Non-affine Multi-agent Systems Research Articles

Reinforcement learning-based adaptive event-triggered control of multi-agent systems with time-varying dead-zone

In this paper, a novel reinforcement learning (RL)-based adaptive event-triggered control problem is studied for non-affine multi-agent systems (MASs) with time-varying dead-zone. The purpose is to design an efficient event-triggered mechanism to achieve optimal control of MASs. Compared with the existing results, an improved smooth event-triggered mechanism is proposed, which not only overcomes the design difficulties caused by discontinuous trigger signals, but also reduces the waste of communication resources. In order to achieve optimal event-triggered control, RL algorithm of the identifier-critic-actor structure based on fuzzy logic systems (FLSs) is applied to estimate system dynamics, evaluate control performance, and execute control behavior, respectively. In addition, considering time-varying dead-zone in non-affine MASs brings obstacles to controller design, which makes system applications more generalized. Through Lyapunov theory, it is proved that the optimal control performance can be achieved and the tracking error converges to a small neighborhood of the origin. Finally, simulation proves the feasibility of the proposed method.

Neural-Network-Based Adaptive Fixed-Time Control for Nonlinear Multiagent Non-Affine Systems.

In this research, the adaptive neural network consensus control problem is addressed for a class of non-affine multiagent systems (MASs) with actuator faults and stochastic disturbances. To overcome difficulties associated with actuator faults and uncertain functions of the designed MAS, a neural network fault-tolerant control scheme is developed. Moreover, an adaptive backstepping controller is developed to solve the non-affine appearance in multiagent stochastic non-affine systems using the mean value theorem. Being different from the existing control methods, the developed adaptive fixed-time control approach can ensure that the outputs of all followers track the reference signal synchronously in the fixed time, and all signals of the controlled system are semi-globally uniformly fixed-time stable. The simulation results confirm that the presented control strategy is effective in achieving control goals.

Distributed data-driven iterative learning point-to-point consensus tracking control for unknown nonlinear multi-agent systems

This paper studies the point-to-point consensus tracking problem for a class of nonlinear non-affine multi-agent systems, where the tracking target is a series of some given ideal output points rather than a complete ideal trajectory. For the unknown nonlinear dynamics of every agent, the relationship between its control input and the corresponding output signal at these given points is acquired, then a data-driven model is constructed based on adjacent-agent dynamic linearization technology. Furthermore, by optimizing two performance index functions, we design a novel point-to-point iterative learning tracking control scheme, which not only ensures the consensus tracking results of all agents only utilizing the I/O data of every agent at the given ideal output points, but also makes all agents reach consensus behavior at the rest of the time instants. The effectiveness of our algorithm is confirmed through rigorous theoretical analysis and two experimental simulations.

Design of data-driven mode-free iterative learning controller based higher order parameter estimation for multi-agent systems consistency tracking

In this study, an adaptive data-driven control protocol design scheme based on higher order parameter (HOP) estimation and iterative learning is proposed for a class of nonaffine multi-agent systems (MAS) with unknown nonlinearity to solve the consistency tracking problem of MAS with fixed and switching topology communications. The control protocol mainly comprises HOP estimation and an iterative learning controller. The iterative learning control (ILC) algorithm is mainly used for system synergy, and the adaptive control algorithm based on HOP estimation mainly completes the system stabilization. The main advantage of the control protocol is that it uses only the input/output (I/O) data of the agents to complete the consensus tracking task and does not require specifying the dynamical system of each agent. The control protocol has a modular design, in which the iterative learning and HOP estimation algorithms complement each other without affecting the structure of the controller. The effectiveness of the control protocol is demonstrated using two simulation experiments.

Observer-Based Adaptive Fuzzy Distributed Control of Non-affine Multi-agent Systems with Input Quantization

Observer-Based Adaptive Fuzzy Distributed Control of Non-affine Multi-agent Systems with Input Quantization

Data-Driven Adaptive Consensus Learning From Network Topologies.

The problem of consensus learning from network topologies is studied for strongly connected nonlinear nonaffine multiagent systems (MASs). A linear spatial dynamic relationship (LSDR) is built at first to formulate the dynamic I/O relationship between an agent and all the other agents that are communicated through the networked topology. The LSDR consists of a linear parametric uncertain term and a residual nonlinear uncertain term. Utilizing the LSDR, a data-driven adaptive learning consensus protocol (DDALCP) is proposed to learn from both time dynamics of agent itself and spatial dynamics of the whole MAS. The parametric uncertainty and nonlinear uncertainty are estimated through an estimator and an observer respectively to improve robustness. The proposed DDALCP has a strong learning ability to improve the consensus performance because time dynamics and network topology information are both considered. The proposed consensus learning method is data-driven and has no dependence on the system model. The theoretical results are demonstrated by simulations.

Adaptive distributed tracking control for non-affine multi-agent systems with state constraints and dead-zone input

In this paper, an adaptive distributed control protocol is proposed for non-affine multi-agent system with nonlinear dead-zone input and state constraints under the condition of directed topology. In order to overcome the difficulties caused by non-affine terms in the system, the nonlinear dynamics system is transformed. Then, the neural network technology is introduced to approximate the unknown non-affine terms for the obtained system. State constraints and dead-zone input are common system problems. In order to solve these problems, the barrier Lyapunov function is introduced in this paper. According to the barrier Lyapunov function and backstepping method, an adaptive distributed controller is designed, so that state variables do not violate constraint bounds and the system is not affected by dead-zone input. By Lyapunov stability theory, it is proved that the signals of each follower are cooperative semi-global uniform ultimate boundedness (CSUUB), and the outputs of the followers track the output of the leader. Simulation example is given to demonstrate the effectiveness of the proposed method.

Containment control of non-affine multi-agent systems based on given precision

This paper concentrates on a containment control issue for multi-agent systems in non-affine form with a given accuracy. In comparison with the existing studies on multi-agent systems, precision-based containment control idea is first formulated. With the aid of the proposed strategy, the main merit of this note is that the synchronization errors converge to arbitrary given positive number. Simultaneously, the particular Layapunov functions are constructed by feat of two auxiliary functions. By employing the backstepping and adaptive control technique, the key variables and the actual controller are designed. Unlike the traditional stability analysis, a novel method is used to analyse the convergence of containment errors. In the end, some simulation results demonstrate the correctness for the proposed protocol.

Observer based switching ILC for consensus of nonlinear nonaffine multi-agent systems

This study considers the main challenges of presenting an iterative observer under a data-driven framework for nonlinear nonaffine multi-agent systems (MASs) that can estimate nonrepetitive uncertainties of initial states and disturbances by using the information from previous iterations. Consequently, an observer-based iterative learning control is proposed for the accurate consensus tracking. First, the dynamic effect of nonrepetitive initial states is transformed as a total disturbance of the linear data model which is developed to describe I/O iteration-dynamic relationship of nonlinear nonaffine MASs. Second, the measurement noises are considered as the main uncertainty of system output. Then, we present an iterative disturbance observer to estimate the total uncertainty caused by the nonrepetitive initial shifts and measurement noises together. Next, we further propose an observer-based switching iterative learning control (OBSILC) using the iterative disturbance observer to compensate the total uncertainty and an iterative parameter estimator to estimate unknown gradient parameters. The proposed OBSILC consists of two learning control algorithms and the only difference between the two is that an iteration-decrement factor is introduced in one of them to further reduce the effect of the total uncertainty. These two algorithms are switched to each other according to a preset error threshold. Theoretical results are demonstrated by the simulation study. The proposed OBSILC can reduce the influence of nonrepetitive initial values and measurement noises in the iterative learning control for MASs by only using I/O data.

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 Leader-Following Tracking Control of Nonaffine Multiagent Systems With Finite-Time Output Constraint and Input Saturation

This article considers the problem of distributed adaptive fuzzy event-based finite-time prescribed performance leader-following tracking control for heterogeneous nonlinear multiagent systems (NMASs) over a directed topology. Each agent is considered in a nonaffine nonstrict-feedback form under input saturation and output constraint which contains unknown dynamics and external disturbances. Fuzzy logic systems (FLSs) are exploited as an effective online approximation tool to tackle system uncertainties. By employing the unique property of FLS, the algebraic loop problem is overcome and by designing novel adaptive laws of the FLS weights, the computation burden is decreased significantly. The threshold of the event-triggered condition is improved compared to the conventional relative-threshold mechanism. A modified performance function called finite-time performance function is introduced to constrain the synchronization errors within the prescribed performance bounds in finite time. The dynamic surface control technique is then developed to avoid the issue of the “explosion of complexity.” Moreover, by developing a new decomposition for the controller gain function resulting from the mean-value theorem and introducing an auxiliary system, the input saturation nonlinearity that affects the nonaffine form stability is handled. Through the Lyapunov stability analyses, it is shown that the developed control algorithm ensures the closed-loop NMAS trajectory to be cooperatively semi-globally uniformly ultimately bounded. Additionally, the tracking errors are driven to a predefined region around zero in finite time. Finally, the efficiency of the established theoretical results is validated by the simulation studies.

Adaptive NN Control for Nonlinear Multi-Agent Systems With Unknown Control Direction and Full State Constraints

This paper proposes an adaptive full state constrained consensus control strategy for a class of non-affine multi-agent systems with partially unknown control directions. Such non-affine systems commonly appear in practical applications and are difficult to control, especially with unknown control directions. Neural network is an excellent approximation tool to solve unknown parameters in the aforementioned consensus systems. The method of one-to-one mapping and mean value theorem can eliminate coupling terms and guarantee that the states of each agent are not violated the predetermined time-varying dynamic constraint boundary. In this way, the original systems can be transformed into an equivalent unconstrained systems, and the transformed systems obtained has the same consensus with the original systems. Considering that directions of control are partially unknown, the Nussbaum function can solve this problem in a novel way. Then the stability of the systems can be proved by Lyapunov function and all signals in the closed-loop systems are bounded. In the end, the simulation demonstrates the effectiveness of the proposed method.

Output-Constrained Control of Non-affine Multi-agent Systems with Actuator Faults and Unknown Dead Zones

This paper presents the output-constrained control algorithm for non-affine multi-agent systems (MASs) with actuator faults and unknown dead zones. The error transformation method is employed to keep initial connectivity patterns in the non-affine MASs for consensus tracking control. The radial basis function neural networks are utilized to estimate the unknown nonlinear functions. Furthermore, the Nussbaum function is used to overcome partially unknown control direction problem. To address the problem of the constrained control, a state transformation technique is presented. In addition, the fault-tolerant consensus tracking protocol is designed to reduce the effects of actuator faults and dead zones. Furthermore, it is shown that the consensus tracking errors are cooperatively semi-globally uniformly ultimately bounded. Finally, the effectiveness of the proposed approach is illustrated by some simulation results.

Event-triggered adaptive consensus tracking control for non-affine multi-agent systems

This paper presents the event-triggered consensus control problem for a class of multi-agent systems (MASs) in the non-affine form. An error-transformation-based design method is presented in the non-affine MASs. The radial basis function neural networks (RBFNNs) are used to approximate the unknown nonlinear functions. The dynamic surface control (DSC) technique is adopted to obtain parameters of the virtual controller through a first-order filter, which can make the calculation easier. An event-triggered control strategy is proposed to reduce communication frequency. Furthermore, it is further shown that the consensus tracking errors are semi-globally uniformly ultimately bounded (SGUUB). Finally, simulation results illustrate the effectiveness of the designed controller.

Output-Constrained Control of Nonaffine Multiagent Systems With Partially Unknown Control Directions

In this paper, an output-constrained control algorithm is presented for the consensus control of a class of unknown nonaffine multiagent systems (MASs) with partially unknown control directions. Our contribution includes a step forward beyond the usual consensus stabilization result to show that the outputs of agents remain within user-defined time-varying constraints. To achieve the new results, an error transformation technique is established to generate an equivalent MAS from the original one. Stabilization and consensus of the transformed agent states ensure both the satisfaction of the time-varying constraints and the consensus of the original agent states. Based on the Nussbaum gain technique, the unknown control direction problem is solved. By the Lyapunov synthesis, the asymptotic consensus result and the satisfaction of the output constraints are theoretically proved, along with all the closed-loop signals being bounded. Additionally, the developed consensus controller is distributed since each agent only exchanges information with its neighbors. Finally, simulations on a nonaffine MAS demonstrate the effectiveness of the proposed control scheme.

Adjacent-Agent Dynamic Linearization-Based Iterative Learning Formation Control.

The dynamical relationship of the multiple agents' behavior in a networked system is explored and utilized to enhance the control performance of the multiagent formation in this paper. An adjacent-agent dynamic linearization is first presented for nonlinear and nonaffine multiagent systems (MASs) and a virtual linear difference model is built between two adjacent agents communicating with each other. Considering causality, the agents are assigned as parent and child, respectively. Communication is from parent to child. Taking the advantage of the repetitive characteristics of a large class of MASs, an adjacent-agent dynamic linearization-based iterative learning formation control (ADL-ILFC) is proposed for the child agent using 3-D control knowledge from iterations, time instants, and the parent agent. The ADL-ILFC is a data-driven method and does not depend on a first-principle physical model but the virtual linear difference model. The validity of the proposed approach is demonstrated through rigorous analysis and extensive simulations.

Distributed fuzzy adaptive consensus states tracking controller for a class of nonlinear non-affine multi-agent systems with dynamic uncertainties

Distributed fuzzy adaptive consensus states tracking controller for a class of nonlinear non-affine multi-agent systems with dynamic uncertainties

Distributed adaptive output-feedback tracking control of non-affine multi-agent systems with prescribed performance

This paper addresses the distributed adaptive output-feedback tracking control problem of uncertain multi-agent systems in non-affine pure-feedback form under a directed communication topology. Since the control input is implicit for each non-affine agent, we introduce an auxiliary first-order dynamics to circumvent the difficulty in control protocol design and avoid the algebraic loop problem in control inputs and the unknown control gain problem. A decentralized input-driven observer is applied to reconstruct state information of each agent, which makes the design and synthesis extremely simplified. Based on the dynamic surface control technique and neural network approximators, a distributed output-feedback control protocol with prescribed tracking performance is derived. Compared with the existing results, the restrictive assumptions on the partial derivative of non-affine functions are removed. Moreover, it is proved that the output tracking errors always stay in a prescribed performance bound. The simulation results are provided to demonstrate the effectiveness of the proposed method.

Distributed Adaptive FBC of Uncertain Nonaffine Multiagent Systems Preceded by Unknown Input Nonlinearities With Unknown Gain Sign

An adaptive filtered backstepping control (FBC) is proposed for cooperative tracking control of uncertain nonaffine nonlinear multiagent systems preceded by input nonlinearities with unknown gain sign. The input nonlinearities can be backlash-like hysteresis and dead-zone. The gains of input nonlinearities are unknown nonlinear functions with unknown sign. To cope with unknown nonlinearities neural networks based on universal approximation theorem are utilized. The weights of neural networks are derived based on appropriate adaptive rules. Using the proposed adaptive FBC desirable steady-state and transient response can be achieved. Based on Lyapunov synthesis approach all the adaptive laws are extracted. It is proved that all the signals in the closed-loop network are semi-globally uniformly ultimately bounded and the outputs of the agents track the leader’s output asymptotically. Simulation results demonstrate the applicability and effectiveness of the proposed method.