Haibo Du

Brief paper: Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics

In this paper, we discuss the finite-time consensus problem for leaderless and leader-follower multi-agent systems with external disturbances. Based on the finite-time control technique, continuous distributed control algorithms are designed for these agents described by double integrators. Firstly, for the leaderless multi-agent systems, it is shown that the states of all agents can reach a consensus in finite time in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a region in finite time. Secondly, for the leader-follower multi-agent systems, finite-time consensus algorithms are also designed based on distributed finite-time observers. Rigorous proof is given by using Lyapunov theory and graph theory. Finally, one example is employed to verify the efficiency of the proposed method.

Finite-Time Attitude Tracking Control of Spacecraft With Application to Attitude Synchronization

This note investigates the finite-time attitude control problems for a single spacecraft and multiple spacecraft. First of all, a finite-time controller is designed to solve finite-time attitude tracking problem for a single spacecraft. Rigorous proof shows that the desired attitude can be tracked in finite time in the absence of disturbances. In the presence of disturbances, the tracking errors can reach a region around the origin in finite time. Then, based on the neighbor rule, a distributed finite-time attitude control law is proposed for a group of spacecraft with a leader-follower architecture. Under the finite-time control law, the attitude synchronization can be achieved in finite time.

Finite-time boundedness and L2-gain analysis for switched delay systems with norm-bounded disturbance

Abstract Finite-time boundedness and finite-time weighted L 2 -gain for a class of switched delay systems with time-varying exogenous disturbances are studied. Based on the average dwell-time technique, sufficient conditions which guarantee the switched linear system with time-delay is finite-time bounded and has finite-time weighted L 2 -gain are given. These conditions are delay-dependent and are given in terms of linear matrix inequalities. Detail proofs are given by using multiple Lyapunov-like functions. An example is employed to verify the efficiency of the proposed method.

Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control

This paper considers the problem of finite-time synchronization for a class of second-order nonlinear multi-agent systems with a leader-follower architecture. By using the finite-time control technique and homogenous systems theory, a finite-time state feedback controller is first proposed. Then to address the lack of velocity measurement, a finite-time convergent observer is constructed to estimate the unknown velocity information in a finite time. Finally, an observer-based finite-time output feedback controller is developed. Rigorous proof shows that the systems output can reach synchronization in a finite time and the final consensus states are the leaders states. In addition, for some special second-order multi-agent systems, a bounded finite-time output feedback controller can also be designed.

Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems

This paper considers the problem of designing globally finite-time convergent observers for a class of nonlinear systems with time-varying and output-dependent coefficients, which make the existing design approaches inapplicable. To solve this problem, a bottom-up design approach is first employed to recursively construct a finite-time convergent observer with time-varying coefficients for the nominal system. Then, using the homogeneous domination approach, we scale the finite-time convergent observer with an appropriate choice of gain for the original nonlinear system satisfying a Holder condition. In addition, we show that the Holder condition imposed on the nonlinearities can be removed for nonlinear systems with bounded trajectories.

Robust consensus algorithm for second-order multi-agent systems with external disturbances

This article investigates the problem of robust consensus for second-order multi-agent systems with external disturbances. Based on a non-smooth backstepping control technique, a class of novel continuous non-smooth consensus algorithms are proposed for the multi-agent network with/without communication delays. The controller design is divided into two steps. First, for the kinematic subsystem, the velocity is regarded as a virtual input and designed such that the states consensus can be achieved asymptotically. Then for the dynamic subsystem, a finite-time control law is designed such that the virtual velocity can be tracked by the real velocity in a finite time. Under the proposed control law, it is shown that if the communication topology graph contains a directed spanning tree, the states consensus can be achieved asymptotically in the absence of disturbances. In the presence of disturbances, the steady-state errors of any two agents can reach a small region around the origin. By building a relationship between control parameters and the bound of steady tracking errors, it is demonstrated that the disturbance rejection performance of the resulting closed-loop system can be enhanced by adjusting the fractional power in the non-smooth controller. Finally, an example is given to verify the efficiency of the proposed method.

Global Output Feedback Stabilization of a Class of Nonlinear Systems via Linear Sampled-Data Control

In the literature, it has been proved that under a lower-triangular linear growth condition, a class of uncertain nonlinear systems can be globally stabilized by a linear state feedback controller (Tsinias) and later by a linear output feedback controller (Qian and Lin), both in the continuous-time form. This technical note shows that the same continuous-time system under the same assumption can be globally stabilized by a sampled-data output feedback controller whose observer and control law are discrete-time and linear, and hence can be easily implemented by computers.

Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer

The consensus tracking problem of multiple nonholonomic high-order chained-form systems is considered in this paper. A finite-time observer-based distributed control strategy is proposed. At the first step, a distributed finite-time convergent observer is proposed for each agent to estimate the leaders state in a finite time. Then, a finite-time tracking controller is designed to track the estimated state and the leaders attitude in a finite time. As an application of the proposed results, finite-time formation control of multiple wheeled mobile robots is studied and a finite-time formation control algorithm is proposed. To show effectiveness of the proposed approach, a simulation example is given.

Finite-time stability and stabilization of switched linear systems

In this paper, finite-time stability and stabilization problems for switched linear systems are discussed. Firstly, the concept of finite-time stability is extended to switched linear systems. Then, based on the state transition matrix of the system, a necessary and sufficient condition for finite-time stability of switched linear systems is presented. For ease of reference, some sufficient conditions under which the switched linear systems are finite-time stable and uniformly finite-time stable are given by virtue of matrix inequalities. Moreover, stabilizing state feedback controllers and a class of switching signals with average dwell-time are designed in detail to solve finite-time stabilization problem. The main results are proved by using the multiple Lyapunov-like functions and common Lyapunov-like function respectively. Finally, two examples are employed to verify the efficiency of the proposed method.

Finite-time tracking control of multiple nonholonomic mobile robots

Abstract This paper investigates finite-time tracking control problem of multiple nonholonomic wheeled mobile robots in dynamic model. First of all, the resulting tracking error dynamic is transformed into two subsystems, i.e., a third-order subsystem and a second-order subsystem for each mobile robot. Then, the two subsystems are discussed respectively, continuous distributed finite-time tracking control laws are designed for each mobile robot. Rigorous proof shows that the group of mobile robots can track the desired trajectory in finite time. Simulation example illustrates the effectiveness of our method.