Order Nonlinear Multi-agent Systems Research Articles

Observer-based distributed convex optimization of bipartite containment control for higher order nonlinear uncertain multi-agent systems

This paper studies the distributed convex optimization of bipartite containment control problem for a class of higher order nonlinear multi-agent systems with uncertain states. For the optimization problem, the penalty function is constructed by summing the local objective function of each agent and combining the penalty term formed by the adjacency matrix. For the unknown nonlinear function and unpredictable states in the system, this paper construct radial basis function Neural-networks and state observer for approaching, respectively. In order to avoid “explosion of complexity,” under the framework of Lyapunov function theory, we propose the dynamic surface control (DSC) technology and design the distributed adaptive backstepping neural network controller to ensure all the signals remain semi-global uniformly ultimately bounded in the closed-loop system and all agents can converge to the convex hull containing each boundary trajectory as well as its opposite trajectory different in sign. Simulation results confirm the feasibility of the proposed control method.

Switched Fractional Order Multiagent Systems Containment Control with Event-Triggered Mechanism and Input Quantization

This paper studies the containment control problem for a class of fractional order nonlinear multiagent systems in the presence of arbitrary switchings, unmeasured states, and quantized input signals by a hysteresis quantizer. Under the framework of the Lyapunov function theory, this paper proposes an event-triggered adaptive neural network dynamic surface quantized controller, in which dynamic surface control technology can avoid “explosion of complexity” and obtain fractional derivatives for virtual control functions continuously. Radial basis function neural networks (RBFNNs) are used to approximate the unknown nonlinear functions, and an observer is designed to obtain the unmeasured states. The proposed distributed protocol can ensure all the signals remain semi-global uniformly ultimately bounded in the closed-loop system, and all followers can converge to the convex hull spanned by the leaders’ trajectory. Utilizing the combination of an event-triggered scheme and quantized control technology, the controller is updated aperiodically only at the event-sampled instants such that transmitting and computational costs are greatly reduced. Simulations compare the event-triggered scheme without quantization control technology with the control method proposed in this paper, and the results show that the event-triggered scheme combined with the quantization mechanism reduces the number of control inputs by 7% to 20%.

Research on complex dynamic behavior control of supply chain finance nonlinear system based on fractional differential operators.

Supply chain management is a kind of behavior for enterprises to create core competitiveness in a complex competitive environment, especially for supply chain finance, which is a typical complex system with dynamic, open, and emergent non-linear characteristics in structure, environment, and behavior. For fractional order non-linear multi-agent systems, the event trigger control protocol is studied, and an event based on the threshold function of decreasing time is designed. According to the properties of the fractional linear differential equations, the consistency criterion is obtained, and the Zeno phenomenon is effectively avoided. Chaos exists in fractional-order electronic oscillators with order lower than 4th order, and the lowest order of chaos in the fractional-order system is only 2.3 orders. The research shows that under the appropriate parameter adjustment, chaos exists in the fractional-order vanderPol oscillator with order less than 4th order, and the lowest order of chaos in the fractional-order system is 2.7.

Distributed robust adaptive control of high order nonlinear multi agent systems

In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust.

Decentralized Robust Synchronization of Unknown High Order Nonlinear Multi-Agent Systems With Prescribed Transient and Steady State Performance

In this paper, we consider the synchronization control problem for uncertain high-order nonlinear multi-agent systems in a leader-follower scheme, under a directed communication protocol. A robust decentralized control law of minimal complexity is proposed that achieves prescribed, arbitrarily fast and accurate synchronization of the following agents with the leader. The control protocol is decentralized in the sense that the control signal of each agent is calculated based solely on local relative state information from its neighborhood set. Additionally, no information regarding the agents' dynamic model is employed in the design procedure. Moreover, provided that the communication graph is connected and contrary to the related works on multi-agent systems, the controller-imposed transient and steady state performance bounds are fully decoupled from: 1) the underlying graph topology, 2) the control gains selection, and 3) the agents' model uncertainties, and are solely prescribed by certain designer-specified performance functions. Extensive simulation results clarify and verify the approach.

Finite time tracking control of higher order nonlinear multi agent systems with actuator saturation

Abstract: In this paper a distributed leader follower finite time tracking control of higher order nonlinear multi agent systems (MAS) is presented subject to actuator saturation. A saturated continuous homogeneous consensus control is developed to obtain finite time convergence. For stability of the saturated actuators the geometric homogeneity theory is used and it is proven that all the states of the followers can converge to that of the leader in finite time. Switching control is designed based on super twisting algorithm to nullify the effect of uncertainties and external disturbances. It is also ensures that the sliding surface reaches the equilibrium in finite time. The control law can be effectively used for more general higher order nonlinear agent dynamics. Simulation results verify the effectiveness of the proposed scheme.

Cooperative global output regulation of heterogeneous second-order nonlinear uncertain multi-agent systems

In this paper, we study the cooperative global output regulation problem for a class of heterogeneous second order nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model that converts the cooperative global output regulation problem into the global robust stabilization problem of the so-called augmented multi-agent system. Then we further globally stabilize this augmented multi-agent system via a distributed state feedback control law, thus leading to the solution of the original problem. A special case of our result leads to the solution of the global leader-following consensus problem for the second order nonlinear multi-agent systems without satisfying the global Lipschitz condition.