Scaled Position Consensus of High-Order Uncertain Multiagent Systems Over Switching Directed Graphs.

We investigate the scaled position consensus of high-order multiagent systems with parametric uncertainties over switching directed graphs, where the agents' position states reach a consensus value with different scales. The intricacy arises from the asymmetry inherent in information interaction. Achieving scaled position consensus in high-order multiagent systems over directed graphs remains a significant challenge, particularly when confronted with the following complex features: 1) uniformly jointly connected switching directed graphs; 2) complex agent dynamics with unknown inertias, unknown control directions, parametric uncertainties, and external disturbances; 3) interacting with each other via only relative scaled position information (without high-order derivatives of relative position); and 4) fully distributed in terms of no shared gains and no global gain dependency. To address these challenges, we propose a distributed adaptive algorithm based on a acrlong MRACon scheme, where a linear high-order reference model is designed for every individual agent employing relative scaled position information as input. A new transformation is proposed which converts the scaled position consensus of high-order linear reference models to that of first-order ones. Theoretical analysis is presented where agents' positions achieve the scaled consensus over switching directed graphs. Numerical simulations are performed to validate the efficacy of our algorithm and some collective behaviors on traditional consensus, bipartite consensus, and cluster consensus are shown by precisely choosing the scales of the agents.

A Hybrid Design of Fault Detection for Nonlinear Systems Based on Dynamic Optimization.

To ensure the safety of an automation system, fault detection (FD) has become an active research topic. With the development of artificial intelligence, model-free FD strategies have been widely investigated over the past 20 years. In this work, a hybrid FD design approach that combines data-driven and model-based is developed for nonlinear dynamic systems whose information is not known beforehand. With the aid of a Takagi-Sugeno (T-S) fuzzy model, the nonlinear system can be identified through a group of least-squares-based optimization. The associated modeling errors are taken into account when designing residual generators. In addition, statistical learning is adopted to obtain an upper bound of modeling errors, based on which an optimization problem is formulated to determine a reliable FD threshold. In the online FD decision, an event-triggered strategy is also involved in saving computational costs and network resources. The effectiveness and feasibility of the proposed hybrid FD method are illustrated through two simulation studies on nonlinear systems.

Fast actuator and sensor fault estimation based on adaptive unknown input observer.

This study evaluates the robust fault estimation problem of systems with actuator and sensor faults though the simultaneous use of unknown input disturbances and measurement noise. Specifically, an augmented descriptor system is preliminarily developed by creating an augmented state consisting of system states and sensor faults. Next, a novel fast adaptive unknown input observer (FAUIO) is proposed for the system to enhance its fault estimation performance. The existence condition of the novel FAUIO is then introduced for linear time-invariant systems with unknown input disturbances. Furthermore, the proposed FAUIO is extended to a class of Lipschitz nonlinear systems with unknown input disturbances and measurement noise to investigate the robust fault estimation problem. Accordingly, an H∞ performance index is employed to attenuate the influence of disturbances on fault estimation. Moreover, the linear matrix inequality (LMI) technique is applied to solve the designed FAUIO. Finally, the effectiveness of the developed FAUIO is validated via the simulation of two examples.

Distributed Formation Control of Multiple Euler-Lagrange Systems: A Multilayer Framework.

In this technical correspondence, a multilayer formation (MLF) control problem is considered and solved by a unified framework. The agents in each layer present a sort of hierarchical distinction: receive information from former layers, communicate inside the current layer, and send information to subsequent layers. With an arbitrary number of layers, we extend the previous result from undirected graphs to directed ones. The proposed controller achieves MLF without using the distributed estimators and the acceleration information. This removes the induced discontinuities and alleviates the system complexity. It is then proved that the closed-loop errors are semiglobally uniformly ultimately bounded. Simulations are presented to illustrate the effectiveness of this approach.

Formation-containment control of multi-agent systems with communication delays.

This paper designs formation-containment control algorithms for a class of second-order nonlinear multi-agent systems governed by Euler-Lagrange dynamics with communication delays. The formation-containment problem consists of leader agents' formation control and follower agents' containment control. Firstly, to make the leaders form a desired formation and move collectively with a constant velocity, a coordinated formation control algorithm is designed and the variable-gain technique is used to eliminate the effect of communication delays on the leaders' formation control. Secondly, considering that only the leaders have access to the desired moving velocity, we propose distributed velocity estimators for followers in which the communication delays also exist in the followers' information interaction. By using the estimated velocity information, coordinated containment control laws are designed for the followers to drive them asymptotically converge to the convex hull spanned by all leaders. Furthermore, to increase the system robustness against uncertainties and external disturbances, the adaptive updating laws are designed for all agents. Finally, simulations are given to demonstrate these obtained results.

Artificial potential function based spacecraft proximity maneuver 6-DOF control under multiple pyramid-type constraints.

This paper addresses the problem of spacecraft six degree of freedom (6-DOF) pose tracking control with collision avoidance and field of view (FOV) pyramid-type constraints during the autonomous proximity maneuver. The constraints are modeled as pyramid envelopes, which can better represent some real cases with less conservativeness comparing with commonly used cone-shaped model. A novel modeling method is proposed to describe the pyramid-type constraints in the dual-quaternion frame. Based on the specific geometric property of the pyramid constraints, a new convex artificial potential function (APF) with only one global minimum is designed, which incorporates the pose constraints into the control design procedure. Then, an integrated APF based control law is presented to simultaneously control the rotational and translational motion of the spacecraft without violating the pyramid constraints. The stability of the closed-loop system is demonstrated through the Lyapunov theory, and numerical simulation results are carried out to show the effectiveness of the proposed control law.

Layered Affine Formation Control of Networked Uncertain Systems: A Fully Distributed Approach Over Directed Graphs.

Distributed formation control is presented for networked Euler-Lagrange systems (ELSs) over a directed interaction topology. This problem is defined by a layered framework in which information flow both among the leaders and among the followers is described by different layers. To empower the formation to make a variety of geometric transformations, we present the necessary and sufficient conditions for affine maneuverability under a directed graph. Unlike most existing results using a diagonal stabilizing matrix to achieve the stabilizability of affine formation, this fully distributed approach is feasible without any global information. Next, we propose an adaptive control law for agents in each layer, where the closed-loop errors are driven to a neighborhood of the origin in finite time. Adaptive neural networks are integrated to tackle the model uncertainties in ELSs by updating the norm of the weight matrix, which can simplify the control design and alleviate the computational burden compared with traditional ones. The simulation results are given to show the effectiveness of the proposed approach.

Cooperative Circumnavigation Control of Networked Microsatellites.

This paper addresses the trajectory analysis, mission design, and control law for multiple microsatellites to cooperatively circumnavigate a host spacecraft. This cooperative circumnavigation (CCN) problem is defined to drive a group of networked microsatellites to a predefined planar ellipse concerning a host spacecraft while maintaining a geometric formation configuration. We first design several potential functions to guide the microsatellites to the given planar elliptical orbit with a proper radius. Next, the affine Laplacian matrix is introduced to characterize the desired formation shape of microsatellites. Based on the potential functions and the Laplacian matrix, a CCN control law is finally proposed. Then, the simulation results of eight microsatellites with earth-orbiting mission scenarios are given, where the natural trajectory motion is incorporated which consumes nearly zero-fuel.

Observer-based prescribed performance attitude control for flexible spacecraft with actuator saturation.

This paper investigates the prescribed performance attitude control problem for flexible spacecraft subject to external disturbances and actuator constraints. By using a new performance function and an error transformation, the attitude control system is transformed into an error system which will be kept bounded to ensure expected dynamic and steady-state responses. Compared with the commonly used performance function, the modified one has an explicit prespecified terminal time which determines the maximum convergence time of the attitude control system. A modal observer and a disturbance observer are designed to deal with the flexible vibration and disturbances, respectively. Furthermore, when considering actuator saturation, an improved control strategy is developed with an auxiliary system utilized to compensate the saturation. The stability of the closed-loop system is analyzed by Lyapunov theory. Simulation results show the effectiveness and performance of the proposed methods.

Distributed coordinated attitude tracking control for spacecraft formation with communication delays.

This paper investigates the distributed coordinated attitude tracking control problem for spacecraft formation with time-varying communication delays under the condition that the dynamic leader spacecraft is a neighbor of only a subset of follower spacecrafts. We consider two cases for the leader spacecraft: i) the attitude derivative is constant, and ii) the attitude derivative is time-varying. In the first case, a distributed estimator is proposed for each follower spacecraft by using its neighbors' information with communication delays. In the second case, to express the dynamic leader's attitude, an improved distributed observer is developed to estimate the leader's information. Based on the estimated values, adaptive coordinated attitude tracking control laws are designed to compensate for parametric uncertainties and unknown disturbances. By employing the Lyapunov-Krasovskii functional approach, the attitude tracking errors and estimation errors are proven to converge to zero asymptotically. Numerical simulations are presented to illustrate the effectiveness of theoretical results.

Dual-quaternion based fault-tolerant control for spacecraft formation flying with finite-time convergence.

Study results of developing control system for spacecraft formation proximity operations between a target and a chaser are presented. In particular, a coupled model using dual quaternion is employed to describe the proximity problem of spacecraft formation, and a nonlinear adaptive fault-tolerant feedback control law is developed to enable the chaser spacecraft to track the position and attitude of the target even though its actuator occurs fault. Multiple-task capability of the proposed control system is further demonstrated in the presence of disturbances and parametric uncertainties as well. In addition, the practical finite-time stability feature of the closed-loop system is guaranteed theoretically under the designed control law. Numerical simulation of the proposed method is presented to demonstrate the advantages with respect to interference suppression, fast tracking, fault tolerant and practical finite-time stability.

Distributed Containment Control for Multiple Unknown Second-Order Nonlinear Systems With Application to Networked Lagrangian Systems.

In this paper, we consider the distributed containment control problem for multiagent systems with unknown nonlinear dynamics. More specifically, we focus on multiple second-order nonlinear systems and networked Lagrangian systems. We first study the distributed containment control problem for multiple second-order nonlinear systems with multiple dynamic leaders in the presence of unknown nonlinearities and external disturbances under a general directed graph that characterizes the interaction among the leaders and the followers. A distributed adaptive control algorithm with an adaptive gain design based on the approximation capability of neural networks is proposed. We present a necessary and sufficient condition on the directed graph such that the containment error can be reduced as small as desired. As a byproduct, the leaderless consensus problem is solved with asymptotical convergence. Because relative velocity measurements between neighbors are generally more difficult to obtain than relative position measurements, we then propose a distributed containment control algorithm without using neighbors' velocity information. A two-step Lyapunov-based method is used to study the convergence of the closed-loop system. Next, we apply the ideas to deal with the containment control problem for networked unknown Lagrangian systems under a general directed graph. All the proposed algorithms are distributed and can be implemented using only local measurements in the absence of communication. Finally, simulation examples are provided to show the effectiveness of the proposed control algorithms.

6 DOF synchronized control for spacecraft formation flying with input constraint and parameter uncertainties.

This paper treats the problem of synchronized control of spacecraft formation flying (SFF) in the presence of input constraint and parameter uncertainties. More specifically, backstepping based robust control is first developed for the total 6 DOF dynamic model of SFF with parameter uncertainties, in which the model consists of relative translation and attitude rotation. Then this controller is redesigned to deal with the input constraint problem by incorporating a command filter such that the generated control could be implementable even under physical or operating constraints on the control input. The convergence of the proposed control algorithms is proved by the Lyapunov stability theorem. Compared with conventional methods, illustrative simulations of spacecraft formation flying are conducted to verify the effectiveness of the proposed approach to achieve the spacecraft track the desired attitude and position trajectories in a synchronized fashion even in the presence of uncertainties, external disturbances and control saturation constraint.

Adaptive backstepping fault-tolerant control for flexible spacecraft with unknown bounded disturbances and actuator failures.

In this paper, a robust adaptive fault-tolerant control approach to attitude tracking of flexible spacecraft is proposed for use in situations when there are reaction wheel/actuator failures, persistent bounded disturbances and unknown inertia parameter uncertainties. The controller is designed based on an adaptive backstepping sliding mode control scheme, and a sufficient condition under which this control law can render the system semi-globally input-to-state stable is also provided such that the closed-loop system is robust with respect to any disturbance within a quantifiable restriction on the amplitude, as well as the set of initial conditions, if the control gains are designed appropriately. Moreover, in the design, the control law does not need a fault detection and isolation mechanism even if the failure time instants, patterns and values on actuator failures are also unknown for the designers, as motivated from a practical spacecraft control application. In addition to detailed derivations of the new controller design and a rigorous sketch of all the associated stability and attitude error convergence proofs, illustrative simulation results of an application to flexible spacecraft show that high precise attitude control and vibration suppression are successfully achieved using various scenarios of controlling effective failures.