Finite-time Containment Control Research Articles

Event-Triggered Adaptive Finite-Time Containment Control for Fractional-Order Nonlinear Multiagent Systems.

This article investigates the finite-time containment control problem for fractional-order nonlinear multiagent systems (FOMASs) with event-triggered inputs. First, a new Lyapunov stability lemma is developed, which provides a basic approach for the completely unknown nonlinear fractional-order system to realize finite-time convergence. Considering the containment control for FOMASs, the restricted assumption that the derivatives of leaders' trajectories are known to the followers is removed, and only the boundedness of derivatives is required in this article, whose upper bound need not be known. To reduce the burden of communication, an event-triggered condition consisting of the control input and a decreasing function related to the containment errors is devised, which can provide more design freedom to balance the system performance and communication resources. According to the proposed fractional-order finite-time convergence lemma, a distributed adaptive containment control scheme is developed, such that each follower can be steered to the convex hull spanned by the leaders in finite time. Simulation examples further demonstrate the effectiveness of our proposed method.

Multi-objective distributed control of WT-PV-BESS integrated weak grid via finite time containment

This paper proposes a finite time containment control scheme to achieve distributed control of a weak grid which is integrated with photovoltaic (PV), wind turbine (WT) and battery energy storage system (BESS). Taking advantage of the containment control in multi-dimensional control, we proposed a multi-objective control scheme of the WT-PV-BESS system in a weak grid, wherein four control objectives are specified, namely, bus voltage regulation, grid frequency control, peak load shaving and economic benefits optimization for the system operator. Firstly, the sizing approach of BESSs to fulfill the operation mission requirements is proposed; meanwhile, the general coordination strategy for the PV, WT and BESS to achieve the demand–supply balance is proposed. Subsequently, the predefined four control objectives are modeled and transferred into the long/short time frame operational constraints of the BESSs. Afterwards, the finite time containment control algorithm is proposed to force the BESSs into achieving containment status within prescribed time. Simulation case studies are conducted on a modified IEEE 9-bus system to show the effectiveness and performance of the proposed scheme.

Distributed Nussbaum-Based Finite-Time Containment Control for Multi-UAVs With Actuator Saturation and Faults

This paper devotes to addressing the distributed adaptive finite-time containment control for the multi-UAVs with actuator saturation, faults, and external disturbances. A hyperbolic tangent function is presented to smooth the symmetric and asymmetric saturation functions. Then, the containment control for UAVs with actuator saturation and faults can be turned into a variable gain control problem. To address this problem, a Nussbaum function is specially designed in this paper to solve the variable gain issue with the known control direction. Besides, the bounds of disturbances are estimated and compensated by adaptive laws. With the presented containment control laws, the follower UAVs will converge into the convex hull spanned by the leaders in a finite time. Finally, the convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations.

Nussbaum-based finite-time containment control for multi-UAVs with input saturation and velocity constraints

This paper devotes to addressing the finite-time containment control for the multi-UAVs with input saturation and velocity constraints. A novel smooth function is presented to estimate the saturation function with adjustable estimate errors. By utilizing the mean-value theorem, the containment control for UAVs with input saturation can be turned into a variable gain control problem. To address this issue, the Nussbaum-based method is used to design the controller in this paper. Besides, based on the backstepping method, the controller can constrain the velocity states of UAVs within a desired time-varying asymmetric region by limiting the values of virtual velocity commands and the Lyapunov function. Finally, the finite-time convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations.

Robust adaptive finite-time containment control for nonlinear multi-agent systems with unknown input saturations

In this article, the distributed adaptive finite-time containment control problem is investigated for nonlinear multi-agent systems with unknown input saturations. Since the leaders are only available to partial subsystems, a distributed estimator is designed to estimate the local reference signals. The saturated function is converted to the combination of a linear part and a nonlinear part, thus overcomes the difficulties caused by unknown saturated bounds. By utilising the command filtered and backstepping control techniques, a two-step method is adopted to construct the controller, under which the effect of unknown input saturations can be compensated well. It is proved that the closed-loop system is practical finite-time stable, and the output of each follower can converge to the dynamic convex hull spanned by the leaders in finite time. Finally, a group of four one-link manipulator systems is used to support the feasibility of the developed control scheme.

Finite-Time Containment Control for Nonlinear Multi-Agent Systems Based on High Order Sliding Mode

Several finite-time containment control issues under stationary and dynamic leadership are the main emphasis of this thesis, which is concerned with a typical class of second-order nonlinear multi-agent systems susceptible to outside intervention. According to a given network topology, the second-order super-twisting sliding mode control is a technique for distributed control that has been developed. In this paper, we mainly consider the situation that the leader moves at a uniform speed. With the proposed method, the followers update status in real time via communication with each other such that all of them are able to eventually converge to the convex hulls consisting of stationary leaders and dynamic leaders in finite time. It leads to make the followers remain stationary or keep moving within the designed region. Eventually, according to the matrix theory and finite-time stability theorem, the paper proves the stability of the finite-time on the proposed control protocol and validates its effectiveness and correctness through simulation.

Finite-Time Containment Control for Nonlinear Second-Order Multiagent System Under Directed Topology

This article investigates the finite-time containment control for a class of second-order multiagent systems with nonlinear dynamics and external disturbances under fixed directed interaction topology. Due to the existence of nonlinear dynamics and unknown but bounded external disturbances, there is an underlying technical difficulty for the design of containment controller. Furthermore, it is a challenge for the theoretical analysis of finite-time containment control problem due to the asymmetric Laplacian matrix arising from the constraint of one-way directed communication among the agents. In response to the above-mentioned challenges, a finite-time containment control algorithm is proposed. First, the multiagent system is considered with inherent nonlinear dynamics and unknown but bounded external disturbances. Second, the desired containment control protocol is presented under a directed interaction topology. Furthermore, by adding a power-integrator technique and Lyapunov function theory, the sufficient conditions are derived for the existence of the finite-time containment controller of a class of second-order multiagent systems. Finally, a numerical example is given to verify the usefulness of the proposed finite-time containment control protocol.

Finite-Time Cooperative Control for Bearing-Defined Leader-Following Formation of Multiple Double-Integrators.

In this article, the finite-time cooperative control problem for leader-following bearing-defined formation tracking of multiagent systems with double-integrator dynamics is investigated. Different from the existing works on finite-time containment control, our objective is to make followers track leaders' trajectories and form a shape-preserving formation rather than a convex hull. The target formation is defined by both leaders' motions and bearing constraints among neighboring agents, which enables the formation not only to form and preserve a geometric pattern but also to have the ability to achieve both translational and scaling formation maneuver. To satisfy the bearing constraints, a matrix-weighted estimator/controller is developed. The finite-time stabilization of the target formation is achieved, though the matrix-weighted design makes the stability analysis complicated. Finally, an illustrative example is presented to demonstrate the effectiveness.

Simplified optimized finite-time containment control for a class of multi-agent systems with actuator faults

Simplified optimized finite-time containment control for a class of multi-agent systems with actuator faults

Finite-time robust containment control for autonomous surface vehicle with input saturation constraint

In this paper, a finite-time containment robust control scheme is proposed for autonomous surface vehicle with input saturation constraint. Firstly, to achieve finite-time containment control, a saturated distributed equivalent control algorithm is proposed based on the position and velocity measurements of neighbors and a part of leaders; In light of the tools from algebraic graph theory and homogeneous theory, it is theoretically proven that all the follower will converge to the convex hull formed by the virtual leaders in finite-time; Then, in order to suppress the influence of external disturbance, a nonlinear integral sliding mode surface based on equivalent control law is designed. Combined with finite-time Lyapunov stability theory, a finite-time cooperative control law is proposed, which makes the system tend to sliding surface in finite-time from any initial state; Finally, simulation results are presented to verify the effectiveness of the proposed control scheme.

Output Feedback-Based Neural Adaptive Finite-Time Containment Control of Non-Strict Feedback Nonlinear Multi-Agent Systems

In this paper, the observer based neural adaptive finite-time containment control strategy for non-strict feedback nonlinear multi-agent systems is studied. The finite-time command filter is used to overcome the explosion of complexity problem and the established fractional power based error compensation signal is applied to compensate the filtering error caused by the filter. The distributed finite-time command filtered backstepping control method combines with the neural adaptive control technology and state observer is given, which ensures the containment control errors reach to the desired neighborhood of the origin in finite-time in the presence of uncertain dynamics and unmeasurable states in the system. The given numerical simulations show the effectiveness of the proposed control strategy.

Finite-time Containment Control of Nonlinear Delayed Fractional Multi-agent Systems

Finite-time Containment Control of Nonlinear Delayed Fractional Multi-agent Systems

Distributed Finite-Time Containment Control for Nonlinear Multiagent Systems With Mismatched Disturbances.

This article proposes a finite-time adaptive containment control scheme for a class of uncertain nonlinear multiagent systems subject to mismatched disturbances and actuator failures. The dynamic surface control technique and adding a power integrator technique are modified to develop the distributed finite-time adaptive containment algorithm, which shows lower computational complexity. In order to overcome the difficulty from the mismatched uncertainties, the disturbance observers are constructed based on the backstepping technique. Moreover, the uncertain actuator faults, including loss of effectiveness model and lock-in-place model, are considered and compensated by the proposed adaptive control scheme in this article. According to the Lyapunov stability theory, it is demonstrated that the containment errors are practically finite-time stable in the presence of actuator faults. Finally, a simulation example is conducted to show the effectiveness of the proposed theoretical results.

Observer-Based Fuzzy Adaptive Finite-Time Containment Control of Nonlinear Multiagent Systems With Input Delay.

This article is concerned with the finite-time containment control problem for nonlinear multiagent systems, in which the states are not available for control design and the control input contains time delay. Fuzzy-logic systems (FLSs) are used to approximate the unknown nonlinear functions and a novel distributed fuzzy state observer is proposed to obtain the unmeasured states. Under the framework of cooperative control and finite-time Lyapunov function theory, an observer-based adaptive fuzzy finite-time output-feedback containment control scheme is developed via the adaptive backstepping control design algorithm and integral compensator technique. The proposed adaptive fuzzy containment control method can ensure that the closed-loop system is stable and all followers can converge to the convex hull built by the leaders in finite time. A simulation example is provided to confirm the effectiveness of the proposed control method.

Adaptive Fuzzy Containment Control for Multiagent Systems With State Constraints Using Unified Transformation Functions

In this article, the finite-time containment control problem of the nonlinear multiagent systems (MAS) is investigated, in which the follower agents are subjected to full state constraints. The fuzzy logic system is employed to approximate the uncertain dynamic of the nonlinear MAS. A new nonlinear transformation function (NTF) is proposed, which serves as a unified tool for coping with the systems subjected to state constraints and no constraint. By combing the variable transformation with the proposed NTF, the original systems with state constraints are converted into the equivalent free-constrained systems. Moreover, as long as the boundedness of the states in transformed systems is guaranteed, the states of the original MAS do not transgress the preassigned boundaries. Based on the finite-time stability theory, the adaptive fuzzy control scheme is constructed for the transformed systems. It is proved that the outputs of all the followers are driven to converge to the convex hull spanned by the leaders in a finite time, and all the signals in the closed-loop systems are bounded in sense of mean square. The full state constraints for the followers are not violated all the time. Especially, the control structure does not need to change even there is no constraint imposes on the state. Finally, simulation examples are given to verify the effectiveness of the proposed finite-time control scheme.

Adaptive neural finite-time containment control for nonlower triangular nonlinear multi-agent systems with dynamics uncertainties

This paper considers the finite-time containment control problem for nonstrict-feedback nonlinear multi-agent systems (MASs) in the presence of unmodeled dynamics. A new variable separation approach is developed to overcome the difficulty of unknown functions with nonstrict-feedback structure in the backstepping design process. The second-order tracking differentiator is extended to the nonstrict-feedback nonlinear MASs for avoiding the problem of “explosion of complexity”. Neural networks are used to approximate the unknown nonlinear functions. With introducing a dynamic signal, the difficulty from the unmodeled dynamics is successfully solved. And, by introducing a finite-time stability criterion, an new adaptive finite-time containment control scheme is designed, which ensures all signals are bounded. Moreover, the output signals of all followers converge to a convex hull spanned by the outputs of the leaders. Finally, a simulation example illustrates the effectiveness of the developed control scheme.

High order robust fast finite time containment control for multi-agent systems

This paper studies the problem of robust containment with trivial sensitivity to both initial conditions and communication topology for multi-agent systems. In this way, based on the homogeneity property of the dynamic systems, a new nonlinear high order sliding surface for containment problem is proposed. This sliding surface has a fast finite time dynamics which causes remarkably reduction of containment sensitivity to the multi-agent initial conditions and communication topology. Accordingly, a high order fast finite time containment control (HOFFT-CC) protocol is established and the containment of multiple agents to a convex hull is realized. The proposed framework solves the fast containment problem for high order dynamics that are subjected to the external disturbance and furthermore, for both directed and undirected graph topology. Moreover, because of decoupling the agents’ dynamics and converting the multi-agent problem to some single agent problems, the structure of the proposed method is simpler and more straightforward in comparison with previous works. The finite time stability of the closed loop multi-agent systems based on the homogeneity theory and Lyapunov theorem, is analyzed and proved. The proof is produced throughout the negative degree homogeneity property of the closed loop dynamics along with asymptotical stability. In addition, simulation for a general third order multi-agent system in a two-dimensional space is accomplished and the results demonstrate the trivial sensitivity of containment to both initial conditions and communication topology.

Distributed finite-time fault-tolerant containment control for multiple ocean bottom flying nodes

The Ocean Bottom Flying Node (OBFN) is a kind of small Autonomous Underwater Vehicle (AUV) used in detection of seabed resources. Based on directed commination topology, this paper investigates the problem of distributed finite-time fault-tolerant containment control for multiple OBFN systems in presence of model uncertainties, external disturbances, and thruster faults. By choosing the nonsingular fast terminal sliding surface and defining the containment error variables, a distributed finite-time containment control method is designed, so as to make the states of the multiple OBFN systems converge to the sliding surface in finite time. The thruster faults, model uncertainties, and external disturbances are considered together and estimated by utilizing Neural Networks (NNs). An adaptive law is designed to compensate the upper bounds of estimation error. Based on the graph theory and matrix theory, it is demonstrated that the follower OBFNs could enter the convex hull formed by the leader OBFNs in finite time through using the Lyapunov approach. Numerical simulation is presented to show the effectiveness of the proposed algorithm.

Distributed chattering-free containment control for multiple Euler–Lagrange systems

This paper investigates the distributed chattering-free containment control problem for multiple Euler–Lagrange systems with general disturbances under a directed topology. It is considered that only a subset of the followers could receive the information of the multiple dynamic leaders. First, by combining a linear sliding surface with a nonsingular terminal sliding manifold, a distributed chattering-free asymptotic containment control method is proposed under the assumption that the upper bounds of the general disturbances are known. Further, based on the high-order sliding mode control technique, an improved distributed chattering-free finite-time containment control algorithm is developed. Besides, adaptive laws are designed to estimate the unknown upper bounds of the general disturbances. It is demonstrated that all the followers could converge into the convex hull spanned by the leaders under both proposed control algorithms by graph theory and Lyapunov theory. Numerical simulations and comparisons are provided to show the effectiveness of both algorithms.

Finite-time containment control for nonlinear multi-agent systems with external disturbances

This paper is concerned with the finite-time containment control for a second-order nonlinear multi-agent system in the presence of external disturbances. First, two finite-time containment control protocols are skillfully developed, of which one is based on a terminal sliding mode and the other is based on a non-singular terminal sliding mode. Second, criteria for designing desired containment control protocols are derived such that the containment performance of the resulting closed-loop leader-following multi-agent system can be guaranteed within a finite time horizon. It is shown that the settling time of the closed-loop system convergence can be estimated under the proposed protocols. Furthermore, finite-time containment control in the scenario of general switching and directed topology is also addressed and the corresponding result is derived. Finally, three illustrative examples are given to verify the effectiveness of the proposed finite-time containment control method.