Distributed adaptive output feedback tracking control for a class of uncertain nonlinear multi-agent systems

This paper addresses the distributed output feedback tracking control problem for multi-agent systems with higher order nonlinear non-strict-feedback dynamics and directed communication graphs. The existing works usually design a distributed consensus controller using all the states of each agent, which are often immeasurable, especially in nonlinear systems. In this paper, based only on the relative output between itself and its neighbours, a distributed adaptive consensus control law is proposed for each agent using the backstepping technique and approximation technique of Fourier series (FS) to solve the output feedback tracking control problem of multi-agent systems. The FS structure is taken not only for tracking the unknown nonlinear dynamics but also the unknown derivatives of virtual controllers in the controller design procedure, which can therefore prevent virtual controllers from containing uncertain terms. The projection algorithm is applied to ensure that the estimated parameters remain in some known bounded sets. Lyapunov stability analysis shows that the proposed control law can guarantee that the output of each agent synchronises to the leader with bounded residual errors and that all the signals in the closed-loop system are uniformly ultimately bounded. Simulation results have verified the performance and feasibility of the proposed distributed adaptive control strategy.     

Containment control of linear multi‐agent systems with multiple leaders of bounded inputs using distributed continuous controllers

This paper considers the containment control problem for multi‐agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and time varying. Based on the relative states of neighboring agents, a distributed static continuous controller is designed, under which the containment error is uniformly ultimately bounded and the upper bound of the containment error can be made arbitrarily small, if the subgraph associated with the followers is undirected and, for each follower, there exists at least one leader that has a directed path to that follower. It is noted that the design of the static controller requires the knowledge of the eigenvalues of the Laplacian matrix and the upper bounds of the leaders’ control inputs. In order to remove these requirements, a distributed adaptive continuous controller is further proposed, which can be designed and implemented by each follower in a fully distributed fashion. Extensions to the case where only local output information is available and to the case of multi‐agent systems with matching uncertainties are also discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

Observer-based event-triggered distributed model predictive control for a class of nonlinear interconnected systems

In this paper, an observer-based event-triggered distributed model predictive control method is proposed for a class of nonlinear interconnected systems with bounded disturbances, considering unmeasurable states. First of all, the state observer is constructed. It is proved that the observation error is bounded. Second, distributed model predictive controller is designed by using observed value. Meanwhile, the event-triggered mechanism is set by using the error between the actual output and the predicted output. The setting of event-triggered mechanism not only ensures the error between the actual output and the predicted output within a certain range, but also reduces the calculation amounts of solving the optimization problem. The states of each subsystem enter the terminal invariant set by distributed model predictive control, and then are stabilized in the invariant set under the action of output feedback control law. In addition, sufficient conditions are given to ensure the feasibility of the algorithm and the stability of the closed-loop system. Finally, the numerical example is given, and the simulation results verify the effectiveness of the proposed algorithm.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Cooperative observers and regulators for discrete‐time multiagent systems

This paper investigates the design of distributed observers for agents with identical linear discrete‐time state‐space dynamics networked on a directed graph interaction topology. The digraph is assumed to have fixed topology and contain a spanning tree. Cooperative observer design guaranteeing convergence of the estimates of all agents to their actual states is proposed. The notion of convergence region for distributed observers on graphs is introduced. It is shown that the proposed cooperative observer design has a robustness property. Application of cooperative observers is made to the synchronization problem. A command trajectory generator and pinning control are employed for synchronizing all the agents to a desired trajectory. Complete knowledge about the agent's state is not assumed. A duality principle is shown for observers and state feedback for distributed discrete‐time systems on graph topologies. Three different observer/controller architectures are proposed for dynamic output feedback regulator design, and they are shown to guarantee convergence of the estimate to the true state and synchronization of all the agents' states to the command state trajectory. This provides design methods for cooperative regulators based on a separation principle. It is shown that the observer convergence region and feedback control synchronizing region for discrete‐time systems are inherently bounded, so that the conditions for observer convergence and state synchronization are stricter than the results for the continuous‐time counterparts. This is in part remedied by using weighting of different feedback coupling gains for every agent. Copyright © 2012 John Wiley & Sons, Ltd.     

Neuro-adaptive cooperative tracking control of unknown higher-order affine nonlinear systems

In this paper we propose a practical design method for distributed cooperative tracking control of a class of higher-order nonlinear multi-agent systems. Dynamics of the agents (also called the nodes) are assumed to be unknown to the controller and are estimated using Neural Networks. Linearization-based robust neuro-adaptive controller driving the follower nodes to track the trajectory of the leader node is proposed. The nodes are connected through a weighted directed graph with a time-invariant topology. In addition to the fact that only few nodes have access to the leader, communication among the follower nodes is limited with some nodes having access to the information of their neighbor nodes only. Command generated by the leader node is ultimately followed by the followers with bounded synchronization error. The proposed controller is well-defined in the sense that control effort is restrained to practical limits. The closed-loop system dynamics are proved to be stable and simulation results demonstrate the effectiveness of the proposed control scheme.     

Robust finite-time consensus tracking for second-order multi-agent systems with input saturation under general directed communication graphs

In this paper, we study the global finite-time consensus tracking problem for uncertain second-order multi-agent systems subject to input saturation. The communication graphs are allowed to be general directed graphs. Sliding-mode observer-based distributed controllers are proposed such that global finite-time consensus tracking is achieved with bounded control inputs. Only relative state or output measurements are used in the proposed controller which reduces the communication requirement on the agents. Simulation examples are given to illustrate the effectiveness of the proposed control strategies.     

Neuro-adaptive cooperative tracking control with prescribed performance of unknown higher-order nonlinear multi-agent systems

This paper is concerned with the design of a distributed cooperative synchronisation controller for a class of higher-order nonlinear multi-agent systems. The objective is to achieve synchronisation and satisfy a predefined time-based performance. Dynamics of the agents (also called the nodes) are assumed to be unknown to the controller and are estimated using neural networks. The proposed robust neuro-adaptive controller drives different states of nodes systematically to synchronise with the state of the leader node within the constraints of the prescribed performance. The nodes are connected through a weighted directed graph with a time-invariant topology. Only few nodes have access to the leader. Lyapunov-based stability proofs demonstrate that the multi-agent system is uniformly ultimately bounded stable. Highly nonlinear heterogeneous networked systems with uncertain parameters and external disturbances were used to validate the robustness and performance of the new novel approach. Simulation results considered two different examples: single-input single-output and multi-input multi-output, which demonstrate the effectiveness of the proposed controller.     

Distributed cooperative stabilisation of continuous-time uncertain nonlinear multi-agent systems

This paper addresses the distributed cooperative stabilisation problem of continuous-time uncertain nonlinear multi-agent systems. By approximating the uncertain dynamics using neural networks, a distributed adaptive cooperative controller, based on the state information of the neighbouring agents, is proposed. The control design is developed for any undirected connected communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case. An observer-based distributed cooperative controller is devised and a parameter dependent Riccati inequality is employed to prove stability of the overall multi-agent systems. This design is less complex than the other design methods and has a favourable decouple property between the observer design and the controller design for uncertain nonlinear multi-agent systems. For both cases, the developed controllers guarantee that all signals in the closed-loop network are uniformly ultimately bounded, and the states of all agents cooperatively converge to a small neighbourhood of origin. A comparative study is given to show the efficacy of the proposed method.     

Fixed-time coordinated tracking for second-order multi-agent systems with bounded input uncertainties

In this paper, we study the fixed-time coordinated tracking problem for second-order integrator systems with bounded input uncertainties. Two novel distributed controllers are proposed with which the convergence time of the tracking errors is globally bounded for any initial condition of the agents. When relative state measurements are available for each follower, an observer-based distributed control strategy is proposed which achieves fixed-time coordinated tracking for the perturbed second-order multi-agent systems. When only relative output measurements are available, uniform robust exact differentiators are employed together with the observer-based controller which is able to achieve fixed-time coordinated tracking with reduced measurements. Simulation examples are provided to demonstrate the performance of the proposed controllers.     

Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs

In this paper, we investigate the cooperative control of networked agents with unknown high-frequency-gain signs. A Nussbaum-type adaptive controller is designed for each agent such that consensus of the network can be achieved while all signals in the overall system maintain bounded. The distributed controller for each agent has two parts: neighborhood error between itself and the neighbors and a Nussbaum-type item for seeking control direction adaptively. The argument of the Nussbaum-type function is tuned on line via an appropriately designed update law. It is proved that when the undirected graph is connected or the balanced digraph is weakly connected, consensus of the network can be realized. Furthermore, a distributed asymptotic regulator is proposed to regulate the overall system to the equilibrium. Simulation results are presented to verify the effectiveness of the proposed controllers.     

Robust finite-time containment control for high-order multi-agent systems with matched uncertainties under directed communication graphs

In this paper, we study the robust finite-time containment control problem for a class of high-order uncertain nonlinear multi-agent systems modelled as high-order integrator systems with bounded matched uncertainties. When relative state information between neighbouring agents is available, an observer-based distributed controller is proposed for each follower using the sliding mode control technique which solves the finite-time containment control problem under general directed communication graphs. When only relative output information is available, robust exact differentiators and high-order sliding-mode controllers are employed together with the distributed finite-time observers. It is shown that robust finite-time containment control can still be achieved in this situation. An application in the coordination of multiple non-holonomic mobile robots is used as an example to illustrate the effectiveness of the proposed control strategies.     

Fully distributed adaptive sliding-mode controller design for containment control of multiple Lagrangian systems

In this paper, we study the containment control problem for multiple Lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties and external disturbances with fully distributed controllers under an undirected graph. We first propose a fully distributed adaptive sliding-mode control algorithm combined with distributed sliding-mode estimators, without requiring the upper bounds of the derivatives of the leaders’ states and any other global information to be known by each follower. To reduce the effect on the varying gain during the adaption mainly caused by the initial error, fully distributed adaptive time-varying sliding-mode control is presented for controller design. To tackle the chattering effect caused by the discontinuous controller, we further propose a fully distributed continuous adaptive controller, under which both the containment errors and the adaptive gains are ultimately bounded. Simulation results are given to illustrate the theoretical results.     

A new finite-time cooperative control algorithm for uncertain multi-agent systems

In this paper, the problem of fixed-time consensus tracking control is investigated for multi-agent networks with input uncertain dynamics under the undirected graph. First, a nonsingular terminal sliding mode manifold is proposed, with which the convergence time is globally bounded irrelevant to initial states. Then, with the aid of the observer method and sliding mode technique, the distributed nonsingular controller is designed for the underlying system to ensure that the consensus tracking errors go into sliding mode manifold and converge to origin within a desired time. Finally, examples are presented to verify the validity of the new control strategy.     

Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions

In this paper, the authors investigate a decentralized adaptive output-feedback controller design for large-scale nonlinear systems with input saturations and time-delayed interconnections unmatched in control inputs. The interaction terms with unknown time-varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems. This point is a main contribution of this paper compared with previous output-feedback control approaches which assume that the time-delayed bounding functions only depend on measurable output variables. The bounding functions are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique based on neural networks. The observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem. In addition, we prove that all signals in the closed-loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Consensus controller for multi-UAV navigation

In this paper, we design consensus algorithms for multiple unmanned aerial vehicles (UAV). We mainly focus on the control design in the face of measurement noise and propose a position consensus controller based on the sliding mode control by using the distributed UAV information. Within the framework of Lyapunov theory, it is shown that all signals in the closed-loop multi-UAV systems are stabilized by the proposed algorithm, while consensus errors are uniformly ultimately bounded. Moreover, for each local UAV, we propose a mechanism to define the trustworthiness, based on which the edge weights are tuned to eliminate negative influence from stubborn agents or agents exposed to extremely noisy measurement. Finally, we develop software for a nano UAV platform, based on which we implement our algorithms to address measurement noises in UAV flight tests. The experimental results validate the effectiveness of the proposed algorithms.     

Adaptive output feedback control of feedforward nonlinear distributed delay systems with unknown delay kernel

This paper considers the problem of global adaptive output feedback regulation for a class of uncertain feedforward nonlinear distributed delay systems. Compared with the existing results, we reduce the conservatism of the restrictive conditions by combining the dynamic scaling technique and the backstepping method, in particular, uncertain control coefficients and unknown delay kernels are admitted. With the help of the Lyapunov–Krasovskii theorem, a delay-independent output feedback controller is proposed by constructing an input-driven observer with a novel dynamic gain, which guarantees that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states globally asymptotically to converge to zero as time goes to infinity. Finally, a numerical example is given to illustrate the usefulness of our results.     

Observer‐based cooperative distributed fault‐tolerant model predictive control with imperfect network communication and asynchronous measurements

Intermittent actuator and sensor faults tolerant are simultaneously considered in a distributed control system with imperfect communication network. The asynchronous measurements of different output variables in one sampling period are synchronized through a novel two‐stage model‐based projection method. Different from centralized control network, in both layer‐to‐layer and in‐layer communication, the packet delay, loss and disordering are corrected by the predicted data from model predictive control. Moreover, a completely distributed state observer is established for both system states and sensor faults problem with bounded noise uncertainties. For the intermittent actuator faults, actuator plug‐and‐play design methods based on model predictive control has been introduced, making the actuator faults estimation omitted. The distributed stability conditions are derived for the proposed fault‐tolerant controller, and the online feasibility is explained in detail. Numerical simulation is given to verify the design procedure.     

Observer-based Finite-time Control of Stochastic Non-strict-feedback Nonlinear Systems

This paper investigates the observer-based adaptive finite-time neural control issue of stochastic non-strict-feedback nonlinear systems. By establishing a state observer and utilizing the approximation property of the neural network, an adaptive neural network output-feedback controller is constructed. The controller solves the issue that the states of stochastic nonlinear system cannot be measured, and assures that all signals in the closed-loop system are bounded. Different from the existing adaptive control researches of stochastic nonlinear systems with unmeasured states, the proposed control scheme can guarantee the finite-time stability of the stochastic nonlinear systems. Furthermore, the effectiveness of the proposed control approach is verified by the simulation results.

     

Robust containment control in a leader–follower network of uncertain Euler–Lagrange systems

A distributed controller is developed that yields cooperative containment control of a network of autonomous dynamical systems. The networked agents are modeled with uncertain nonlinear Euler–Lagrange dynamics affected by an unknown time‐varying exogenous disturbance. The developed continuous controller is robust to input disturbances and uncertain dynamics such that asymptotic convergence of the follower agents' states to the dynamic convex hull formed by the leaders' time‐varying states is achieved. Simulation results are provided to demonstrate the effectiveness of the developed controller. Copyright © 2016 John Wiley & Sons, Ltd.