Distributed Model Reference Adaptive Control Research Articles

Leader‐following consensus of a class of heterogeneous uncertain multi‐agent systems with a distributed model reference adaptive control law

SummaryThis paper considers the leader‐following consensus problem of a multi‐agent system whose agents have heterogeneous uncertain dynamics in homogeneous state dimensions. Each agent utilizes a distributed model reference adaptive control (MRAC) law to deal with uncertainties. The nominal part of the MRAC is a distributed static state feedback control law. The reference model is the leader‐following consensus problem of reference agents with homogeneous linear time‐invariant dynamics. This problem becomes an N‐player graphical differential game under a given cost function. The reference agents utilize distributed static state feedback controllers that constitute a Nash equilibrium solution to the graphical differential game. This paper provides the conditions for the distributed MRAC to guarantee that each agent asymptotically tracks the corresponding reference agent; consequently, the multi‐agent system solves the leader‐following consensus problem as the reference model does. These conditions yield a straightforward design method for the MRAC. A numerical example demonstrates an application of the proposed approach to a multi‐robot system with nonlinear dynamics.

Distributed Model Reference Adaptive Control Based on Cooperative Observer with Optimal Control Modification for Synchronization of Heterogeneous Vehicle Platoon

Many distributed controllers for vehicle platoon are designed based on homogeneous assumption and full state information. In reality, vehicle platoon may consist of heterogeneous vehicles and may have limited information due to sensor constraints. Therefore, this paper proposes a distributed model reference adaptive control based on cooperative observer for a heterogeneous vehicle platoon with limited output information and subjected to uncertain dynamics. Cooperative observer provides a full state estimation of the system. Each follower has a reference model that is designed based on its nominal model and cooperative state variable feedback. Main control system is composed of (i) nominal control that utilized the cooperative state estimation tracking error and (ii) adaptive term that adopted an optimal control modification as an adaptation law. The tracking error of followers to the reference model is shown uniformly bounded and the stability of the platoon is guaranteed through detailed analysis. Performance of the proposed controller is verified by using numerical simulation. To show the advantage of the proposed control, simulation results are compared to the standard distributed model reference adaptive control that is applied for heterogeneous vehicle platoon. It is shown that the proposed control eliminated the high frequency oscillation in the control input.

Adaptive Control of Second-Order Safety-Critical Multiagent Systems With Nonlinear Dynamics

In this article, we propose a distributed adaptive control architecture for leader-following consensus of uncertain multiagent systems with second-order nonlinear dynamics. A nonlinear reference model system captures an ideal behavior of the agents for the leader-following consensus problem. We design a modified nonlinear reference model system and propose a distributed model reference adaptive control architecture to suppress the effects of system uncertainties without a strict knowledge of their magnitude and rate upper bounds. Consequently, each agent evolves within a (possibly different) prescribed distance from the corresponding modified reference system trajectories. Based on an input-to-state stability analysis, it is shown that the trajectories of the modified reference model system can get arbitrarily close to the trajectories of the ideal reference model system. As a result, the trajectories of the agents evolve within a user-specified prescribed distance from their ideal system trajectories, satisfying the safety constraints. The key feature of the presented control architecture in this article is the elimination of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ad hoc</i> tuning process for the adaptation rate that is conventionally required in model reference adaptive control systems to ensure safety. An illustrative numerical example finally demonstrates the efficacy of the proposed distributed adaptive control architecture.

Closed-Loop Reference Model Based Distributed MRAC Using Cooperative Initial Excitation and Distributed Reference Input Estimation

This article proposes a novel closed-loop reference model (CRM) architecture for a distributed model reference adaptive control (DMRAC) algorithm, called CRM-DMRAC. The idea of CRM has been recently conceptualized in the literature for a single agent system where the reference model (leader) receives feedback from the plant (follower) while enabling the use of high gain tuners without adding more transients in the parameter estimation. In this article, a CRM formulation is proposed where the leader receives feedback from a subset of follower agents (which are called neighbors of the leader). The external input to the leader is not shared with any of the followers unlike traditional MRAC algorithms. A novel external input estimator is proposed inspired from dynamic surface control in a hierarchical and cooperative manner. Further, the adaptation scheme is based on a newly defined excitation condition, called cooperative initial excitation (C-IE). The C-IE condition is significantly relaxed as compared to cooperative persistence of excitation, which is required for parameter convergence in traditional distributed adaptive controllers. The closed-loop system using the proposed adaptive controller has proven to be globally uniformly ultimately bounded. As a special case, it is shown that the closed-loop error dynamics will be exponentially converging to zero if the external input is available to all the followers. Numerical simulations validate the proof of concept, which illustrates the superiority in terms of transients response, estimation performance, and control effort for the proposed method over conventional open-loop reference model DMRAC and CRM-DMRAC without C-IE.

Observer-Based Adaptive Synchronization Control of Unknown Discrete-Time Nonlinear Heterogeneous Systems.

This article is concerned with the optimal synchronization problem for discrete-time nonlinear heterogeneous multiagent systems (MASs) with an active leader. To overcome the difficulty in the derivation of the optimal control protocols for these systems, we develop an observer-based adaptive synchronization control approach, including the designs of a distributed observer and a distributed model reference adaptive controller with no prior knowledge of all agents' dynamics. To begin with, for the purpose of estimating the state of a nonlinear active leader for each follower, an adaptive neural network distributed observer is designed. Such an observer serves as a reference model in the distributed model reference adaptive control (MRAC). Then, a reinforcement learning-based distributed MRAC algorithm is presented to make every follower track its corresponding reference model on behavior in real time. In this algorithm, a distributed actor-critic network is employed to approximate the optimal distributed control protocols and the cost function. Through convergence analysis, the overall observer estimation error, the model reference tracking error, and the weight estimation errors are proved to be uniformly ultimately bounded. The developed approach further achieves the synchronization by means of synthesizing these results. The effectiveness of the developed approach is verified through a numerical example.

Distributed Model Reference Adaptive Control for Vehicle Platoons with Uncertain Dynamics

Distributed Model Reference Adaptive Control for Vehicle Platoons with Uncertain Dynamics

Distributed robust adaptive output-feedback synchronization

This paper addresses the output synchronization of heterogeneous uncertain linear systems in the presence of input disturbance. The synchronization problem is solved by introducing the distributed model reference adaptive control. The distinguishing features of the proposed approach are the capability to synchronize the entire network output by using only the control input and the output of neighbouring systems. It also provides synchronization in the presence of bounded control input disturbance. The control input disturbance is handled by extending the proposed method with the sigma-modification. By using the distributed matching condition assumptions, the coupling gains between the agents can be updated adaptively. The distributed robust adaptive controller is first analysed by using the distributed Lyapunov function. Its effectiveness is validated in the simulation of the cart inverted pendulum systems stabilization problem.

A minimal sensing and communication control strategy for adaptive platooning

SummarySeveral cooperative driving strategies proposed in literature, sometimes known as cooperative adaptive cruise control strategies, assume that both relative spacing and relative velocity with preceding vehicle are available from on‐board sensors (laser or radar). Alternatively, these strategies assume communication of both velocity states and acceleration inputs from preceding vehicle. However, in practice, on‐board sensors can only measure relative spacing with preceding vehicle (since getting relative velocity requires additional filtering algorithms); also, reducing the number of variables communicated from preceding vehicle is crucial to save bandwidth. In this work we show that, after framing the cooperative driving task as a distributed model reference adaptive control problem, the platooning task can be achieved in a minimal sensing and communication scenario, that is, by removing relative velocity measurements with preceding vehicle and by removing communication from preceding vehicle of velocity states. In the framework we propose, vehicle parametric uncertainty is taken into account by appropriately designed adaptive laws. The proposed framework is illustrated and shown to be flexible to several standard architectures used in cooperative driving (one‐vehicle look‐ahead topology, leader‐to‐all topology, multivehicle look‐ahead topology).

Closed-Loop Reference Model Based Distributed Model Reference Adaptive Control for Multi-Agent Systems

This letter confluences ideas from distributed model reference adaptive control (MRAC) architecture for multi-agent systems and closed-loop reference model (CRM) based MRAC algorithm. The concept of CRM is recently proposed in literature for single-agent MRAC problems, where the reference model (leader) gets feedback from the plant (agent/follower) to facilitate improved transient performance. This letter coins the concept of CRM based distributed MRAC, where it is assumed that the leader/reference model is connected only to a subset of followers and incorporates feedback from them in a multi-agent setting. Distributed parameter estimator and controller are designed, which incorporate inter-agent cooperation via communication over a bi-directional graph. The leader state and the time-varying leader input (also known as reference input in MRAC literature) are only accessible to its neighbours. A novel distributed dynamic surface control (DSC)-like strategy is invoked for each follower to cooperatively estimate the unknown reference input required for control design. Simulation results dictate that the proposed closed-loop leader based formulation leads to better transient performance as compared to the status quo and also enables the use of high gain tuners for adaptive update law. As far as the authors are aware, this is the first work which introduces a distributed protocol of CRM-MRAC for multi-agent systems (CRM-DMRAC) with rigorous Lyapunov analysis.

Event-Triggered Robust Control for Output Consensus of Unknown Discrete-Time Multiagent Systems With Unmodeled Dynamics.

This article investigates the event-triggered output consensus problem for a class of unknown heterogeneous discrete-time linear multiagent systems in the presence of unmodeled dynamics. The agents have individual nominal dynamics with unknown parameters, and the unmodeled dynamics are in the form of multiplicative perturbations. A novel design framework is developed based on an event-triggered internal reference model and a distributed model reference adaptive controller. To deal with the heterogeneity of the multiagent system, the event-triggered internal reference model is designed to generate a virtual reference signal for each agent with a dynamic event-triggering mechanism being adopted to reduce the communication burden between neighboring agents. To handle the unknown parameters and unmodeled dynamics, the robust model reference adaptive controller is then designed to follow the generated virtual reference signal. It is shown that if the unmodeled dynamics satisfy certain conditions, then the boundedness of all the signals and variables in the closed-loop system and convergence of consensus errors to a residual set are guaranteed. Moreover, the consensus errors will converge to zero asymptotically in the absence of unmodeled dynamics. Compared with existing related works, the proposed framework is able to deal with the agents with individual unknown nominal dynamics and unmodeled dynamics. Moreover, the proposed framework is fully distributed in the sense that no knowledge of any global information is needed. Finally, the performance of the proposed method is validated by examples.

Distributed Model Reference Adaptive Optimization of Disturbed Multiagent Systems With Intermittent Communications.

This article pays close attention to a distributed optimization problem for multiagent systems subject to exogenous disturbances. A novel distributed model reference adaptive control (D-MRAC) scheme is proposed that no explicit disturbance observer or internal model unit is involved, which not only enhances robustness but also improves transient performance. In contrast to the continuous communication that is often assumed in the existing distributed optimization works, the new method allows for more realistic scenarios in which the agents communicate with each other at discrete-time instants. It is shown by Lyapunov analysis that the concerned distributed optimization problem can be solved by the proposed D-MRAC scheme as long as the communication interval is smaller than a given threshold, which can be calculated by following the steps given in this article. Numerical simulations have shown the effectiveness of the presented method.

Leader–Follower Synchronization of Uncertain Euler–Lagrange Dynamics with Input Constraints

This paper addresses the problem of leader–follower synchronization of uncertain Euler–Lagrange systems under input constraints. The problem is solved in a distributed model reference adaptive control framework that includes positive μ-modification to address input constraints. The proposed design has the distinguishing features of updating the gains to synchronize the uncertain systems and of providing stable adaptation in the presence of input saturation. By using a matching condition assumption, a distributed inverse dynamics architecture is adopted to guarantee convergence to common dynamics. The design is studied analytically, and its performance is validated in simulation using spacecraft dynamics.

Adaptive hierarchical formation control for uncertain Euler–Lagrange systems using distributed inverse dynamics

This paper establishes a novel adaptive hierarchical formation control method for uncertain heterogeneous nonlinear agents described by Euler–Lagrange (EL) dynamics. Formation control is framed as a synchronization problem where a distributed model reference adaptive control is used to synchronize the EL systems. The idea behind the proposed adaptive formation algorithm is that each agent must converge to the model defined by its hierarchically superior neighbors. Using a distributed inverse dynamics structure, we prove that distributed nonlinear matching conditions between connected agents hold, so that matching gains exist to make the entire formation converge to same homogeneous dynamics: to compensate for the presence of uncertainties, estimation laws are devised for such matching gains, leading to adaptive synchronization. An appropriately designed distributed Lyapunov function is used to derive asymptotic convergence of the synchronization error. The effectiveness of the proposed methodology is supported by simulations of a formation of Unmanned Aerial Vehicles (UAVs).

Distributed model reference adaptive containment control of heterogeneous uncertain multi-agent systems

In this paper, a distributed model reference adaptive control (MRAC) design framework is proposed for containment control of heterogeneous uncertain multi-agent systems (MAS). Both groups of leaders and followers are considered to have general linear dynamics with the leaders subject to bounded external inputs and the followers subject to uncertain system dynamics. Two distributed adaptive control protocols are developed under this framework. The first protocol assumes measurable leaders’ input signals for a subset of the followers, and employs distributed observers with state-feedback adaptive controllers to achieve exact containment control performance. The second protocol incorporates robust adaptive control with nonlinear compensator techniques to handle a more challenging scenario of unmeasurable bounded leaders’ inputs. Convergence of the containment control errors to an arbitrarily adjustable neighborhood of the origin is guaranteed with the second protocol. The proposed MRAC framework provides a promising alternative solution over the prevailing cooperative output regulation framework for heterogeneous linear MAS containment control. It enables us to handle more general system settings under more stringent control environments with limited accessibility of leaders’ information and uncertain follower dynamics. Effectiveness and usefulness of the proposed approaches are demonstrated through extensive simulation studies, including an application to containment control of multiple nonholonomic mobile robots.

Adaptive state-feedback synchronization with distributed input: the cyclic case

Abstract Using a setting in which the input is communicated among neighbors (without exchanging any distributed observer variables), the problem of synchronizing an acyclic network of linear uncertain agents has been formulated recently as a distributed model reference adaptive control (MRAC) where each agent tries to converge to the model defined by its neighbors. In this work we show how to parametrize the distributed MRAC in cyclic and undirected graphs.

Distributed model reference adaptive control for cooperative tracking of uncertain dynamical multi‐agent systems

In this study, a distributed model reference adaptive control architecture is developed to achieve the cooperative tracking of uncertain dynamical multi-agent systems, where the reference model serves as a virtual leader for the group to track. Two adaptive laws, with one adjusting the coupling weights and the other adjusting the neural network weights, are designed based on the relative state information of neighbouring agents. The proposed controller guarantees that the state of each agent synchronizes to that of the reference model over any undirected connected communication graphs, and all signals in the closed-loop network are uniformly ultimately bounded. In contrast to the existing results, the developed controller can be implemented in a fully distributed manner by each agent without using any global information and the accurate model of each agent. An extension to asymptotic stability is further studied.