High-order Nonlinear Multi-agent Systems Research Articles

Hierarchical Robust Generalized Nash Equilibrium Seeking of High-Order Uncertain Nonlinear Systems.

This article investigates the distributed generalized Nash equilibrium (GNE) seeking problem of noncooperative games (NGs) for high-order strict-feedback nonlinear multiagent systems (MASs). In particular, the feasible action set of each agent is not only subject to local set and inequality constraints but also coupled through an equality constraint with other agents. This constraint structure is more general and covers most of the constraints in the GNE seeking literature. To accomplish the concerned GNE seeking objective, we propose a novel hierarchical GNE seeking approach in this article to decouple the distributed GNE seeking algorithm design into two layers. First, we construct a distributed primary-dual GNE estimator to generate virtual reference signals that converge to the GNE. Then, with the output of the estimator as the reference signal, we develop an adaptive tracking controller to solve the resultant tracking problems under output constraints. To overcome the negative effects of the disturbances, novel compensating terms associated with smooth functions and positive integrable time-varying functions are incorporated in the controller design, which thereby realizes the exact GNE seeking in the presence of nonvanishing mismatched disturbances. At last, an example is given to support the theoretical analysis of the proposed algorithms.

Multi-group formation tracking fault-tolerant control for matched nonlinear multi-agent systems with switching topologies and unknown control inputs

The multi-group formation fault-tolerant control problem for high-order nonlinear multi-agent systems with parameter uncertainties, unknown external disturbances, switching topologies, and non-cooperative targets are investigated in this paper. A fully distributed formation tracking control protocol is proposed based on the total interaction information between subgroups being zero and the neighboring relative information of multi-agent in the subgroups. In addition, an algorithm is proposed to design the parameters of time-varying formation tracking control protocol. At the same time, it does not require knowing the bounds of actuator faults, parameter uncertainties, control inputs of the leaders, and unknown disturbances. Then, it is proved that the designed control protocols can make the high-order nonlinear multi-agent systems accomplish the desired time-varying multi-group formation, and the errors are uniformly asymptotically bounded stable. Finally, the effectiveness of the designed control protocol is demonstrated by simulation examples of three subgroups.

Finite-Time Output-Feedback Formation Control for High-Order Nonlinear Multiagent Systems With Obstacle Avoidance

This paper investigates the finite-time formation control problem for high-order nonlinear multiagent systems (MASs) with the consideration of obstacle avoidance, unmeasurable states and dead-zone input. A neural networks k-filter observer is designed to estimate the unmeasurable states and cope with the problem of dead-zone input. Also, by using an integral-multiplicative tangent Lyapunov-barrier function (LBF), the obstacle avoidance mission can be completed for MASs without dynamic mismatching. Then, combining the finite-time method and the backstepping theory, an output-feedback finite-time controller is designed for high-order nonlinear MASs. Theoretical analysis indicates that the control algorithm can not only make agents accomplish the formation obstacle avoidance task but also guarantee the boundedness of signals in the system. A simulation demonstrates the effectiveness of the proposed control algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This article studies the formation obstacle avoidance problem for MASs which plays an important role in transportation, exploration and rescue activities. Unmeasurable states and dead-zone input, which often occur in practice, are also considered and handled by a neural networks k-filter observer. An integral-multiplicative tangent LBF is utilized to complete the obstacle avoid task which is necessary for actual systems. Moreover, to be more feasible in industrial applications, the finite-time control strategy is used in the controller design.

Fixed-Time Fault-Tolerant Consensus Control for High-Order Nonlinear Multiagent Systems Under Directed Topology

This paper addresses the fixed-time fault-tolerant consensus control problem for high-order nonstrict-feedback nonlinear multi-agent systems under directed topology. A distributed high-order fixed-time observer is proposed to obtain the accurate estimations of the full states of the leader. Different from the fixed-time observer design methods, a much more concise estimate for the upper bound of the convergence time is provided. Based on the fixed-time observer and adding a power technique, a fixed-time tracking protocol is designed for a group of followers subject to unknown nonidentical dynamics and unpredictable actuation faults. It is shown that there is no need to know the information of the nonstrict-feedback nonlinear dynamics, the control gains, and the actuation faults in the control design and implementation completely, which is deemed favorable in practice. Simulation results are provided to validate the effectiveness of the developed control scheme.

Cooperative Control of Multiagent Systems: A Quantization Feedback-Based Event-Triggered Approach.

This article addresses the synchronization tracking problem for high-order uncertain nonlinear multiagent systems via intermittent feedback under a directed graph. By resorting to a novel storer-based triggering transmission strategy in the state channels, we propose an event-triggered neuroadaptive control method with quantitative state feedback that exhibits several salient features: 1) avoiding continuous control updates by making the parameter estimations updated intermittently at the trigger instants; 2) resulting in lower-frequency triggering transmissions by using one event detector to monitor the triggering condition such that each agent only needs to broadcast information at its own trigger times; and 3) saving communication and computation resources by designing the intermittent updating of neural network weights using a dual-phase technique during the triggering period. Besides, it is shown that the proposed scheme is capable of steering the tracking/disagreement errors into an adjustable neighborhood close to the origin, and the existence of a strictly positive dwell time is proved to circumvent Zeno behavior. Both theoretical analysis and numerical simulation authenticate and validate the efficiency of the proposed protocols.

Optimized bipartite formation control for multiagent systems with obstacle and collision avoidance

This paper considers an optimal bipartite formation control problem for high-order nonlinear multiagent systems (MASs) with the consideration of obstacle/collision avoidance. Contrary to existing literature, the control strategy designed in this paper can render the agents in a bipartite formation to complete the obstacle/collision avoidance tasks without requiring the obstacles to be located on the coordinate axis. To save resources, an identifier-critic-actor-based optimized formation control scheme is designed for MASs. An obstacle/collision avoidance approach based on dynamical systems (DS) is designed for high-order nonlinear MASs. Different from the existing related results, the proposed DS-based obstacle/collision avoidance approach can avoid the phenomenon that the control quantities approach infinity near obstacles or other agents, and eliminate the dependence on global information. Finally, a simulation example is given to validate the proposed control method.

Genetic algorithm-based secure cooperative control for high-order nonlinear multi-agent systems with unknown dynamics

AbstractResearch has recently grown on multi-agent systems (MAS) and their coordination and secure cooperative control, for example in the field of edge-cloud computing. MAS offers robustness and flexibility compared to centralized systems by distributing control across decentralized agents, allowing the system to adapt and scale without overhaul. The collective behavior emerging from agent interactions can solve complex tasks beyond individual capabilities. However, controlling high-order nonlinear MAS with unknown dynamics raises challenges. This paper proposes an enhanced genetic algorithm strategy to enhance secure cooperative control performance. An efficient encoding method, adaptive decoding schemes, and heuristic initialization are introduced. These innovations enable compelling exploration of the solution space and accelerate convergence. Individual enhancement via load balancing, communication avoidance, and iterative refinement intensifies local search. Simulations demonstrate superior performance over conventional algorithms for complex control problems with uncertainty. The proposed method promises robust, efficient, and consistent solutions by adapting to find optimal points and exploiting promising areas in the space. This has implications for securely controlling real-world MAS across domains like robotics, power systems, and autonomous vehicles.

Sampled-Data-Based Distributed Output Feedback Leader–Following Consensus for Time-Delay Multiagent Systems

This paper addresses the distributed output feedback leader-following consensus problem for high-order nonlinear multiagent systems (MASs) with time delays and disturbances under the directed network. Using sampled relative outputs to neighbors and the discrete control input, the continuous-discrete time compensator is constructed in each agent to compensate for the consensus errors, where the sampling time instants can be asynchronous and aperiodic without exceeding an explicit upper bound of sampling intervals. Based on the compensator, we propose a co-design algorithm for constructing the dynamic event-triggered protocol with a corresponding event-triggering mechanism which is a combination of discrete-time control input, continuous dynamic variables of each agent's own compensator, and a given threshold. The proposed methods can not only achieve consensus tracking under the effects of time delays in states and communications but also implement the discrete-time execution of measurement, communication, and control. Based on the novel lemmas, it is proved that the resulting closed-loop consensus error system is globally stable. Finally, a simulation is given to illustrate the effectiveness of proposed methods.

Distributed Optimal Resource Allocation for High-Order Nonlinear Multi-Agent Systems Over Unbalanced Digraphs

Distributed Optimal Resource Allocation for High-Order Nonlinear Multi-Agent Systems Over Unbalanced Digraphs

Observer-based distributed convex optimization of bipartite containment control for higher order nonlinear uncertain multi-agent systems

This paper studies the distributed convex optimization of bipartite containment control problem for a class of higher order nonlinear multi-agent systems with uncertain states. For the optimization problem, the penalty function is constructed by summing the local objective function of each agent and combining the penalty term formed by the adjacency matrix. For the unknown nonlinear function and unpredictable states in the system, this paper construct radial basis function Neural-networks and state observer for approaching, respectively. In order to avoid “explosion of complexity,” under the framework of Lyapunov function theory, we propose the dynamic surface control (DSC) technology and design the distributed adaptive backstepping neural network controller to ensure all the signals remain semi-global uniformly ultimately bounded in the closed-loop system and all agents can converge to the convex hull containing each boundary trajectory as well as its opposite trajectory different in sign. Simulation results confirm the feasibility of the proposed control method.

Event-Triggered Cooperative Exponential Practical Tracking for a Class of Higher-Order Uncertain Nonlinear Multiagent Systems

Event-Triggered Cooperative Exponential Practical Tracking for a Class of Higher-Order Uncertain Nonlinear Multiagent Systems

Global Consensus Tracking Control for High-Order Nonlinear Multiagent Systems With Prescribed Performance.

In this article, we investigate the prescribed performance tracking control problem for high-order nonlinear multiagent systems (MASs) under directed communication topology and unknown control directions. Different from most existing prescribed performance consensus control methods where certain initial conditions are needed to be satisfied, here the restriction related to the initial conditions is removed and global tracking result irrespective of initial condition is established. Furthermore, output consensus tracking is achieved asymptotically with arbitrarily prescribed transient performance in spite of the directed topology and unknown control directions. Our development benefits from the performance function and prescribed-time observer. Both theoretical analysis and numerical simulation confirm the validity of the developed control scheme.

Neuro-Based Consensus Seeking for Nonlinear Uncertainty Multi-Agent Systems Constrained by Dead-Zone Input

The topic about consensus target track seeking for high-order nonlinear multi-agent systems (MASs) with unmodeled dynamics, dynamic disturbances, and dead-zone input is considered in the paper. Using the strong nonlinear map characteristic of radial basis function neural networks (RBFNNs), the complex functions arising from recursive procedure are simplified. Also, inspired by input-to-state practical stability (ISpS), the authors construct a dynamical signal in order to counteract the impact of unmodeled dynamics and dynamic disturbances. The bounded inequality expression has been applied to tackle the unknown input of dead zone. Based on this, consensus control protocol suitable for nonlinear constraints has been constructed by using the recursive backstepping technique and adaptive neural network method. Theoretical analysis indicates not only the uniform boundary of all signals in the closed-loop under the neuro-based consensus controller, but uniform ultimate convergence of consensus tracking errors. The final simulations also confirmed the correctness of the theoretical analysis.

Fully distributed consensus for high-order strict-feedback nonlinear multiagent systems with switched topologies

Fully distributed consensus for high-order strict-feedback nonlinear multiagent systems with switched topologies

Distributed Optimization for Uncertain High-Order Nonlinear Multiagent Systems via Dynamic Gain Approach

In this article, we investigate the distributed output optimization for general uncertain high-order nonlinear multiagent systems (MASs), where nonlinear functions are constrained by a linear growth condition. The dynamic gain approach is utilized to cope with the influence of the unknown optimal solution. First, the distributed optimal coordinators (DOCs) with an adjustable parameter are constructed to steer the generated signals converging to the optimal solution. By developing the iterative design strategy, the dynamic reference-tracking controllers are then designed so that the output of each agent follows the generated value of coordinators, respectively. It is proved that all states are globally bounded, as well as the tracking error between the outputs and optimal solution can be bounded in a finite time by an arbitrarily small constant. Simulation studies demonstrate the validness of the main idea.

Adaptive approximated inverse control for a class of multi-agent systems with unknown control directions

An adaptive approximated inverse control scheme for a class of high-order nonlinear multi-agent systems with unknown control directions is proposed in this paper. The adaptive control problem under the case it is not required to be identical for the unknown control directions is solved by some novel Nussbaum functions and a monotonously increasing sequence, leading our multiple Nussbaum functions reinforce rather than counteract each other. Also, it is introduced in the design and analysis like some integrable auxiliary signals and a novel contradiction argument. Moreover, hysteresis nonlinearity is counteracted by constructing its approximated inverse compensator. With these efforts, stability analysis ensures that all the closed-loop system signals are uniformly bounded, and it is successfully achieved the asymptotic convergence of tracking error to zero, circumventing the obstacle caused by the unknown control directions. Experiment results illustrate the effectiveness of the proposed scheme.

Prescribed-time containment control of high-order nonlinear multi-agent systems based on distributed observer

This paper investigates the prescribed-time containment control problem for multi-agent systems with high-order nonlinear dynamics under a directed communication topology. Firstly, in view of the fact that only some follower agents can directly access the state information of multiple leader agents, a prescribed-time distributed observer is put forward to estimate the convex hull spanned by these leaders. Then, with the help of the distributed observer, a novel containment control method is developed for each follower based on a time-varying scaling function, so that all followers can converge to the convex hull spanned by the states of multiple leaders within a prescribed time. The comparison with the finite-time and fixed-time control methods differs in that the convergence time of the method proposed in this paper is independent of the initial conditions and control parameters and can be arbitrarily preassigned according to actual needs. Finally, an example is given to demonstrate the usefulness of the prescribed-time containment control method.

Fuzzy observer-based adaptive fixed-time leader-following control for high-order nonlinear multiagent systems

Most current research on fixed-time leader-following control of high-order nonlinear multiagent systems requires prior knowledge of the system dynamics or that each follower has state information about the leader. To release the above restriction, this article presents a fixed-time fuzzy observer for high-order multiagent systems with uncertain nonlinearities. Based on adaptive fuzzy control, we achieve consensus control of fixed-time pre-described accuracy for uncertain high-order nonlinear multiagent systems and overcome the difficulty of having information gaps between leaders and followers. According to the proposed observer and stability criterion, not only can the leader’s state be estimated in fixed time, but the consensus tracking error can also converge to the pre-described interval within a fixed time. The proposed control protocol guarantees the following properties:1.The proposed observer can estimate the leader’s state in a fixed time.2.Boundedness is satisfied for all closed-loop signals.3.Each follower can achieve fixed-time and predefined accuracy tracking for the leader.

Event-Based Output Feedback Consensus Control for Multiagent Systems With Unknown Non-Identical Control Directions

This article studies the event-triggered output feedback consensus problem for a class of high-order uncertain nonlinear multiagent systems with totally unknown non-identical control directions. Firstly, the reduced-order filters are constructed by utilizing the dynamic gain technique to compensate the system uncertainties and unmeasurable states of the followers. Based on the filter states and output information, the asymptotic output consensus result is guaranteed with the developed distributed adaptive output feedback control protocol, while the inherent issue “complexity explosion” in backstepping design is avoided. Then, to solve the interaction of multiple Nussbaum functions in a single inequality, the Nussbaum functions with different frequencies are adopted, with which the unknown directions of multiagent system are no longer limited in identical. In addition, we propose a dynamic triggering strategy with time-varying threshold parameters to reduce the updates of controller without Zeno phenomenon. Finally, simulation results are provided to illustrate the effectiveness of theoretical algorithm.

Finite-Time Adaptive Fuzzy Prescribed Performance Formation Control for High-Order Nonlinear Multiagent Systems Based on Event-Triggered Mechanism

This paper investigates the finite-time adaptive fuzzy prescribed performance formation control problem for high-order nonlinear multi-agent systems (MASs). Fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics. By combining the dynamic surface control (DSC) technique and backstepping recursive design, an adaptive fuzzy prescribed performance formation control algorithm is developed. To reduce unnecessary transmission of network resources, a novel event-triggered mechanism is proposed in the control method. Subsequently, based on the adding power integral method and finite-time stability theory, it is proved that all signals of the controlled system are bounded and the tracking errors do not exceed the prescribed performance bounds in a finite time. Simulation results are given to verify that the presented formation control scheme achieves desired results.