Lixia Liu

Bio: Lixia Liu is an academic researcher from Qilu University of Technology. The author has contributed to research in topics: Control system & Network topology. The author has an hindex of 1, co-authored 1 publications receiving 29 citations.

Consensus Control for Networked Manipulators With Switched Parameters and Topologies

Abstract: To solve abruptly occurrence of parameters jumping and directed communication topologies changing in the control process of networked manipulators, in this paper, distributed switched consensus control algorithms are formulated for a group of robot manipulators in realizing cooperative consensus performance. In fact, networked Lagrange systems are modeled as switched systems regarding the different parameters and topologies. Namely, the dynamic models switch when the system parameters or the topology structures change. The consensus control strategy is constructed by resorting to (improved) average dwell time (ADT) method and sliding-mode control technique, and a unified analysis methodology is developed to perform the convergence analysis for the closed-loop system by Lyapunov stable theory. The main contribution of this paper is the development of a systematically adaptive consensus algorithm by simultaneously considering shifting parameters and switching communication network (as two unavoidable key factors) in the process of communication interaction among robots. A distinctive feature of the developed consensus protocol is to introduce the directed network topology characterizing the local communication interaction among robots, which is especially suitable for representing the the structures and features of the realistic cooperative multi-robotic systems. Accordingly, the developed consensus tracking strategy for manipulators possess prominent advantages including robustness,stability and effectiveness over the existing concentrated on single robot counterparts. Finally, numerical simulations of two-link manipulators are performed to illustrate the effectiveness of the obtained control algorithm.

Stabilization of a Class of Fractional Order Systems With Both Uncertainty and Disturbance

Abstract: This paper investigates the stabilization problem of fractional order systems with both model uncertainty and external disturbance. By combining the linear feedback control method, the dynamic feedback control method, and the uncertainty and disturbance estimator (UDE)-based control method, respectively, two new UDE-based control methods are developed. Using these methods, the fractional order systems can be stabilized by three steps. In the first step, the linear feedback and dynamic feedback controllers are designed to stabilize the nominal fractional order systems. The second step is to design a UDE-based fractional order controller to estimate the model uncertainty and external disturbance. In the third step, the two controllers are combined into a new controller to realize the stabilization of those fractional order systems. Finally, a numerical example is given to verify the correctness and validity of the proposed methods.

Dynamics Analysis and Fractional-Order Approximate Entropy of Nonlinear Inventory Management Systems

Abstract: Inventory management is complex nonlinear systems that are affected by various external factors, including course human action and policy. We study the inventory management model under special circumstances and analyse the equilibrium point of the system. The dynamics of the system is analysed by means of the eigenvalue trajectory, bifurcations, chaotic attractor, and largest Lyapunov exponent diagram. At the same time, according to the definition of fractional calculus, the fractional approximate entropy is used to analyse the system, and the results are consistent with those of the largest Lyapunov exponent diagram, which shows the effectiveness of this method.

Partial Anti-Synchronization in a Class of Chaotic and Hyper-Chaotic Systems

Abstract: This paper investigates the partial anti-synchronization in a class of chaotic and hyper-chaotic systems. Firstly, the existence of the partial anti-synchronization for the chaotic system is proved. By a systematic method including two algorithms, all solutions of the partial anti-synchronization for a given chaotic system are then derived, and physical controllers are designed. Finally, some illustrative examples with numerical simulations are used to verify the validity and effectiveness of the theoretical results.

A Novel Memristor Chaotic System with a Hidden Attractor and Multistability and Its Implementation in a Circuit

Abstract: By introducing an ideal and active flux-controlled memristor and tangent function into an existing chaotic system, an interesting memristor-based self-replication chaotic system is proposed. The most striking feature is that this system has infinite line equilibria and exhibits the extreme multistability phenomenon of coexisting infinitely many attractors. In this paper, bifurcation diagrams and Lyapunov exponential spectrum are used to analyze in detail the influence of various parameter changes on the dynamic behavior of the system; it shows that the newly proposed chaotic system has the phenomenon of alternating chaos and limit cycle. Especially, transition behavior of the transient period with steady chaos can be also found for some initial conditions. Moreover, a hardware circuit is designed by PSpice and fabricated, and its experimental results effectively verify the truth of extreme multistability.

Some Properties of Numerical Solutions for Semilinear Stochastic Delay Differential Equations Driven by G-Brownian Motion

Abstract: This paper is concerned with the numerical solutions of semilinear stochastic delay differential equations driven by G-Brownian motion (G-SLSDDEs). The existence and uniqueness of exact solutions of G-SLSDDEs are studied by using some inequalities and the Picard iteration scheme first. Then the numerical approximation of exponential Euler method for G-SLSDDEs is constructed, and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent, and it can reproduce the stability of the analytical solution under some restrictions. Numerical experiments are presented to confirm the theoretical results.