This paper addresses the containment control problem of multi-agent systems (MASs) under directed topologies, where the model of each agent is an unknown nonlinear non-affine pure-feedback dynamic and at the same time the outputs and their derivatives of the leaders are unknown. To avoid the complex design process with the recursive methods (i.e., backstepping and dynamic surface), each unknown higher-order nonlinear dynamic is transformed into a simple high-order integral model with unknown affine nonlinear terms in the last-order dynamic at first. Then the fuzzy logic systems (FLSs) and the fuzzy state observers are constructed to approximate the unknown affine nonlinear terms and the unknown transformed states. Finally, a novel fully distributed fuzzy adaptive containment control law is generated according to the state observers and the supervised control. The stability of the closed-loop system is analyzed in the Lyapunov sense and the containment errors converge to a small neighborhood of the origin. Simulation results show the feasibility and effectiveness of the proposed scheme.

This paper addresses the tracking control problem of uncertain nonlinear strict-feedback systems. Firstly, to enhance the tracking performance of control system, an improved prescribed performance function is constructed, which yields that the convergence accuracy of tracking error can reach a preset factor than that of the traditional prescribed performance function-based control method. Then the fuzzy logic system is used to approximate the unknown nonlinear dynamics on a compact set integrated by an ideal controller, from which an adaptive fuzzy control law is designed by combining the improved prescribed performance function and fuzzy logic system. The stability of closed-loop system and the convergence of tracking error are analyzed in the Lyapunov sense. Finally, simulation and experimental results show the feasibility and effectiveness of the proposed method.

In this paper, a design method of indirect adaptive fuzzy controller is proposed for a class of SISO nonlinear systems with input-output nonlinear relationship. In this method, fuzzy systems are utilized to approximate unknown nonlinear functions, and a state observer is designed to estimate the unmeasured state. Under the given constraint conditions of the system parameters, the adaptive law is given. Meanwhile, the stability of the closed-loop system is proven with all state variables being uniformly bounded in the Lyapunov sense. Moreover, the convergence of the fuzzy control system is analyzed. The simulation results show the feasibility, effectiveness and universality of the designed method.

In this paper, an indirect adaptive fuzzy control scheme is proposed for single-input, single-output (SISO) nonaffine nonlinear systems in a pure-feedback form. In this scheme, the unknown nonlinear functions are approximated by Takagi-Sugeno (T-S) fuzzy logic systems with an state observer. The adaptive laws are developed to adjust the parameters of the fuzzy systems. The stability of the closed-loop system is proved with all state variables being uniformly bounded in the Lyapunov sense and the tracking error is confirmed to zero asymptotically. Finally, simulation results obtained for two practical examples show the feasibility and effectiveness of the proposed scheme.

This article addresses the tracking control problem of nonlinear pure-feedback systems, where the control coefficients and the dynamics of the references are unknown. Fuzzy-logic systems (FLSs) are used to approximate the unknown control coefficients and at the same time the adaptive projection law is designed to allow each fuzzy approximation to cross zero, which yields that the proposed method avoids the assumption of using Nussbaum function, that is, the unknown control coefficients never cross zeros. Another adaptive law is designed to estimate the unknown reference and then it is intergraded into the saturated tracking control law to achieve the uniformly ultimately bounded (UUB) performance of the resulting closed-loop system. Simulations show the feasibility and effectiveness of the proposed scheme.