Stochastic Nonlinear Multi-agent Systems Research Articles

Optimized distributed formation control using identifier-critic-actor reinforcement learning for a class of stochastic nonlinear multi-agent systems

This article is to propose an adaptive reinforcement learning (RL)-based optimized distributed formation control for the unknown stochastic nonlinear single-integrator dynamic multi-agent system (MAS). For solving the issue of unknown dynamic, an adaptive identifier neural network (NN) is developed to determine the stochastic MAS under expectation sense. And then, for deriving the optimized formation control, the RL is putted into effect via constructing a pair of critic and actor NNs. With regard of the traditional RL optimal controls, their algorithm exists the inherent complexity, because their adaptive RL algorithm are derived from negative gradient of the square of Hamilton–Jacobi-Bellman (HJB) equation. As a result, these methods are difficultly extended to stochastic dynamical systems. However, since this adaptive RL laws are derived from a simple positive function rather than the square of HJB equation, it can make optimal control with simple algorithm. Therefore, this optimized formation scheme can be smoothly performed to the stochastic MAS. Finally, according to theorem proof and computer simulation, the optimized method can realize the required control objective.

Optimized Adaptive Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems With Non-Affine Nonlinear Faults

Optimized Adaptive Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems With Non-Affine Nonlinear Faults

Distributed Adaptive Optimization Algorithm for High-Order Nonlinear Multi-Agent Stochastic Systems with Lévy Noise.

An adaptive neural network output-feedback control strategy is proposed in this paper for the distributed optimization problem (DOP) of high-order nonlinear stochastic multi-agent systems (MASs) driven by Lévy noise. On the basis of the penalty-function method, the consensus constraint is removed and the global objective function (GOF) is reconstructed. The stability of the system is analyzed by combining the generalized Itô's formula with the Lyapunov function method. Moreover, the command filtering mechanism is introduced to solve the "complexity explosion" problem in the process of designing virtual controller, and the filter errors are compensated by introducing compensating signals. The proposed algorithm has been proved that the outputs of all agents converge to the optimal solution of the DOP with bounded errors. The simulation results demonstrate the effectiveness of the proposed approach.

Distributed Adaptive Output Feedback Consensus for Nonlinear Stochastic Multiagent Systems by Reference Generator Approach.

This article investigates the distributed leader-following consensus for a class of nonlinear stochastic multiagent systems (MASs) under directed communication topology. In order to estimate unmeasured system states, a dynamic gain filter is designed for each control input with reduced filtering variables. Then, a novel reference generator is proposed, which plays a key role in relaxing the restriction on communication topology. Based on the reference generators and filters, a distributed output feedback consensus protocol is proposed by a recursive control design approach, which incorporates adaptive radial basis function (RBF) neural networks to approximate the unknown parameters and functions. Compared with existing works on stochastic MASs, the proposed approach can significantly reduce the number of dynamic variables in filters. Furthermore, the agents considered in this article are quite general with multiple uncertain/unmatched inputs and stochastic disturbance. Finally, a simulation example is given to demonstrate the effectiveness of our results.

Preassigned Time Adaptive Neural Tracking Control for Stochastic Nonlinear Multiagent Systems With Deferred Constraints.

This article studies a preassigned time adaptive tracking control problem for stochastic multiagent systems (MASs) with deferred full state constraints and deferred prescribed performance. A modified nonlinear mapping is designed, which incorporates a class of shift functions, to eliminate the constraints on the initial value conditions. By virtue of this nonlinear mapping, the feasibility conditions of the full state constraints for stochastic MASs can also be circumvented. In addition, the Lyapunov function codesigned by the shift function and the fixed-time prescribed performance function is constructed. The unknown nonlinear terms of the converted systems are handled based on the approximation property of the neural networks. Furthermore, a preassigned time adaptive tracking controller is established, which can achieve deferred prescribed performance for stochastic MASs that provide only local information. Finally, a numerical example is given to demonstrate the effectiveness of the proposed scheme.

Distributed consensus of nonlinear stochastic multi-agent systems with input and output delays via predictive control

Distributed consensus of nonlinear stochastic multi-agent systems with input and output delays via predictive control

WITHDRAWN: Adaptive fuzzy fixed-time bipartite consensus control for stochastic nonlinear multi-agent systems with performance constraints

This paper investigates the fixed-time bipartite consensus control problem of stochastic nonlinear multi-agent systems (MASs) with performance constraints. A constraint scaling function is proposed to model the performance constraints with user-predefined steady-state accuracy and settling time without relying on the initial condition. Technically, the local synchronization error of each follower is mapped to a new error variable using the constraint scaling function and an error transformation function before being used to design the controller. To achieve fixed-time convergence of the local tracking error, a barrier function transforms the scaled synchronization error to a new variable to guarantee the prescribed performance. Then, an adaptive fuzzy fixed-time bipartite consensus controller is developed. The fuzzy logic system handles the uncertainties in the designing procedures, and one adaptive parameter needs to be estimated online. It is shown that the closed-loop system has practical fixed-time stability in probability, and the antagonistic network’s consensus error evolves within user-predefined performance constraints. The simulation results evaluate the effectiveness of the developed control scheme.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

Consensus of stochastic multi-agent systems with time-delay and Markov jump

In this paper, the H ∞ consensus problem of stochastic nonlinear multi-agent systems with time-delay, Markov jump and ( x , u , v ) -dependent noises is studied. Firstly, the H ∞ consensus problem is transformed into a standard H ∞ control problem by model transformation. Then, a dynamic output feedback control protocol is constructed by solving a set of linear matrix inequalities to ensure that the closed-loop system achieves the mean square consensus and meets the specified H ∞ performance level. After that, both delay-independent and delay-dependent stochastic bounded real lemmas are established by taking advantage of the Lyapunov–Krasovskii function method and the generalised It o ^ formula. Finally, we illustrate the validity of the developed method with numerical simulations.

Adaptive finite‐time optimal time‐varying formation control for second‐order stochastic nonlinear multiagent systems

SummaryThis work addresses a fuzzy‐based finite‐time optimal time‐varying formation (TVF) control issue for a class of second‐order stochastic multi‐agent systems (SMASs) with unknown nonlinearities. First, novel optimal cost functions with exponential power terms are constructed, which enables the SMASs to achieve finite‐time stability in the mean square sense with minimum cost. Then, based on the cost functions, an optimal controller is proposed, in which fuzzy logic systems (FLSs) are used as universal approximators to identify the unknown uncertainties. Theorem analyses show that the proposed control strategy can guarantee the mean‐square finite‐time bounded of all signals in the system and then the TVF control task can be simultaneously realized with minimum cost. Finally, the effectiveness of the presented control method is verified by a multiple omni‐directional robot system.

Adaptive fuzzy fault‐tolerant control of stochastic nonlinear multiagent systems with input quantization and state constraints

SummaryThis paper is dedicated to the problem of adaptive fuzzy fault‐tolerant control (FTC) for a class of stochastic nonstrict feedback nonlinear multi‐agent systems (MASs) with input quantization and full state constraints. Firstly, based on the backstepping technique and the bounded estimation method, the effect of actuator faults can be eliminated by the proposed adaptive updating laws. Secondly, the stochastic barrier Lyapunov functions (BLFs) are constructed to ensure that all state constraints are not violated. Meanwhile, the introduction of input quantization can effectively save network resources and reduce computational burden. It is further shown that all the closed‐loop signals are uniformly bounded, and the consensus tracking errors asymptotically tend to zero. The effectiveness of the proposed control scheme is illustrated by a numerical example.

Adaptive fuzzy consensus secure control of stochastic nonlinear multi-agent systems with false data injection attacks

This paper discusses the fuzzy adaptive consensus secure control problem for a class of stochastic nonlinear multi-agent systems (MASs) with unknown false data injection attacks. Fuzzy logic systems (FLSs) are used to model unknown nonlinear functions. A distributed filter is proposed to obtain the information of the leader since leaders information is only available to partial agents. To deal with the unknown virtual time-varying gains caused by false data injection attacks, an adaptive compensation method is developed via re-codesigning the virtual controllers. Based on backstepping control methodology and bounded estimation algorithms, an adaptive fuzzy consensus secure controller is proposed. It is proved that all the signals in the closed-loop systems are bounded in probability, and all the output of followers can track the leader under false data injection attacks. Finally, simulation results and comparative results show the effectiveness of the proposed control method.

Fixed-time consensus control of stochastic nonlinear multi-agent systems with input saturation using command-filtered backstepping

<abstract><p>In this paper, a fixed-time consensus control algorithm is proposed for non-triangular structure stochastic nonlinear multi-agent systems (SNMASs) with input saturation via the command-filtered backstepping design method. Fuzzy logic systems are employed to identify the nonlinear dynamics of each agent. By introducing the fixed-time command filter and constructing the fractional power error compensation mechanism, the "complexity explosion" problem is effectively avoided, and the influence of filtered errors is eliminated in a fixed time. Based on the fixed-time stability theory, it strictly proves that all signals in the closed-loop system are fixed-time bounded in probability, and the consensus error converges to a sufficiently small neighborhood of the origin in probability within a fixed time. Finally, a comparison simulation example verifies the effectiveness and superiority of the proposed fixed-time consensus control strategy.</p></abstract>

Distributed Fuzzy Containment Control for Stochastic Nonlinear Multiagent Systems Under Denial-of-Service Attacks

The paper investigates distributed fuzzy adaptive containment control problem of stochastic nonlinear multi-agent systems under an directed communication topology suffering Denial-of-Service (DoS) attacks. Firstly, considering unknown stochastic disturbance and nonlinear characteristics for the followers, the mathematical models are modeled as It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\hat{o}$</tex-math></inline-formula> stochastic nonlinearities terms approximated through fuzzy logic systems (FLS). Secondly, the proposed dynamically adjusted event-triggered condition can effectively avoid inefficient transmission behavior. Moreover, an adaptive compensation protocol for input saturation is constructed to eliminate the effects of nonlinearities caused by input saturation. Finally, instead of the previous uniformly ultimately bounded containment control results, stability and asymptotic performance are guaranteed through valid reasonable adaptive control laws acquired through backstepping control approach despite suffers DoS cyber attacks. Moreover, a simulation is given to verify the feasibility of the proposed method.

Adaptive Finite-Time Consensus for Stochastic Multiagent Systems With Uncertain Actuator Faults

This paper aims to develop fully distributed adaptive protocols and establish the finite-time consensus criteria for nonlinear stochastic multi-agent systems that are subjected to serious multiple uncertainties not only in the agents' states and inherent nonlinearities but also in their actuators. Firstly, we propose a new continuous fully distributed consensus protocol for leaderless stochastic multi-agent systems by leveraging the adaptive technology, enabling the agents to achieve the finite-time consensus in probability efficiently. Secondly, we develop an adaptive protocol for leader-following multi-agent systems, and remarkably our protocol contains only one dynamic gain, which is adequate to resist serious multiple uncertainties and to ensure the realization of finite-time consensus in probability. Finally, we provide numerical simulations to verify the effectiveness of our protocols.

ADP-based event-sampled optimized consensus tracking of stochastic multi-agent systems with actuator faults

This article concentrates on the event-triggered optimized leader-follower consensus control for stochastic nonlinear multi-agent systems (MASs) with actuator bias faults. An adaptive state identifier is designed to estimate unknown states in real time. In addition, an adaptive dynamic programming (ADP)-based algorithm with a critic-actor architecture is developed to learn the optimized control policy online. Based on the online estimating information from the designed fault estimator, a fault-tolerant (FT) controller is designed to compensate for the deleterious effects of actuator bias faults. The proposed control scheme employs a dynamic event-triggered mechanism (ETM) to reduce network resources by tuning dynamic parameters. All the signals can be proven to be bounded by utilizing the Lyapunov stability method, and the Zeno behavior can be excluded. Simulation results show the merit and validity of the proposed control scheme.

Distributed Adaptive-Neural Finite-Time Consensus Control for Stochastic Nonlinear Multiagent Systems Subject to Saturated Inputs.

In this article, the problem of distributed finite-time consensus control for a class of stochastic nonlinear multiagent systems (MASs) (with directed graph communication) in the presence of unknown dynamics of agents, stochastic perturbations, external disturbances (mismatched and matched), and input saturation nonlinearities is addressed and studied. By combining the backstepping control method, the command filter technique, a finite-time auxiliary system, and artificial neural networks, innovative control inputs are designed and proposed such that outputs of follower agents converge to the output of the leader agent within a finite time. Radial-basis function neural networks (RBFNNs) are employed to approximate unknown dynamics, stochastic perturbations, and external disturbances. To overcome the complexity explosion problem of the conventional backstepping method, a novel finite-time command filter approach is proposed. Then, to deal with the destructive effects of input saturation nonlinearities, the finite-time auxiliary system is designed and developed. By mathematical analysis, it is proven that the mentioned MAS (injected by the proposed control inputs) is semiglobally finite-time stable in probability (SGFSP) and all consensus tracking errors converge to a small neighborhood of the zero during a finite time. Finally, a numerical simulation onto a group of four single-link robot manipulators is carried out to illustrate the effectiveness of the suggested control scheme.

Collision-Free Adaptive Fuzzy Formation Control for Stochastic Nonlinear Multiagent Systems

This article considers the collision-free fuzzy output-feedback formation control problem for stochastic nonlinear multiagent systems (MASs) with immeasurable states. The fuzzy state observers are established to estimate the unmeasurable states of MASs, and fuzzy-logic systems (FLSs) are utilized to identify the unknown internal dynamics. The prescribed performance functions (PPFs) are introduced to establish the collision avoidance conditions between the follower agent and its leader agent. Then, a novel collision-free adaptive output-feedback formation controller is constructed by utilizing a suitable error transformation. The presented formation control method can guarantee all the variables of the stochastic nonlinear MASs are bounded in probability and each follower agent and the leader agent are free of collision. Finally, the presented formation control method is applied to the unmanned surface vehicle (USV) systems, and the effectiveness and superiorities are checked by the simulation results and comprehensive comparisons.

Observer-based event-triggered optimal control for unknown nonlinear stochastic multi-agent systems with input constraints

This paper addresses the observer-based event-triggered optimal control (ETOC) for unknown nonlinear Ito^-type stochastic multi-agent systems (SMASs) with input constraints. To begin with, the event-triggered stochastic Hamilton-Jacobi-Bellman (HJB) equation with input constraints is presented, and a sufficient criterion on optimal mean-square leader-following consensus of constrained-input SMASs is derived. Next, a novel event-triggered policy iteration algorithm of constrained-input SMASs is designed to obtain the ETOC strategy. Then, an identifier-critic framework is designed where the observer-based identifier network is utilized to recover the knowledge of unknown stochastic dynamics and the constrained-input approximate event-triggered optimal controller is designed via event-triggered adaptive critic designs (ET-ACDs). Moreover, it is proved that the Zeno behavior can be excluded in the sense of expectation. Finally, we present two examples to further verify the validity of the ETOC scheme.

Distributed Output-Feedback Bipartite Consensus for Stochastic Nonlinear Multiagent Systems Under Directed Switching Networks

This article investigates the distributed dynamic output-feedback bipartite consensus for a class of stochastic nonlinear multiagent systems (MASs) with time delays and actuators faults under directed switching graphs. First, a distributed extended state compensator is constructed for each agent to compensate for the consensus errors and actuators’ faults only using the output information of neighbors. Then, based on the compensator, a linear memoryless output-feedback controller is designed. Using a technical lemma and the stochastic Lyapunov stability theory, it is proved that combined with the given constraint conditions on graphs switching the 2nd-moment asymptotic bipartite consensus for the MASs can be achieved. Different from existing results, the proposed compensator can not only save the network bandwidth but also compensate for the actuators’ faults. The proposed scheme also significantly relaxes the conditions on the communication network to directed switching graphs and even allows the graph to be disconnected over some time intervals. The common design parameters under any graphs can avoid the detection of graph switching, which will need global topology information. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.