Adaptive Distributed Observer Research Articles

Resilient Neuroadaptive Distributed Fixed-Time Attitude Coordination Control for Multiple Spacecraft.

This work studies the attitude coordination tracking problem for multiple spacecraft with consideration of unintended faults (communication link faults and actuator faults), inertial uncertainties, and external disturbances under a directed communication graph. A resilient neuroadaptive distributed fixed-time control scheme is investigated to solve this challenging problem. First, an improved adaptive distributed observer is established for followers to estimate the states of the leader when considering communication link faults. The proposed observer improves the resilience against communication link faults. Subsequently, to further cope with the problem of actuator faults, inertial uncertainties, and external disturbances, based on the proposed observer and the technique of adding a power integrator, a neuroadaptive distributed fixed-time attitude coordination controller is developed. Unlike the existing controllers, the proposed one requires less information when dealing with faults and lumped uncertainties, and has a lower-computational cost. Moreover, the fixed-time stability of the closed-loop system is ensured under the designed resilient neuroadaptive distributed control scheme. Finally, comparative simulations are carried out to manifest the effectiveness of the investigated coordination control method.

Fixed-time cooperative output regulation for second-order nonlinear multiagent systems with an unknown exosystem

This paper investigates the fixed-time cooperative output regulation (FTCOR) problem with unknown exosystem of second-order nonlinear multiagent systems. To solve this problem, it is necessary to ensure that each agent can obtain the reference trajectory originating from an unknown exosystem and reconstruct the solution of the regulator equation containing the exogenous signal and unknown parameter vectors within a fixed time, and the unknown exosystem makes it difficult to solve these two problems with existing tools. By using auxiliary filtering variables, we propose a fixed-time adaptive distributed observer (FTADO) and design a fixed-time distributed internal model (FTDIM) based on this FTADO. These two new tools ensure the solvability of the two problems just mentioned. Then, based on these two tools, we transform the problem into a fixed-time stabilization problem of a so-called augmented system. Through the backstepping technique, we propose a distributed controller that solves this fixed-time stabilization problem while relaxing the assumptions of similar references.

Optimal Tracking Control of Heterogeneous MASs Using Event-Driven Adaptive Observer and Reinforcement Learning.

This article considers the output tracking control problem of nonidentical linear multiagent systems (MASs) using a model-free reinforcement learning (RL) algorithm, where partial followers have no prior knowledge of the leader's information. To lower the communication and computing burden among agents, an event-driven adaptive distributed observer is proposed to predict the leader's system matrix and state, which consists of the estimated value of relative states governed by an edge-based predictor. Meanwhile, the integral input-based triggering condition is exploited to decide whether to transmit its private control input to its neighbors. Then, an RL-based state feedback controller for each agent is developed to solve the output tracking control problem, which is further converted into the optimal control problem by introducing a discounted performance function. Inhomogeneous algebraic Riccati equations (AREs) are derived to obtain the optimal solution of AREs. An off-policy RL algorithm is used to learn the solution of inhomogeneous AREs online without requiring any knowledge of the system dynamics. Rigorous analysis shows that under the proposed event-driven adaptive observer mechanism and RL algorithm, all followers are able to synchronize the leader's output asymptotically. Finally, a numerical simulation is demonstrated to verify the proposed approach in theory.

Sampled-Data Cooperative Output Regulation: An Adaptive Distributed Continuous-Discrete Observer Approach

This paper studies the sampled-data cooperative output regulation problem for linear multi-agent systems. Firstly, a novel adaptive distributed continuous-discrete observer is established to recover the leader's state, which, on one hand, only relies on the sampling output of the leader, and on the other hand, does not need to store the sampled message from neighbors. Secondly, by solely making use of the digital states of both the agent and the distributed observer, a certainty equivalence control law is synthesized featuring a time-varying feedforward gain. It is rigorously proven that, with this time-varying feedforward gain, the proposed control approach can achieve exponential convergence of the tracking errors given arbitrary time-varying leader's signal, and the upper bound for the sampling intervals is explicitly given. Thirdly, for the class of chain-integrator multi-agent systems, the proposed control approach does not need any restriction on the upper bound of the sampling intervals, and thus would be more practical in certain application scenarios from the perspective of energy saving. The performance of the proposed control approach is validated by the simulation results of inverter-based distributed generation systems.

Adaptive output observers-based distributed tracking

This paper proposes a novel adaptive output observer method for the distributed output tracking control of heterogeneous systems. Unlike the existing adaptive distributed state observer, an output-based adaptive distributed output observer (OADOO) that only relies on the leader’s output is proposed to estimate the leader’s information. Meanwhile, an input-based triggering mechanism is exploited to avoid continuous interactions between agents, and between the leader and its neighboring agents, respectively. Then, a local controller is developed to achieve the output tracking control. In comparison with the existing results for the similar research problem, our results not only handle the tracking control subject to only relative output measurement, but also considerably lower the data exchange traffic and dimension among agents of the developed OADOO.

Distributed Observer-Based Leader-Follower Consensus of Multiple Euler-Lagrange Systems.

This article investigates the leader-follower consensus problem of multiple Euler-Lagrange (EL) systems, where each agent suffers uncertain external disturbances, and the communication links among agents experience faults. Besides, we consider a more general case that only a portion of followers can measure partial components of leader's output and access the dynamic information of leader. The main idea of solving the consensus problem in this article is proceeded in two steps. First, we design an adaptive distributed observer to estimate the full state information of leader in real time with resilience to communication link faults. Second, based on the proposed distributed observer, we propose a proportional-integral (PI) control protocol for each agent to track the trajectory of leader, which is model-independent and robust to uncertain external disturbances. Distinct from the existing leader-follower consensus protocols of multiple EL systems, the proposed distributed observer-based PI consensus protocol in this article is model-independent, which is irrelevant to the structures or features of EL system model. Finally, we present a simulation example to show the resilience of the above adaptive distributed observer and the robustness of the distributed observer-based consensus protocol.

Consensus for Multiple Random Mechanical Systems With Applications on Robot Manipulator

This paper studies the consensus problem of multiple random mechanical/Euler-Lagrange systems. First, an event-triggered adaptive distributed observer is proposed. It can estimate both the system matrix and states of the leader. Compared with the existing works, the leader system contains unknown parameters, which makes the design of the observer challenging. Second, an event-triggered adaptive control method is proposed. The proposed method not only can deal with the random disturbance, but also can save the energy and execution times of the actuators by event-triggered mechanisms. Finally, a practical application on a real multiple-joint robot is conducted. Each joint of the robot is regarded as a mechanical system. We show that by the presented controller, the angular position of each joint can track a reference signal despite uncertainties and random disturbances.

Discrete-time adaptive distributed output observer for time-varying formation tracking of heterogeneous multi-agent systems

This paper presents discrete-time distributed algorithms to achieve time-varying output formation tracking of heterogeneous linear multi-agent systems subject to time-varying faults and directed graphs. To overcome the impacts caused by unknown faults and directed graphs, a discrete-time adaptive distributed output observer-based control architecture is established to guarantee time-varying output formation tracking exponentially. In particular, several distributed leader observers are firstly given to estimate and reconstruct the leader’s state over a directed graph. The new discrete-time adaptive distributed output observer is presented to remove the need of having fully access to the leader’s system matrices and to reduce the dimension and information exchange in the developed distributed observers. In terms of this estimated information from the adaptive distributed output observer, a distributed output feedback controller integrated with an observer-based scheme is developed to compensate for the impact of unknown faults such that time-varying output formation tracking is achieved with a global exponential convergence. Two examples and simulation results are provided to validate the effectiveness of the proposed designs.

Event-triggered output-based adaptive distributed observer over jointly connected networks and its application

The adaptive distributed observer for a leader system is a fully distributed dynamic compensator for estimating the state variables and the system matrix of a linear leader system over a communication network. In this paper, we first propose an event-triggered implementation of the output-based adaptive distributed observer for a linear leader system over jointly connected communication networks. Then we show that the proposed triggering mechanism not only retains the exponential convergence property of the analog adaptive distributed observer but also prevents the Zeno phenomenon from happening. Our result includes several existing results as special cases and is applicable when the state of the leader system is unavailable. Finally, we apply the proposed event-triggered output-based adaptive distributed observer to solve the cooperative linear output regulation problem. A numerical example is used to validate our design.

Output-based adaptive distributed observer for general linear leader systems over periodic switching digraphs

In this paper, we present a sufficient condition for the exponential stability of a class of linear switched systems. As an application of this stability result, we establish an output-based adaptive distributed observer for a general linear leader system over a periodic jointly connected switching communication network, which extends the applicability of the output-based adaptive distributed observer from a marginally stable linear leader system to any linear leader system and from an undirected switching graph to a directed switching graph. This output-based adaptive distributed observer will be applied to solve the leader-following consensus problem for multiple double-integrator systems.

Adaptive distributed observer-based predictive formation tracking control for autonomous underwater vehicles

Numerous existing autonomous underwater vehicles (AUVs) formation control works have focused on the observation of external time-varying disturbances in trajectory tracking control. However, external time-varying disturbance outliers cannot be ignored due to the complex marine environment. It is rarely considered in previous research. In this paper, a double-layer distributed formation prediction control scheme is designed, including an upper-level adaptive distributed observer and a lower-level predictive controller. Firstly, the velocity is observed and regarded as an unknown variable by the expectation maximization algorithm. The gain in the observer will be optimized by adaptive cubature Kalman to improve the anti-disturbance performance of the adaptive distributed observer. Then, the constraints of internal safety distance and input saturation are fully considered. The distributed cooperative cost function is constructed based on the virtual trajectory, which is further introduced into local rolling domain optimization to realize formation predictive control. The boundedness of innovation and Lyapunov stability are utilized to prove the reliability of the control system. Some comparative simulation experiments are designed to demonstrate the effectiveness and robustness of the proposed method.

Leader-Following Consensus of Heterogeneous Linear Multiagent Systems With Communication Time-Delays via Adaptive Distributed Observers.

This article investigates the leader-following consensus problem of heterogeneous linear multiagent systems under switching and directed topologies. It is assumed that the communication between agents suffers from time-varying delays and only the neighboring agents of the leader are able to get access to the information of the leader agent, including its agent matrices. A key technical lemma on the input to state stability of time-delayed systems is first established with which the main results of this article can be obtained. An adaptive distributed observer, taking into consideration of communication time delays, is proposed for each follower to estimate the leader's system matrices and its state. Then, a distributed controller based on this adaptive observer is developed. We show that the resulting closed-loop multiagent system achieves the leader-following output consensus. Two examples are finally given to illustrate the effectiveness of the proposed controller.

Fully distributed event‐triggered asymptotic attitude coordination of multiple spacecraft systems with disturbances

AbstractThis article studies the leader‐following attitude coordination problem of a group of rigid spacecraft subject to communication constraint, disturbances and uncertain control coefficient matrices. A fully distributed adaptive anti‐disturbance attitude coordinated control scheme with event‐triggering mechanism is developed. First, the event‐triggered adaptive distributed observer is designed for each follower to estimate the leader's information without continuous communication requirement. Based on the estimated information, the adaptive anti‐disturbance attitude tracking controller is designed such that asymptotic coordinated tracking can be achieved under additive disturbances and actuators' partial loss of efficiency. The proposed control scheme ensures that all the closed‐loop signals are bounded and the positive lower bound of inter‐event times exists in each subsystem. Simulation results illustrate the effectiveness and flexibility of the proposed control scheme.

Fully Heterogeneous Containment Control of a Network of Leader–Follower Systems

This article develops a distributed solution to the fully heterogeneous containment control problem (CCP), for which not only the followers’ dynamics but also the leaders’ dynamics are nonidentical. A novel formulation of the fully heterogeneous CCP is first presented in which each follower constructs its virtual exosystem. To build these virtual exosystems by followers, a novel distributed algorithm is developed to calculate the so-called normalized level of influences (NLIs) of all leaders on each follower, and a novel adaptive distributed observer is designed to estimate the dynamics and states of all leaders that have an influence on each follower. Then, a distributed control protocol is proposed based on the cooperative output regulation framework, utilizing this virtual exosystem. Based on the estimations of leaders’ dynamics and states and NLIs of leaders on each follower, the solutions of the so-called linear regulator equations are calculated in a distributed manner, and consequently, a distributed control protocol is designed for solving the output containment problem. Finally, theoretical results are verified by performing numerical simulations.

Fully Distributed Robust Formation Flying Control of Drones Swarm Based on Minimal Virtual Leader Information

This paper studies the robust formation flying problem for a swarm of drones, which are modeled as uncertain second order systems. By making use of minimal virtual leader information, a fully distributed robust control scheme is proposed, which includes three parts. First, the output based adaptive distributed observer is adopted to recover the global flying path vector as well as the coefficients of the minimal polynomial of the system matrix of the virtual leader system for each drone based on neighboring information from the communication network. Second, based on the estimated minimal polynomial of the system matrix of the virtual leader system, an asymptotic internal model is conceived to deal with uncertain system parameters. Third, by combining the asymptotic internal model and a certainty equivalent dynamic state feedback control law, a local trajectory tracking controller is synthesized to solve the robust formation flying problem. Numerical simulations are provided to validate the proposed control scheme.

Fixed-time leader-following consensus of multiple uncertain nonholonomic systems: An adaptive distributed observer approach

This paper discusses the fixed-time leader-following consensus problem for multiple uncertain nonholonomic systems, which are widely used in engineering models. According to our literature review, either the system is assumed to be known, or the uncertainty only contains state information, which does not meet the actual requirements. For this reason, this paper investigates more general nonholonomic systems with uncertainties driven by inputs and states. First, a fixed-time adaptive distributed observer is proposed to estimate the leader’s state and structural parameters, which ensures that the estimation errors converge to zero within a fixed time. Second, two regulator equations based on the idea of cooperative output regulation are constructed, and a novel observer-based distributed switching control law is proposed. This control law overcomes the nonholonomic constraints and appropriately relaxes the assumptions of uncertain functions in the existing references. Finally, the simulation results verify the effectiveness of the proposed control scheme.

Fully Distributed Event-Triggered Cooperative Output Regulation of Multi-Agent Systems under Jointly Connected Digraphs

This paper addresses the cooperative output regulation problem of heterogeneous linear multi-agent systems (MASs) with <i>jointly connected digraphs</i> under the assumption that the exosystem matrix is only known by the neighbors of the exosystem. First, a novel event-based adaptive distributed observer with time-dependent power functions as the event-triggering threshold is proposed to estimate the exosystem matrix and the exogenous signal simultaneously. A new analytical method based on the weighted mean-value theorem for integrals and Bellman-Gronwall lemma is developed to prove the estimation errors converge to zero asymptotically. Second, a distributed dynamic control law is proposed based on the event-based adaptive observer, and it is shown that the tracking errors of the resulting closed-loop system converge to zero asymptotically. Two distinctive advantages of this work are (i) the event-triggered control (ETC) protocol is fully distributed, and (ii) a positive minimum inter-event time (MIET) is explicitly given so that Zeno behavior is strictly excluded. Finally, the effectiveness of the proposed fully distributed ETC protocol is illustrated by a numerical example.

Adaptive distributed observer for general linear leader systems over periodic switching digraphs

A standard assumption on the existence of the distributed observer or adaptive distributed observer for a linear leader system over jointly connected switching networks is that none of the eigenvalues of the system matrix of the leader system have positive real parts. In this paper, after establishing a stability result for a class of linear periodic switched systems, we present sufficient conditions for the existence of both the distributed observer and the adaptive distributed observer for general linear leader systems over periodic jointly connected switching networks. As an application of the distributed observer, we solve the cooperative output regulation problem for linear multi-agent systems with general linear leader systems over periodic jointly connected switching networks. A numerical example is provided to illustrate our design.

Leader-following bipartite consensus with disturbance rejection for uncertain multiple Euler–Lagrange systems over signed networks

In this paper, the leader-following bipartite consensus is investigated for a group of uncertain multiple Euler–Lagrange systems with disturbances. An innovative adaptive distributed observer is developed without requiring that followers surely acquire the leader’s auxiliary state and system matrix. A directed signed network satisfying the principle of structural balance is exploited to describe the interaction among agents. Then a novel bipartite consensus control protocol is proposed to solve the bipartite consensus problem of multiple Euler–Lagrange systems. The theoretical proof is provided via constructing a Lyapunov function and applying Barbalat lemma to analyze the convergence problem. Finally, a numerical simulation is utilized to demonstrate the effectiveness of proposed method.

Output based adaptive distributed output observer for leader–follower multiagent systems

The adaptive distributed observer approach has been an effective tool for synthesizing a distributed control law for solving various control problems of leader–follower multiagent systems. However, the existing adaptive distributed observer needs to make use of the full state of the leader system. This assumption not only precludes many practical applications in which only the output of the leader system is available, but also leads to a high dimension observer. In this communique, we propose an adaptive distributed output observer which only makes use of the output of the leader system, and is thus more practical than the state based adaptive distributed observer. Moreover, the dimension and the information exchange among agents of the proposed adaptive distributed output observer can be significantly smaller than those of the state based adaptive distributed output observer.