Containment Control Scheme Research Articles

Distributed two-channel dynamic event-triggered adaptive finite-time fault-tolerant containment control for multi-leader UAV formations

This paper addresses the distributed adaptive finite-time containment control problem in multi-leader UAV formations with actuator failures, limited communication, and external disturbances. A two-channel dynamic event-triggered strategy based on adaptive and sliding mode control is proposed as a containment control scheme, which solves the contradiction between the need to include containment error in the continuous term of the sliding mode surface in the adaptive law and the discontinuity of the communication between neighboring subsystems (follower UAVs) by constructing intermediate variables. Unlike the traditional event triggering condition that can only be applied to asymptotically convergent systems, the dynamic triggering condition designed in this paper, based on auxiliary variables, hyperbolic tangent function, and adaptive techniques, realizes finite-time convergence during the adjustment of the system and sets a more reasonable lower limit for the triggering thresholds, thus further reducing the communication frequency and ensuring the finite-time convergence of the system. The stability of the closed-loop system can be proved by the Lyapunov theorem. Zeno behavior can be avoided. The simulation results verify the effectiveness of the developed control algorithm.

Data-Driven Model-Free Adaptive Containment Control for Uncertain Rehabilitation Exoskeleton Robots with Input Constraints

This paper presents a data-driven model-free adaptive containment control (MFACC) scheme for uncertain rehabilitation exoskeleton robots, where the robotic exoskeleton dynamics are uncertain with saturation constraints. To handle uncertainties of the robotic dynamics, a model-free adaptive control (MFAC) strategy is established by linearizing the robotic exoskeleton dynamics into an equivalent data model. Considering the integral additive effect of the traditional MFAC method, an improved MFAC controller is designed in this paper. Since actuators with saturation constraints constantly affect the safety of patients during rehabilitation training, we construct a new criterion function with active constraints for the critical function of the MFAC algorithm and adopt the Hildreth quadratic programming algorithm to find the constrained optimal solution to overcome this limitation. The proposed MFACC scheme is rigorously proven by the compression mapping method to demonstrate model-free stability. Finally, the proposed control scheme is verified to be effective by simulation studies of the robotic SimMechanics model.

Distributed deadband event-triggered observer-based containment control for unmanned surface vehicles with channel fading

This article investigates the distributed deadband event-triggered containment control problem for multiple underactuated surface vehicles (USV) systems whose communication networks are subject to channel fading. The first distributed deadband event-triggered observer (DDETO) was proposed to observe the target positions of the followers in the convex hulls formed by the leaders. It also manages the internal communication between the followers in the presence of channel fading. In addition, the deadband event-triggered mechanism (DETM) in DDETO guarantees a strictly positive minimum inter-event times (MIET), which can be accurately calculated and adjusted according to the design parameters. Afterward, an adaptive controller is designed by backstepping based on the desired position information observed by DDETO. It is worth noting that the containment control scheme proposed in this paper is based on relative position measurement only, which reduces the amount of information transfer compared to transmitting position and velocity information when wireless signals are fading in the channel, improves the control accuracy, and also reduces the system’s requirements for sensors. Theoretical analysis leads to the conclusion that the error signals are uniformly ultimately bounded (UUB). Finally, the effectiveness of the control scheme is verified by numerical simulation.

Event-triggered based adjustable containment control scheme design for multi-agent systems

The traditional containment control problem uses a mapping method with a fixed communication topology to generate a set of reference signals for followers, which may lead to a situation where the position of the reference signal cannot be adjusted and causes collisions. Therefore, based on backstepping theory, we propose a novel containment control scheme to address this problem, where the generated reference signals can be adjusted arbitrarily. In particular, it is important to point out that an estimator is designed to guide the follower if the reference signal is not available, so that the collision problem is avoided. In addition, the computational complexity of the controller is also reduced and the communication resources are saved by introducing the command filters and event-triggered mechanism. It is proved that the tracking errors of the closed multi-agent systems are uniformly and ultimately bounded through Lyapunov theory. Finally, experimental simulations verify that the proposed control scheme is reasonable and effective. Furthermore, the proposed scheme provides a more flexible solution for containment control studies, especially for collision avoidance research of multi-agents.

Distributed Estimator-Based Containment Control for Multi-AUV Systems Subject to Input Saturation and Unknown Disturbance

This article addresses the containment control issue for multi-AUV systems with the intervention of both external disturbance and input saturation. Firstly, a distributed estimator is established for the sake of acquiring precise estimation information of the desired position and its derivative for each follower AUV in the system. Next, on the basis of the proposed distributed estimator, a virtual control law is designed for each follower AUV. Then, due to the difficulty in obtaining accurate information about the derivative of the virtual control law, a linear tracking differentiator is introduced. Additionally, a disturbance observer is employed to tackle the composite disturbance, which mainly contains the internal model uncertainties and external bounded disturbances. Meanwhile, the issue of input saturation is handled by constructing the auxiliary system. Furthermore, a containment control law is designed with the assistance of the introduced linear tracking differentiator, the established disturbance observer, and the constructed auxiliary system. Additionally, the Lyapunov stability theory is applied to analyze the stability of the multi-AUV system. Finally, simulation results are given to confirm the feasibility of the proposed containment control scheme.

Observer-based adaptive neutral network inverse optimal containment control for nonlinear multiagent systems with input quantization

This article focuses on the issue of addressing an adaptive neural network (NN) inverse optimal containment control for nonlinear multiagent systems (MASs), which are subject to immeasurable states and quantized input signals simultaneously. To tackle this problem, we utilize a NN to model unknown agents and design a NN observer to estimate the immeasurable states. Additionally, we decompose the hysteretic quantized input into two bounded nonlinear functions. By employing the adaptive backstepping approach and inverse optimal principle, we formulate an adaptive NN inverse optimal containment control method. The developed inverse optimal containment control scheme guarantees that the controlled system is input-to-state stabilizable (ISS). Finally, we validate the effectiveness of our proposed control scheme through simulation results.

Distributed adaptive prescribed-time orbit containment control for satellite cluster flight

The distributed prescribed-time orbit containment control for the satellite cluster flight with multiple dynamic leaders is investigated. The directed information communication topology between followers is taken into account in the overall paper. When the satellite mass is assumed to be constant, a distributed prescribed-time orbit containment controller is, firstly, presented to drive the followers into the dynamic convex hull produced by multiple leaders. Then, the parameter uncertainty is considered, and a prescribed-time sliding mode estimator is introduced to estimate the desired velocity of each follower. Based on the estimated state, a novel distributed adaptive prescribed-time orbit containment control scheme is proposed. The Lyapunov stability theory is utilized to prove the prescribed-time stability of the closed-loop system. Finally, several numerical simulations and comparison of different control methods are provided to verify the effectiveness and superiority of the proposed control method.

Distributed finite‐time backstepping adaptive containment control for multiple unmanned aerial vehicles with input saturation

AbstractThis paper investigates a distributed adaptive finite‐time containment control scheme for multiple unmanned aerial vehicles subject to external disturbances and input saturation. Combined with a novel indicator of the saturation degree designed by the hyperbolic tangent function, an adaptive method is proposed to deal with the input saturation issue, which considers both symmetry and asymmetry saturation. Moreover, to address the problem of the “explosion of terms” inherent in the traditional backstepping controller design, a fixed‐time sliding mode differentiator is utilized to approximate the derivative of the virtual signal in the command‐filtered backstepping method. Finally, the convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations.

Event‐triggered adaptive fuzzy bipartite containment control for switched nonlinear multi‐agent systems with actuator attacks

AbstractThis paper considers the event‐triggered adaptive fuzzy bipartite containment control problem for switched nonlinear multi‐agent systems (MASs) with actuator attacks. To handle the completely unknown nonlinear functions in the considered system, fuzzy logic systems (FLSs) are applied to approximate the unknown nonlinear functions. In addition, an adaptive bipartite containment control approach is designed to deal with the actuator attacks, which can reduce the burden of communication. According to the designed adaptive bipartite containment control scheme, it is shown that all the signals are semi‐globally uniformly ultimately bounded (SGUUB), and all the outputs of the followers achieve the bipartite consensus and finally enter the convex set spanned by leaders' in the presence of actuator attacks. Eventually, a simulation example is presented to illustrate the availability of the developed strategy.

Distributed observer‐based containment control for unknown time‐varying P‐normal nonlinear multiagent systems

AbstractThis work investigates the containment control for unknown time‐varying p‐normal (TVP) nonlinear multiagent systems (MASs) under directed topology. First, by innovatively constructing the dynamic update law in the distributed observer design process, the corresponding virtual leader trajectory can be accurately estimated at an exponential rate. Subsequently, the containment problem of MASs is transformed into a tracking problem through appropriate state transformation. Then, based on backstepping and power integrator techniques, a recursive algorithm is proposed to construct the adaptive controller to guarantee that the followers are driven into the convex hull consisting of dynamic leaders and the closed‐loop system is stable. Finally, the effectiveness of the containment control scheme is verified through a numerical simulation and a practical example of single‐link manipulators.

Output feedback containment fuzzy control for multi-agent systems with quantitative input and tunable reference signals

For multi-agent systems with quantitative input, we propose a novel containment control scheme to guarantee that the agents can enter a convex hull generated by the leader's signals after starting from any initial position. The problem with existing schemes is that the reference signals of the agents are affected by the communication topology such that the position of the reference signal cannot be changed when this communication topology is determined. To solve this problem, the proposed scheme can generate a flexible and adjustable reference signal for each agent. This has the advantage of reducing the probability of collisions among agents. Meanwhile, to address the situation where some agents cannot receive reference signals, we design an estimator to generate an adjustable estimation signal for each specific agent to ensure that all agents continue moving within the convex hull. In addition, by combining the fuzzy observer with the command filter design method, we devise a novel controller design scheme for quantitative input, which ensures that all signals in closed-loop multi-agent systems are uniformly and ultimately bounded. Finally, the simulation results demonstrate the feasibility and superiority of the proposed scheme for controlling multi-agent systems.

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.

A Modular Event-Triggered Containment Control Scheme for Nonlinear Heterogeneous Multiagent Systems With Unknown Leaders.

This article addresses the containment control problem in multiagent systems with nonlinear heterogeneous followers and multiple unknown leaders whose dynamics are exclusively known to their neighbors. The primary goal is to ensure the convergence of each follower to the dynamic convex hull spanned by the leaders under the constraints of limited communication resources. To achieve this, this article introduces a modular event-triggered containment control scheme with three modules. The first module, Module I-signal generator, is designed for each follower to generate a reference signal asymptotically entering the dynamic convex hull without relying on follower dynamics. The second module, Module II-event-triggered mechanism, is tailored to save communication resources effectively by determining when to broadcast information based on perturbed system stability and input-to-state stability theories. The third module, Module III-tracking controller, treats each follower as an independent agent and is crafted to track the reference signal generated by Module I using an output regulation approach. It is established that the system achieves containment control without Zeno behavior under the influence of these modules, and the theoretical results are validated through simulation examples, demonstrating the practical validity of the proposed approach.

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.

Properties of interconnected negative imaginary systems and extension to formation‐containment control of networked multi‐UAV systems with experimental validation results

AbstractThis paper extends the properties of a positive feedback interconnection of two negative imaginary (NI) systems to multi‐agent NI systems and proposes a new formation‐containment control methodology relying on the characteristic loci technique. Inspired by recent applications of NI and passivity‐based control techniques in the multi‐agent systems (MAS) domain, a new formation‐tracking and containment control scheme is developed for a class of networked multi‐UAV systems. The proposed scheme offers a two‐stage and two‐loop control configuration where the inner loop uses a cascaded PID controller to ensure stable hovering of the UAVs, and the outer loop deploys a distributed “mixed” SNI and strictly passive controller to achieve the formation‐containment objectives. This scheme works with a dynamic output feedback control strategy; hence, it offers advantages when the full‐state measurement is not possible. In contrast to the well‐known Lyapunov theory‐based cooperative control schemes, the present one exploits the characteristic loci technique to prove the formation‐tracking and containment phenomena theoretically. The paper also provides experimental validation results on a fleet of Crazyflie 2.1 nano quadcopters.

Adaptive Neural Network Event-Triggered Output-Feedback Containment Control for Nonlinear MASs With Input Quantization.

This article investigates the adaptive neural network (NN) event-triggered containment control problem for a class of nonlinear multiagent systems (MASs). Since the considered nonlinear MASs contain unknown nonlinear dynamics, immeasurable states, and quantized input signals, the NNs are adopted to model unknown agents, and an NN state observer is established by using the intermittent output signal. Subsequently, a novel event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels are established. By decomposing quantized input signals into the sum of two bounded nonlinear functions and based on the adaptive backstepping control and first-order filter design theories, an adaptive NN event-triggered output-feedback containment control scheme is formulated. It is proved that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) and the followers are within a convex hull formed by the leaders. Finally, a simulation example is given to validate the effectiveness of the presented NN containment control scheme.

Adaptive Containment Control for Heterogeneous MIMO Nonlinear Multiagent Systems With Unknown Direction Actuator Faults

In this article, a novel output-feedback adaptive containment control scheme is proposed for a class of heterogeneous multi-agent systems, where the agents are nonlinear multi-input multi-output (MIMO) systems whose relative degrees are allowed to be different. Unlike existing results, we only require the leading principal minors of agents' control gain matrices (CGMs) to be nonzero and take into account unknown direction actuator faults, which relaxes the restrictions on CGMs and enhances system reliability. The difficulties jointly caused by the unknown CGMs, unknown parameters, and unknown jumps introduced by the actuator faults are successfully overcome by a novel recursive contradiction argument based on some Nussbaum functions and a matrix similarity transformation. Moreover, an event-triggering mechanism is introduced to avoid continuous communication among agents and reduce the communication burden. It is shown that all closed-loop signals are globally uniformly bounded and the containment errors converge to a residual set that can be made arbitrarily small. Simulation results illustrate the effectiveness of the proposed scheme.

Fixed‐time disturbance observer based distributed cooperative containment control with fixed‐time anti‐saturation compensator for multi‐unmanned aerial vehicles

AbstractThis article proposes a fixed‐time backstepping distributed cooperative containment control scheme for multiple unmanned aerial vehicles (UAVs). A fixed‐time compensator is designed for the fixed‐wing UAVs actuator saturation problem. Based on this, an improved fixed‐time disturbance observer is proposed for the problem of the excessive initial peak. The problem of “complexity explosion” is solved by the fixed‐time differential filter. For the distributed containment control of multiple UAVs, a cooperative control architecture based on a fixed‐time anti‐saturation compensation system is proposed. The proposed algorithm can be shown practicable by using Lyapunov stability theory and graph theory. Simulation results are given to demonstrate the effectiveness of the proposed control scheme.

Command filtered backstepping‐based containment control for a class of multi‐agent systems with uncertainty

SummaryIn this paper, a novel containment control scheme is designed for multi‐agent systems with unknown parameters and unknown control coefficients. To achieve the containment control goal, containment reference signals are generated using a certain number of dynamic leaders. Then, the followers directly receiving the reference signals can track their generated reference signals, and the rest of the followers track a certain number of estimated signals generated by designed dynamic equations. Under the backstepping framework, uncertainties of a multi‐agent system are compensated for through the adaptive bound estimation method. Additionally, the command filtered technique is adopted to avoid the cumbersome steps of multiple derivative calculations, and to simplify the operations of the control scheme. Finally, the stability of the closed‐loop multi‐agent system is proved based on the Lyapunov theory. The advantage of the proposed scheme is that the containment reference signal and the position between followers can be adjusted arbitrarily by adjusting the relevant parameters. Through simulations, the effectiveness and superiority of the designed controller are verified.

Neural network-based adaptive optimal containment control for non-affine nonlinear multi-agent systems within an identifier-actor-critic framework

This paper addresses the adaptive optimal containment control issue for non-affine nonlinear multi-agent systems in the presence of periodic disturbances. To deal with the disturbed internal dynamics, a fourier series expansion-neural networks-based adaptive identifier is designed for each follower, such that the restrictions posed on the system dynamics are released. Then,an adaptive dynamic programming technique is adopted to acquire the optimized virtual and actual controllers under a simplified actor-critic architecture, where the critic aims to appraise control performance and the actor aims to perform control task. Note that the above updating laws are constructed by the negative gradient of a designed function, which is constructed on the basis of the partial derivative of Hamilton-Jacobi-Bellman equation. Finally, simulation results are provided to show the applicability and effectiveness of the containment control scheme.