Pure-feedback Multi-agent Systems Research Articles

Cooperative ETM-Based Adaptive Neural Network Tracking Control for Nonlinear Pure-Feedback MASs: A Special-Shaped Laplacian Matrix Method.

This article solves the cooperative adaptive tracking control problem for nonlinear pure-feedback multi-agent systems (MASs). Compared with the previous achievements of adaptive control of pure-feedback MASs, the partial derivative of the nonaffine function may not exist by using decoupling technology. In the controller design framework based on the backstepping technique, the additional state variables are processed using the special properties of the radial basis function neural networks (RBF NNs). A special-shaped Laplacian matrix is proposed to unify the leader gain form in the tracking error design process (the coefficient in the second term of tracking error). Furthermore, an event trigger mechanism (ETM) is introduced to save resources. The constructed controller under the ETM can not only stabilize the system states but also make the tracking error reach a small accuracy. Finally, the simulation results demonstrated the feasibility of the proposed method.

Distributed Control for Uncertain Multiagent Systems With the Powers of Positive-Odd Numbers: A Low-Complexity Design Approach

This work shows that low-complexity prescribed performance control (PPC) can be used to realize leader-following consensus for uncertain second-order multi-agent systems (MASs) with the powers of positive odd numbers, i.e., agents whose dynamics are a chain of integrators with positive odd powers. Low-complexity PPC is a control methodology whose strongest feature is its adaptation-free structural simplicity: uncertainty can be handled without estimation of unknown parameters nor approximation structures (neural networks, fuzzy logic systems, etc.) being involved in the control design. While the state of the art has focused on strict- and pure-feedback MASs, i.e., dynamics including a chain of integrators with powers equal to one: in this note, we show that the same low-complexity can be retained for more general integrator dynamics (with positive-odd-integer powers). To this purpose, several new technical tools are proposed to handle the challenges caused by the presence of high powers in the integrators both in leader and follower agents. A dynamical boiler-turbine units system is used to validate the effectiveness of the theoretical findings.

Event-Triggered-Based Consensus Neural Network Tracking Control for Nonlinear Pure-Feedback Multiagent Systems With Delayed Full-State Constraints

Event-Triggered-Based Consensus Neural Network Tracking Control for Nonlinear Pure-Feedback Multiagent Systems With Delayed Full-State Constraints

Adaptive fuzzy singularity-free finite-time optimal control for nonlinear pure-feedback multiagent systems

In this paper, we investigate the adaptive fuzzy singularity-free finite-time optimal consensus problem for nonlinear pure-feedback multiagent systems (MASs). For purpose of achieving the optimized control, the fuzzy approximation-based reinforcement learning is employed under critic-actor architecture. By virtue of Butterworth low-pass filter, a distributed adaptive finite-time optimal consensus method is developed for nonlinear pure-feedback MASs, which solves algebraic loop problem produced in the construction of the optimal controller. Most importantly, to be free of singularity, we design a new dynamic filtering optimized backstepping method to avoid the differentiations of virtual optimal controllers, and the errors between first-order filter signals and virtual optimal controllers can be counteracted by designing the smooth robust compensators for the first time. It is shown that, with the developed adaptive finite-time optimal consensus control, both the optimal consensus tracking performance and finite-time convergence for the closed-loop systems are ensured. Three simulation examples are presented to verify the effectiveness of the proposed approach.

Distributed Containment Control of MIMO Pure-Feedback Multiagent Systems Using Filter-Driven-Approximation Approach

This article addresses a filter-driven-approximation (FDA)-based design problem for the distributed containment control of multi-input-multi-output pure-feedback multiagent systems with completely unknown nonlinearities. Local filter-driven approximators are designed to compensate for unknown nonaffine nonlinear functions lumped in the local controller design procedure where the first-order filtered signals of the error surfaces, state variables, and control inputs are linearly combined for the design of the filter-driven approximators. A containment control scheme using the filter-driven function approximators is recursively constructed to ensure that the outputs of the followers converge to the convex hull spanned by multiple time-varying leaders. Compared with existing containment control results using adaptive neural-network-based or fuzzy-based approximators, the proposed FDA-based containment control scheme depends only on the relative output information among agents and does not require any adaptive techniques. Thus, the proposed control structure can be simplified. It is shown that the closed-loop signals, including approximation errors are semi-globally uniformly ultimately bounded. Simulation examples are provided to validate the effectiveness of the proposed theoretical strategy.

Finite-time consensus control for a class of multi-agent systems with dead-zone input

This paper investigates a finite-time consensus issue for non-affine pure-feedback multi-agent systems with dead-zone input. Compared with the existing results on multi-agent systems, finite-time consensus problem of non-affine multi-agent systems is proposed for the first time. Based on the backsteppting technique, adaptive finite-time consensus control scheme is presented. With the help of this strategy, adaptive virtual variables, adaptive laws and the actual controller are designed to guarantee that the consensus errors converge to a small scale of the origin in finite time. Finally, a practical example is applied to verify the feasibility of the proposed method.

Event-triggered fuzzy adaptive quantized control for nonlinear multi-agent systems in nonaffine pure-feedback form

In this paper, we address the problem of event-triggered fuzzy adaptive quantized control for stochastic nonlinear non-affine pure-feedback multi-agent systems. The fuzzy logic system is used to estimate the stochastic disturbance term and unknown nonlinear functions. A nonlinearity decomposition method of asymmetric hysteresis quantizer is proposed by applying sector bound property. Moreover, to reduce the communication burden, an adaptive event-triggered protocol with a varying threshold is constructed. Based on the backstepping technique and stochastic Lyapunov function method, a novel adaptive event-triggered fuzzy control protocol and adaptive laws are constructed. By using stochastic Lyapunov stability theory, it is demonstrated that all signals are bounded in the closed-loop systems in probability and all the outputs of followers converge to the neighborhood of the leader output. Simulation results illustrate the effectiveness of our proposed scheme.

Neural Network-Based Distributed Finite-Time Tracking Control of Uncertain Multi-Agent Systems With Full State Constraints

This paper addresses the distributed tracking control problem of pure-feedback multi-agent systems with full state constraints under a directed graph in finite time. By introducing the nonlinear mapping technique, the system with full state constraints is converted into the form without state constraints. Furthermore, by combining fractional dynamic surface and radial basis function neural networks, a novel finite-time adaptive tracking controller is conducted recursively. In light of Lyapunov stability theory, it is proven that all signals of multi-agent systems are semi-globally uniformly ultimately bounded in finite time and the full states satisfy the constraints. Lastly, numerical simulations are supplied to demonstrate the effectiveness of the proposed control strategy.

Distributed low-complexity fault-tolerant consensus tracking of switched uncertain nonlinear pure-feedback multi-agent systems under asynchronous switching

This paper addresses a distributed low-complexity design problem for ensuring preassigned fault-tolerant consensus tracking quality of uncertain switched nonlinear pure-feedback multi-agent systems under arbitrary and asynchronous switching. Switched non-affine nonlinearities and unexpected nonlinear and actuator faults of each system are assumed to be unknown. Compared with existing results in the literature, the main contribution of this paper is to provide a simplified robust control strategy to deal with asynchronously switched nonlinearities and faults among systems in the consensus tracking field. Using nonlinearly transformed error surfaces and the common Lyapunov function method, a common robust consensus tracking design strategy is established to ensure the preassigned fault-tolerant consensus tracking performance and the system reliability on the switched faults, without using any adaptive fault compensation techniques based on neural networks or fuzzy logic systems. It is shown that the distributed consensus tracking errors remain within preselected bounds even at switching and fault occurrence instants and finally converge to a preselected neighborhood of the origin.

Distributed adaptive output consensus control of a class of heterogeneous multi-agent systems under switching directed topologies

In this paper, we consider a leader-follower output consensus problem for a class of uncertain heterogeneous non-affine pure-feedback multi-agent systems (MASs) in the presence of time-delay items and input saturation restrictions under switching directed topologies. A distributed adaptive control scheme is constructed by combining Lyapunov–Krasovskii functionals, backstepping methods, neural networks (NNs), auxiliary systems, graph theory, the mean value theorem and the implicit function theory along with the dynamic surface control (DSC) technique. The key advantages of the designed control approach are that there is no requirement of precise knowledge about uncertain dynamics and time-delay items of individual agents and the computational burden can drastically be reduced by employing the DSC technique. Also, norms of unknown weight of neural networks are estimated online instead of weight vectors themselves. In theory, it can be proven that the output signals of follower agents can synchronize with the leader’s and all signals in the closed-loop system are cooperatively semiglobally uniformly ultimately bounded (CSUUB) by suitable choice of design parameters. Two simulation examples are presented to demonstrate the effectiveness of the proposed strategy.