Contents I. Introduction
The investigations on stabilization/tracking control problems for nonlinear systems have drawn researchers’ attention during the past decades due to their widely potential applications in real engineering world and the fact that actual physical plants are always naturally nonlinear, and numerous methods have been proposed, see for example [1]–[7]. In order to solve the control problems for different types of nonlinear systems, different control strategies such as sliding mode, feedback linearize, and distributed control were proposed. Among these different nonlinear control methods, adaptive backstepping control method, which was first introduced in [8], is one of the most effective way to handle the tracking/stabilization design problems for nonlinear systems subject to lower triangular structure, i.e., strict-feedback structure. For example, the problem of adaptive control for nonlinear systems with strict-feedback structure under the effect of umodeled dynamics and uncertainties was studied in [9] by introducing a combined small-gain and backstepping strategy. Furthermore, in order to achieve the tracking control of nonlinear systems that have high-frequency gains, Nussbaum gain function was introduced in the backstepping designing process in [10] to achieve the asymptotic tracking performance. Due to that traditional adaptive backstepping design technique requires iterative differentials of the modeled nonlinearities, the authors in [11] introduced a simplified dynamic surface control (DSC) strategy, in which the computational burden of the traditional backstepping-based algorithms was greatly reduced. Furthermore, if there exist unknown nonlinear terms in the overall closed-loop dynamics, intelligent modeling technique, such as fuzzy logic systems (FLSs) were utilized by making use of its universal approximation ability [12]–[21]. Take some results for example, the authors in [12] considered a class of large-scale nonlinear systems with nonstrict feedback type structure, which contains unknown terms, uncertainties, and interconnected terms. A novel adaptive control method was then introduced by incorporating decentralized methodology and sampled-data state observer, in which only the output was sampled and transmitted. Under the recursive design, the overall closed-loop system and signals were finally guaranteed to be bounded. The authors in [14] investigated the DSC for a class of multiinput multioutput (MIMO) nonlinear systems with the help of a novel fuzzy state observer, and the computational burden was greatly reduced by avoiding iterative derivations. The authors in [16] studied the control problem for the same type of systems with system uncertainties and time-varying state constraints, in which barrier Lyapunov functions were introduced for constraints compensation. While the authors in [17] investigated the output feedback control strategy for uncertain nonstrict feedback large-scale interconnected systems via a novel fuzzy decentralized control mechanism, in which an innovative sampled-data nonlinear state state observer was introduced to estimate the unmeasured states. The authors in [18] investigated the event mechanism of dynamical nonlinear systems, in which a novel self-triggered control scheme was proposed by predicting system state and error values, which shows its advantages over static event-triggered mechanism. The authors in [19] investigated the control problem for a class of nonlinear systems by introducing Takagi–Sugeno (T–S) fuzzy modeling technique, and a novel repetitive control scheme incorporating T–S model was presented with the aim of reducing the conservatism of existing results and increasing the feasibility solution space regarding the stabilization conditions. The authors in [21] introduced a novel function to compensate the constraints. The closed-loop nonlinear system was then transformed from constrained to free-constrained. The advantage is that the proposed strategy relaxed the feasibility condition of the intermediate virtual controller. Similar results can also be found by considering different cases [22]–[26]. However, the aforementioned results are mainly focused on the traditional nonlinear systems without taking consideration on the external stochastic disturbances.
