Adaptive Consensus of Nonlinear Multi-Agent Systems With Non-Identical Partially Unknown Control Directions and Bounded Modelling Errors
TL;DR: This note proposes an adaptive method to relax such a requirement to allow non-identical control directions, under the condition that some control directions are known.
Abstract: Existing Nussbaum function based results on consensus of multi-agent systems require that the unknown control directions of all the agents should be the same. This note proposes an adaptive method to relax such a requirement to allow non-identical control directions, under the condition that some control directions are known. Technically, a novel idea is proposed to construct a new Nussbaum function, from which a conditional inequality is developed to handle time-varying input gains. Then, the inequality is integrated with adaptive control technique such that the proposed Nussbaum function for each agent is adaptively updated. Moreover, in addition to parametric uncertainties, each agent has non-parametric bounded modelling errors which may include external disturbances and approximation errors of static input nonlinearities. Even in the presence of such uncertainties, the proposed control scheme is still able to ensure the states of all the agents asymptotically reach perfect consensus. Finally, simulation study is performed to show the effectiveness of the proposed approach.
Citations
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TL;DR: A decentralized adaptive formation controller is designed that ensures uniformly ultimate boundedness of the closed-loop system with prescribed performance and avoids collision between each vehicle and its leader.
Abstract: This paper addresses a decentralized leader–follower formation control problem for a group of fully actuated unmanned surface vehicles with prescribed performance and collision avoidance. The vehicles are subject to time-varying external disturbances, and the vehicle dynamics include both parametric uncertainties and uncertain nonlinear functions. The control objective is to make each vehicle follow its reference trajectory and avoid collision between each vehicle and its leader. We consider prescribed performance constraints, including transient and steady-state performance constraints, on formation tracking errors. In the kinematic design, we introduce the dynamic surface control technique to avoid the use of vehicle's acceleration. To compensate for the uncertainties and disturbances, we apply an adaptive control technique to estimate the uncertain parameters including the upper bounds of the disturbances and present neural network approximators to estimate uncertain nonlinear dynamics. Consequently, we design a decentralized adaptive formation controller that ensures uniformly ultimate boundedness of the closed-loop system with prescribed performance and avoids collision between each vehicle and its leader. Simulation results illustrate the effectiveness of the decentralized formation controller.
273 citations
Cites methods from "Adaptive Consensus of Nonlinear Mul..."
...Based on the dynamic surface control (DSC) technique [27]–[29], the PPC methodology [21], adaptive control techniques [30]–[32], neural network (NN) approximators [33]– [37], the backstepping procedure, and the Lyapunov synthesis, we propose decentralized leader–follower formation control that guarantees the satisfaction of the prescribed performance constraints on formation tracking errors and the nonviolation of the collision avoidance constraint between the follower and its leader despite the presence of modeling uncertainties and external disturbances....
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TL;DR: In this paper, an adaptive neural tracking control of underactuated surface vessels with modeling uncertainties and time-varying external disturbances is presented, where the tracking errors consisting of position and orientation errors are required to keep inside their predefined feasible regions in which the controller singularity problem does not happen.
Abstract: This paper presents adaptive neural tracking control of underactuated surface vessels with modeling uncertainties and time-varying external disturbances, where the tracking errors consisting of position and orientation errors are required to keep inside their predefined feasible regions in which the controller singularity problem does not happen. To provide the preselected specifications on the transient and steady-state performances of the tracking errors, the boundary functions of the predefined regions are taken as exponentially decaying functions of time. The unknown external disturbances are estimated by disturbance observers and then are compensated in the feedforward control loop to improve the robustness against the disturbances. Based on the dynamic surface control technique, backstepping procedure, logarithmic barrier functions, and control Lyapunov synthesis, singularity-free controllers are presented to guarantee the satisfaction of predefined performance requirements. In addition to the nominal case when the accurate model of a marine vessel is known a priori , the modeling uncertainties in the form of unknown nonlinear functions are also discussed. Adaptive neural control with the compensations of modeling uncertainties and external disturbances is developed to achieve the boundedness of the signals in the closed-loop system with guaranteed transient and steady-state tracking performances. Simulation results show the performance of the vessel control systems.
199 citations
Cites background from "Adaptive Consensus of Nonlinear Mul..."
...The external disturbances could severely influence the control system performance [12]....
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TL;DR: With the proposed two-layer distributed hierarchical controller, the leader-following output consensus is achieved and the obtained result is further extended to the formation control problem.
Abstract: In this paper, the leader-following output consensus problem for a class of uncertain nonlinear multiagent systems with unknown control directions is investigated. Each agent system has nonidentical dynamics and is subject to external disturbances and uncertain parameters. The agents are connected through a directed and jointly connected switching network. A novel two-layer distributed hierarchical control scheme is proposed. In the upper layer, to save the communication resources and to handle the switching networks, an event-triggered communication scheme is proposed, and a Zeno-free event-triggered mechanism is designed for each agent to generate the asynchronous triggering time instants. Furthermore, to avoid the continuous monitoring of the system states, a Zeno-free self-triggering algorithm is proposed. In the lower layer, to handle the unknown control directions problem and to achieve the output tracking of the local references generated in the upper layer, the Nussbaum-type function-based technique is combined with internal model principle. With the proposed two-layer distributed hierarchical controller, the leader-following output consensus is achieved. The obtained result is further extended to the formation control problem. Finally, three numerical examples are provided to demonstrate the effectiveness of the proposed theoretical results.
161 citations
Cites background from "Adaptive Consensus of Nonlinear Mul..."
...tion than the conditions in [21], [22], [32], and [33]....
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...have also been extended to the case of nonidentical control directions in [32] and [33]....
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TL;DR: An adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated is proposed.
Abstract: The guaranteed-performance consensualization for high-order linear and nonlinear multiagent systems with switching topologies is respectively realized in a completely distributed manner in the sense that consensus design criteria are independent of interaction topologies and switching motions. This paper first proposes an adaptive consensus protocol with guaranteed-performance constraints and switching topologies, where interaction weights among neighboring agents are adaptively adjusted and state errors among all agents can be regulated. Then, a new translation-adaptive strategy is shown to realize completely distributed guaranteed-performance consensus control and an adaptive guaranteed-performance consensualization criterion is given on the basis of the Riccati inequality. Furthermore, an approach to regulate the consensus control gain and the guaranteed-performance cost is proposed in terms of linear matrix inequalities. Moreover, main conclusions for linear multiagent systems are extended to Lipschitz nonlinear cases. Finally, two numerical examples are provided to demonstrate theoretical results.
100 citations
TL;DR: An adaptive neural network (NN)-based tracking control algorithm is proposed for the wheeled mobile robotic (WMR) system with full state constraints and can guarantee the uniform ultimate boundedness for all signals in the WMR system, and the tracking error converge to a bounded compact set to zero.
Abstract: In this paper, an adaptive neural network (NN)-based tracking control algorithm is proposed for the wheeled mobile robotic (WMR) system with full state constraints. It is the first time to design an adaptive NN-based control algorithm for the dynamic WMR system with full state constraints. The constraints come from the limitations of the wheels’ forward speed and steering angular velocity, which depends on the motors’ driving performance. By employing adaptive NNs and a barrier Lyapunov function with error variables, then, the unknown functions in the systems are estimated, and the constraints are not violated. Based on the assumptions and lemmas given in this paper and the references, while the design and the system parameters chose properly, our proposed scheme can guarantee the uniform ultimate boundedness for all signals in the WMR system, and the tracking error converge to a bounded compact set to zero. The numerical experiment of a WMR system is presented to illustrate the good performance of the proposed control algorithm.
100 citations
Cites background from "Adaptive Consensus of Nonlinear Mul..."
...The NNs can approximate different types of nonlinear equations with arbitrary precision under certain conditions [23]–[28], and have been widely used in control algorithm for the uncertain nonlinear systems [29]–[35]....
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References
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TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Abstract: In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
8,233 citations
TL;DR: Numerical evidence is presented that this model results in a kinetic phase transition from no transport to finite net transport through spontaneous symmetry breaking of the rotational symmetry.
Abstract: A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $(\ensuremath{\eta})$ added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $|{\mathbf{v}}_{a}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since $|{\mathbf{v}}_{a}|$ is found to scale as $({\ensuremath{\eta}}_{c}\ensuremath{-}\ensuremath{\eta}{)}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}\ensuremath{\simeq}0.45$.
6,514 citations
TL;DR: A Nyquist criterion is proved that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability, and a method for decentralized information exchange between vehicles is proposed.
Abstract: We consider the problem of cooperation among a collection of vehicles performing a shared task using intervehicle communication to coordinate their actions. Tools from algebraic graph theory prove useful in modeling the communication network and relating its topology to formation stability. We prove a Nyquist criterion that uses the eigenvalues of the graph Laplacian matrix to determine the effect of the communication topology on formation stability. We also propose a method for decentralized information exchange between vehicles. This approach realizes a dynamical system that supplies each vehicle with a common reference to be used for cooperative motion. We prove a separation principle that decomposes formation stability into two components: Stability of this is achieved information flow for the given graph and stability of an individual vehicle for the given controller. The information flow can thus be rendered highly robust to changes in the graph, enabling tight formation control despite limitations in intervehicle communication capability.
4,377 citations
"Adaptive Consensus of Nonlinear Mul..." refers background in this paper
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TL;DR: A model for asynchronous distributed computation is presented and it is shown that natural asynchronous distributed versions of a large class of deterministic and stochastic gradient-like algorithms retain the desirable convergence properties of their centralized counterparts.
Abstract: We present a model for asynchronous distributed computation and then proceed to analyze the convergence of natural asynchronous distributed versions of a large class of deterministic and stochastic gradient-like algorithms. We show that such algorithms retain the desirable convergence properties of their centralized counterparts, provided that the time between consecutive interprocessor communications and the communication delays are not too large.
1,761 citations
06 Jun 1984
TL;DR: A model for asynchronous distributed computation is presented and it is shown that natural asynchronous distributed versions of a large class of deterministic and stochastic gradient-like algorithms retain the desirable convergence properties of their centralized counterparts.
Abstract: We present a model for asynchronous distributed computation and then proceed to analyze the convergence of natural asynchronous distributed versions of a large class of deterministic and stochastic gradient-like algorithms. We show that such algorithms retain the desirable convergence properties of their centralized counterparts, provided that the time between consecutive communications between processors plus communication delays are not too large.
1,278 citations
"Adaptive Consensus of Nonlinear Mul..." refers background in this paper
...Last decades have witnessed substantial development of multi-agent systems [1]–[4] with a great variety of promising progresses in...
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