some existing control schemes for systems with hysteresis, the developed backstepping controllers do not require the uncertain parameters within known intervals. Also, no knowledge is assumed on the bound of the "disturbance-like" term, a combination of the external disturbances and a term separated from the hysteresis model. It is shown that the proposed controllers not only can guarantee global stability, but also transient performance.