Adaptive Fuzzy Containment Control Research Articles

Distributed Adaptive Fuzzy Containment Control for State-Constrained Multiagent Systems With Uncertain Leaders

This article investigates the containment control for state-constrained multiagent systems. Existing results assume that the dynamic of the multiple leaders is known as prior knowledge. First, a distributed adaptive observer is used to estimate the leader's unknown parameters. The local reference signal and its high-order derivatives are generated by an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> th-order filter, which will be employed in the backstepping design procedures. Second, a log-type nonlinear state-dependent barrier function is established to cope with the time-varying asymmetric full-state constraints. The constrained system is equivalently transformed into a nonconstrained one. Finally, a distributed adaptive fuzzy containment control scheme is developed for the nonconstrained system. Only one adaptive law is required in each distributed controller, and no feasibility conditions and partial-derivative terms are involved in the virtual and actual controllers. In addition, the time derivatives of the candidate Lyapunov functions are guaranteed to be negative semidefinite by introducing a series of reduced-order smooth functions. It is proved that the containment error converges to a user-predefined interval, and all the signals in the closed-loop system are bounded. The time-varying asymmetric full-state constraints imposed on the followers are not violated. Two illustrative examples demonstrate the effectiveness of the suggested approach.

Observer-based adaptive fuzzy containment control for state-constrained nonlinear MASs based on quantization communication

In this article, the fuzzy adaptive output feedback quantized containment control problem is investigated for state-constrained nonlinear multi-agent systems (MASs). The state observer and FLSs are utilized to obtain the state estimations and approximate the unknown nonlinear dynamics, respectively. An estimation is designed to model the unknown local reference signal caused by the unavailability of the global information. To solve the nondifferential problem of the virtual controllers caused by the quantized outputs of neighbors, an auxiliary system is designed, under which the noncontinuous filter errors can be replaced by the auxiliary signals. By introducing the log-type barrier Lyapunov function (BLF) to backstepping recursive design, an adaptive fuzzy quantized containment controller is developed. Based on the Lyapunov stability theory, it is proved that the closed-loop system is stable, the output of each follower can be driven into the dynamic convex hull spanned by the leaders, and the states of system will not exceed their constrained bounds. Finally, a group of two virtual leaders and three unmanned surface vehicles (USVs) are utilized to test the effectiveness of the developed control approach.

Fixed-Time Adaptive Fuzzy Containment Dynamic Surface Control for Nonlinear Multiagent Systems

This article investigates the fixed-time adaptive fuzzy containment control problem for nonlinear multiagent systems under the directed communication topologies. The controlled systems have the unknown internal dynamics and mismatched disturbances, and fuzzy logic systems are utilized to identify the unknown internal dynamics. The mismatched disturbances and approximate errors are reconstructed via a disturbance observer. Then, by introducing an adding power integral method, a fixed-time adaptive fuzzy containment DSC scheme is developed to deal with the problem of “computation complexity.” The presented containment control method can not only guarantee that the controlled system is semiglobal practical fixed-time stable, but also avoid the “singular problem” in fixed-time backstepping recursive control technology. Finally, an application of marine surface vehicle is provided to verify the effectiveness of the presented fixed-time fuzzy containment control method.

Event-Triggered Practical Fixed-Time Fuzzy Containment Control for Stochastic Multiagent Systems

In this article, an event-triggered practical fixed-time containment control issue for stochastic nonlinear multiagent systems is addressed. The event-triggering mechanism is designed for the controller update which is reduced update frequency. In combination with the backstepping technique and fuzzy logic systems, an adaptive fuzzy containment control strategy is developed for stochastic uncertain multiagent systems. By adopting the protocol, an adaptive containment controller is devised, which can ensure that the containment errors gather to a small range in fixed time. Finally, simulation results for the practical example demonstrate the correctness of the proposed scheme.

Adaptive fuzzy containment control for nonlinear multi-agent systems with input delay

This paper focuses on a problem of adaptive fuzzy containment control for nonlinear multi-agent systems with input delay. Through the Pade approximation and intermediate variable, the positive constant delays of nonlinear systems inputs are transferred to the coefficients of the next dynamic equation. The phenomenon of “complexity explosion” in traditional backstepping control technique is avoided by introducing first-order filters, in which a new variable replaces the derivative of the virtual controller. In addition, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear functions of nonlinear multi-agent systems. No matter what the order of the nonlinear multi-agent systems is, only two adaptive laws need to be designed in the adaptive fuzzy containment controller design process for each follower. Using the proposed control method, all followers can converge to the convex hull established by the leaders, and the closed-loop system is stable. The simulation results can further illustrate the effectiveness of the proposed control method.

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.

Observer-Based Adaptive Fuzzy Containment Control for Multiple Uncertain Nonlinear Systems

The adaptive fuzzy containment control problem is addressed for multiple uncertain nonlinear strict-feedback systems with immeasurable states and multiple leaders under directed communication graphs. By utilizing fuzzy logic systems to model the followers’ dynamics, a distributed fuzzy state observer is designed for the state estimation using only the relative position information. Then, an observer-based containment control scheme is constructed by the adaptive fuzzy control technique as well as the command filter. The filtering error loop is introduced to compensate the error arising from the command filter. The proposed adaptive fuzzy containment control scheme guarantees that all followers are driven into the dynamic convex hull spanned by the leaders with a bounded containment error, if there exists at least one of the leaders who has a directed path to the follower. Simulation results are given to illustrate the control performance of the proposed containment control method.

Adaptive Fuzzy Containment Control of Nonlinear Strict-Feedback Systems With Full State Constraints

In this paper, the distributed adaptive fuzzy containment control problem is investigated for a class of uncertain nonlinear systems guided by multiple dynamic leaders. Each follower is modeled by nonlinear strict-feedback systems subject to full state constraints. The function approximation technique using fuzzy logic systems is utilized to identify the unknown nonlinearities of each follower. Both the state feedback containment control and the observer-based output feedback containment control are constructed by combining distributed sliding-mode estimators with adaptive fuzzy backstepping control. To prevent constraint violation, multiple barrier Lyapunov functions associated with error surfaces are introduced in the control design. It is proven that uniformly ultimately bounded containment control is achieved without violating full state constraints under the condition that for each follower, there exists at least one leader that has a directed path to that follower. Simulation studies are performed to show the effectiveness of the proposed theoretical results.

Adaptive Fuzzy Containment Control for Multiple Uncertain Euler–Lagrange Systems With an Event-Based Observer

This paper considers the containment control problem for multiple Euler-Lagrange systems with unknown nonlinear dynamics, where the dynamics of the leaders are different from those of the followers. In addition, some followers cannot obtain information of the leaders owing to the limited communication range. We first adopt an event-based observer to estimate a trajectory inside the convex hull spanned by states of the leaders, in which continuous communication can be avoided as well. Then, we further utilize the fuzzy logic systems to approximate the unknown nonlinear dynamics and propose an adaptive control scheme. Under the proposed scheme, we can ensure that the states of the followers can converge to the convex hull formed by these states of the leaders. Finally, a simulation example is given to validate the effectiveness of the proposed control scheme.

Distributed Adaptive Fuzzy Containment Control of Stochastic Pure-Feedback Nonlinear Multiagent Systems With Local Quantized Controller and Tracking Constraint

This paper studies the distributed adaptive fuzzy containment tracking control for a class of high-order stochastic pure-feedback nonlinear multiagent systems with multiple dynamic leaders and performance constraint requirement. The control inputs are quantized by hysteresis quantizers. Mean value theorems are used to transfer the nonaffine systems into affine forms and a nonlinear decomposition is employed to solve the quantized input control problem. With a novel structure barrier Lyapunov function, the distributed control strategy is developed. It is strictly proved that the outputs of the followers converge to the convex hull spanned by the multiple dynamic leaders, the containment tracking errors satisfy the performance constraint requirement and the resulting leader-following multiagent system is stable in probability based on Lyapunov stability theory. At last, simulation is provided to show the validity and the advantages of the proposed techniques.

Adaptive Fuzzy Containment Control of Nonlinear Systems With Unmeasurable States.

The adaptive fuzzy containment control problem is discussed for high-order systems with unknown nonlinear dynamics and unmeasurable states guided by multiple dynamic leaders. A high gain observer is introduced to reconstruct the system states. Then, utilizing fuzzy logic systems to model followers' dynamics, an observer-based adaptive fuzzy containment control approach is presented using only the relative position of the neighbors. It is shown that the uniformly ultimately bounded containment control is realized under the condition that, each follower can obtain the information from at least one leader through a directed path. As an extension, an observer-based containment control with prescribed performance is developed, which guarantees the relative position error to be bounded by a specified bound. The obtained theoretical results are validated by simulation examples.