In this brief, the practical finite-time consensus (FTC) problem is investigated for the second-order heterogeneous switched nonlinear multi-agent systems (MASs), where the subsystems and the switching signal for each agent are different. Mainly due to that agents’ dynamics are switched and the unknown nonlinearities in the systems are more general, the practical FTC problem of the MASs is rather difficult to be solved by existing methods. As such, a new protocol design framework for the FTC problem is developed. Then, a novel adaptive protocol is proposed for the switched nonlinear MASs based on the developed design framework and the neural network method. The sufficient conditions for the practical FTC of nonlinear MASs under arbitrary switching are given. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed control scheme.

Finite-Time Consensus of Second-Order Switched Nonlinear Multi-Agent Systems

The adaptive fuzzy finite-time tracking control problem of a class of switched nonlinear systems is investigated in this study. Fuzzy logic systems are introduced to handle the unknown nonlinear terms in the considered system. To overcome the drawback in the recursive design method, a finite-time command filter is employed. By constructing a new state-dependent switching law and adaptive fuzzy control signal, the existing restrictions on subsystems of switched systems are relaxed, all subsystems of the considered system are allowed to be unstabilizable. To avoid the Zeno behavior, a new hysteresis switching law is derived. It is proven that all states of the closed-loop system are bounded in finite time under the proposed fuzzy finite-time control scheme. Additionally, the proposed control method is extended to a class of more general switched large-scale nonlinear systems. Finally, two examples are provided to verify the developed method's effectiveness.

Command-Filter-Based Adaptive Fuzzy Finite-Time Control for Switched Nonlinear Systems Using State-Dependent Switching Method

A constructive method is presented to design controllers that force the output of nonlinear systems in a strict feedback form to track a bounded and sufficiently smooth reference trajectory asymptotically. Under a suitable condition on the initial output tracking error, the proposed controllers guarantee the output tracking error within a symmetric or an asymmetric pre-specified limit range, and boundedness of all signals of the closed-loop system. A transformation is introduced to take care of the output tracking error constraint. Smooth and/or p-times differentiable step functions are proposed and incorporated in the output tracking error transformation to overcome difficulties due to the asymmetric limit range on the output tracking error. As a result, there are no switchings in the proposed controllers despite the asymmetric limit range. The proposed control design is then applied to design a tracking controller for active magnetic bearings as an illustrating application.

Control of Nonlinear Systems with Output Tracking Error Constraints

This paper deals with the predefined-time stabilisation problem for a class of uncertain chained-form nonholonomic systems. Based on a novel generalised Lyapunov-like characterisation of predefined...

Predefined-time stabilisation of a class of nonholonomic systems

The finite/fixed-time stabilization and tracking control is currently a hot field in various systems since the faster convergence can be obtained. By contrast to the asymptotic stability, the finite-time stability possesses the better control performance and disturbance rejection property. Different from the finite-time stability, the fixed-time stability has a faster convergence speed and the upper bound of the settling time can be estimated. Moreover, the convergent time does not rely on the initial information. This work aims at presenting an overview of the finite/fixed-time stabilization and tracking control and its applications in engineering systems. Firstly, several fundamental definitions on the finite/fixed-time stability are recalled. Then, the research results on the finite/fixed-time stabilization and tracking control are reviewed in detail and categorized via diverse input signal structures and engineering applications. Finally, some challenging problems needed to be solved are presented. 

An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application

The global fixed-time stabilization of a class of perturbed planar nonlinear systems using output feedback is addressed in this brief. Under a generalized Lipschitz continuous condition, a constructive controller design of global output feedback is proposed based on a continuous fixed-time observer. The bi-limit homogeneity technique is employed to show global fixed-time stability of the closed-loop system. Simulation of a MEMS mirror model illustrates the appealing performance of the proposed method.

Global Fixed-Time Output Feedback Stabilization of Perturbed Planar Nonlinear Systems

This paper studies the problem of finite-time stabilisation for a class of uncertain nonholonomic systems in chained form with output constraint. A nonlinear mapping is first introduced to transfor...

Finite-time stabilisation for a class of output-constrained nonholonomic systems with its application

The design of global fixed-time observer for a category of lower-triangular nonlinear systems is reported in this brief. Under a wild condition that admits the Holder continuous conditions as a special case, a constructive algorithm of global fixed-time observer design is proposed by virtue of non-recursive combining bi-limit homogeneous technique. Rigorous stability analysis as well as robustness with respect to exogenous disturbances is provided to show the proposed observer ensuring global fixed-time convergent performance of the estimation error dynamics. Simulation results of an example of MEMS mirror with the nonlinear viscous damping dissipative load are given to confirm the effectiveness of the proposed algorithm.

Fangzheng Gao

Papers

Finite‐time stabilization for a class of switched stochastic nonlinear systems with dead‐zone input nonlinearities

Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application

Global Fixed-Time Output Feedback Stabilization of Perturbed Planar Nonlinear Systems

Finite-time stabilisation for a class of output-constrained nonholonomic systems with its application

A General Fixed-Time Observer for Lower-Triangular Nonlinear Systems