This paper considers the fuzzy finite-time tracking control problem for a class of nonlinear systems with input saturation. A novel fuzzy finite-time command filtered backstepping approach is proposed by introducing the fuzzy finite-time command filter, designing the new virtual control signals and the modified error compensation signals. The proposed approach not only holds the advantages of the conventional command-filtered backstepping control, but also guarantees the finite-time convergence. A practical example is included to show the effectiveness of the proposed method.

In this paper, the tracking control problem is considered for a class of multiple-input multiple-output (MIMO) nonlinear systems with input saturation and unknown direction control gains. A command filtered adaptive neural networks (NNs) control method is presented with regard to the MIMO systems by designing the virtual controllers and error compensation signals. First, the command filtering is used to solve the ``explosion of complexity'' problem in the conventional backstepping design and the nonlinearities are approximated by NNs. Then, the error compensation signals are developed to conquer the shortcoming of the dynamic surface method. In addition, the Nussbaum-type functions are utilized to cope with the unknown direction control gains. The effectiveness of the proposed new design scheme is illustrated by simulation examples.

A terminal sliding mode control method based on nonlinear disturbance observer is investigated to realize the speed and current tracking control for PMSM drive system in this paper. The proposed method adopts the speed-current single-loop control structure instead of the traditional cascade control in the vector control of PMSM. Firstly, considering the nonlinear and the coupling characteristic, a single-loop terminal sliding mode controller is designed for PMSM drive system through feedback linearization technology. This method can make the motor speed and current reach the reference value in finite time, which can realize the fast transient response. Although the sliding mode control is less sensitive to parameter uncertainties and external disturbance, it may produce a large switching gain, which may cause the undesired chattering. Meanwhile, the sliding mode control cannot keep the property of invariance in the presence of unmatched uncertainties. Then, a nonlinear disturbance observer is proposed to the estimate the lump disturbance, which is used in the feed-forward compensation control. Thus, a composite control scheme is developed for the PMSM drive system. The results show that the motor control system based on the proposed method has good speed and current tracking performance and strong robustness.

This paper proposes an adaptive funnel control (FC) scheme for servo mechanisms with an unknown dead-zone. To improve the transient and steady-state performance, a modified funnel variable, which relaxes the limitation of the original FC (e.g., systems with relative degree 1 or 2), is developed using the tracking error to replace the scaling factor. Then, by applying the error transformation method, the original error is transformed into a new error variable which is used in the controller design. By using an improved funnel function in a dynamic surface control procedure, an adaptive funnel controller is proposed to guarantee that the output error remains within a predefined funnel boundary. A novel command filter technique is introduced by using the Levant differentiator to eliminate the ``explosion of complexity'' problem in the conventional backstepping procedure. Neural networks are used to approximate the unknown dead-zone and unknown nonlinear functions. Comparative experiments on a turntable servo mechanism confirm the effectiveness of the devised control method.

In this paper, the adaptive finite-time attitude tracking control problem for rigid spacecraft with upper bounds unknown external disturbances is studied by using a novel combining control scheme of adaptive control technique and adding a power integrator (AAPI) technique. An adaptive finitetime control law with boundary layer is firstly established under the proposed combined control scheme, which can attenuate the influences of disturbances and contain the advantages of AAPI technique. Then, another adaptive finite-time control law without boundary layer is further given, which can simply the control design. It is proofed that both the two control laws can ensure the tracking errors converge to the desired regions in finite-time. Moreover, since the established two control laws are both designed with continuous control architecture, the chattering problem is eliminated, which are more adopt to practical engineering applications. An example is included to show the effectiveness of the proposed methods.

It is well known that all agents in a multiagent system can asymptotically converge to a common value based on consensus protocols. Besides, the associated convergence rate depends on the magnitude of the smallest nonzero eigenvalue of Laplacian matrix L. In this paper, we introduce a superposition system to superpose to the original system and study how to change the convergence rate without destroying the connectivity of undirected communication graphs. And we find the result if the eigenvector x of eigenvalue λ has two identical entries x_i = x_j, then the weight and existence of the edge e_ij do not affect the magnitude of λ, which is the argument of this paper. By taking advantage of the inequality of eigenvalues, conditions are derived to achieve the largest convergence rate with the largest delay margin, and, at the same time, the corresponding topology structure is characterized in detail. In addition, a method of constructing invalid algebraic connectivity weights is proposed to keep the convergence rate unchanged. Finally, simulations are given to demonstrate the effectiveness of the results.