Fixed-Time Leader-Following Consensus for Multiple Wheeled Mobile Robots

Bipartite Fault-Tolerant Consensus Control for Multi-Agent Systems with a Leader of Unknown Input Under a Signed Digraph

This paper addresses the bipartite consensus problem of signed directed multi-agent systems (MASs) subject to actuator faults. This problem plays a crucial role in various real-world systems where agents exhibit both cooperative and competitive interactions, such as autonomous vehicle fleets, smart grids, and robotic networks. To address this, unlike most existing works, an intermediate observer is designed using newly introduced intermediate variables, enabling simultaneous estimation of both agent states and faults. Furthermore, a distributed adaptive observer is developed to help followers estimate the leader's state, overcoming limitations of prior bounded-input assumptions. Finally, simulation results demonstrate the method's effectiveness, showing that consensus tracking errors converge to zero under under various fault scenarios and input uncertainties.

Relational Maneuvering of Leader-Follower Unmanned Aerial Vehicles for Flexible Formation

In this article, we propose a new formation scheme for a leader-follower unmanned aerial vehicle (UAV) system inspired by a human pilot's behavior wherein the formation geometry does not necessarily remain fixed as the vehicles maneuver. In other words, the position and the orientation of the follower with respect to the leader are subject to change as they maneuver while satisfying some constraints. Our strategy ensures that the follower UAV maintains a desired fixed relative distance with respect to the leader UAV, whereas its orientation with respect to the leader UAV may change to reduce its control effort and provide it with a tactical advantage. We call this new relational maneuvering scheme flexible since the set of feasible positions for the follower UAV is not fixed, as is common in close proximity two-ship formations in air-to-air combat. By assigning the follower UAV's linear and angular velocities as its control inputs, our approach tries to emulate a human pilot's behavior in UAVs by taking anticipatory maneuvers when the leader UAV makes aggressive turns. The proposed flexible-geometry formation scheme is robust to the leader's maneuver changes since the follower UAV's control law does not need the information of the leader's angular speed control and only uses relative measurements. This makes the design lucrative even when the vehicles are heterogeneous, global measurements are unavailable, or if the leader UAV is noncooperative. Finally, we present multiple simulations to highlight the merits of the flexible formation control laws.

Leader-following output-feedback consensus for second order multiagent systems with arbitrary convergence time and prescribed performance

This paper investigates the prescribed-time leader-following output-feedback consensus problem for second order multiagent systems without velocity measurement. Firstly, by introducing a time-scaling function, novel prescribed-time state observers are designed to estimate the second-order states of the agents. Then, a distributed output-feedback scheme is proposed to achieve leader-following consensus, where the transient performance, including the convergence rate and the overshoot, can be offline pre-assigned. It should be noted that the singularity-like problem is solved for the system under measurement errors by adopting a form of piecewise functions. Moreover, the control strategy is modified by introducing an auxiliary system when taking the common saturation problem into account. Finally, the efficiency of the proposed schemes is illustrated by numerical simulation examples.

A Linear Time-Varying Inequality Approach for Prescribed Time Stability and Stabilization

This article studies the problem of finite-time, fixed-time, and prescribed-time stability analysis and stabilization. First, a linear time-varying (LTV) inequality-based approach is introduced for prescribed-time stability analysis. Then, it is shown that the existing nonlinear Lyapunov inequalities-based finite- and fixed-time stability criteria can be recast into the unified framework of the LTV inequality-based approach for prescribed-time stability. Finally, the unified LTV inequality-based approach is used to solve the global prescribed-time stabilization problem of the attitude control system of a rigid spacecraft with disturbance, and a bounded nonlinear time-varying controller is proposed via back stepping. Numerical simulations are presented to show the effectiveness of the proposed methods.

Leader-Follower Formation Learning Control of Discrete-Time Nonlinear Multiagent Systems

This article investigates the leader-follower formation learning control (FLC) problem for discrete-time strict-feedback multiagent systems (MASs). The objective is to acquire the experience knowledge from the stable leader-follower adaptive formation control process and improve the control performance by reusing the experiential knowledge. First, a two-layer control scheme is proposed to solve the leader-follower formation control problem. In the first layer, by combining adaptive distributed observers and constructed i_n -step predictors, the leader's future state is predicted by the followers in a distributed manner. In the second layer, the adaptive neural network (NN) controllers are constructed for the followers to ensure that all the followers track the predicted output of the leader. In the stable formation control process, the NN weights are verified to exponentially converge to their optimal values by developing an extended stability corollary of linear time-varying (LTV) system. Second, by constructing some specific "learning rules," the NN weights with convergent sequences are synthetically acquired and stored in the followers as experience knowledge. Then, the stored knowledge is reused to construct the FLC. The proposed FLC method not only solves the leader-follower formation problem but also improves the transient control performance. Finally, the validity of the presented FLC scheme is illustrated by simulations.

Consensus of Matrix-Weighted Hybrid Multiagent Systems

As we all know, heterogeneity is a very important feature of multiagent systems (MASs). In this article, we examine the consensus control problems of matrix-weighted hybrid MASs, which contain discrete-time and continuous-time dynamic agents. Under fixed and switched undirected networks, three consensus algorithms are proposed for matrix-weighted hybrid MASs. In the three consensus algorithms, the sampled data control method is utilized in the continuous-time subsystem to analyze the convergence of different dynamic agents in the matrix-weighted interaction mode. For the symmetric matrix-weighted fixed and switched multiagent networks, when the sampling period meets certain conditions, the consensus criteria are established via the matrix theory, Lyapunov stability theory, and analysis theory. Moreover, asymmetric matrix-weighted fixed multiagent networks which can be applied to some scenarios with scaled and rotated updates constraints are considered, and consensus criteria are also obtained when the sampling period meets certain conditions. Finally, a few simulation examples are supplied to validate the correctness of the obtained theoretical results.

Trajectory Tracking and Obstacle Avoidance for Wheeled Mobile Robots Based on EMPC With an Adaptive Prediction Horizon

This article develops an event-triggered model-predictive control (EMPC) strategy to realize trajectory tracking and obstacle avoidance for a wheeled mobile robot (WMR) subject to input constraints and external disturbances. In the EMPC strategy, a potential field is introduced in the cost function to guarantee a smooth path for the WMR. An event-triggered mechanism is designed to reduce the computational load of solving an optimal control problem (OCP). Moreover, an adaptive prediction horizon is utilized to further achieve computation reduction. Both recursive feasibility of the OCP and practical stability of the resulting closed-loop system are analyzed for the WMR with the input constraints and the external disturbances. Simulation results are provided to demonstrate the effectiveness and superiority of the proposed EMPC strategy.

Roto-Translation Invariant Formation of Multiple Underactuated Planar Rigid Bodies

This article investigates the roto-translation invariant (RTI) formation of multiple underactuated planar rigid bodies, which are established under the framework of matrix Lie groups. The main contribution is that we define the RTI and pseudo RTI (P-RTI) formation of planar rigid bodies. Different from the common formation given in the earth-fixed frame, the RTI formation is defined in the body-fixed frame so that it possesses a rigid-body motion obtained by composing rotation and translation simultaneously. Moreover, regarding fully actuated planar rigid bodies, we propose the velocity and force requirements to maintain the RTI formation, which are derived based on the kinematic and dynamic model, respectively. Another contribution of this article is that the RTI formation feasibility is investigated for underactuated planar rigid bodies subject to nonholonomic constraints on velocities and accelerations. To be more specific, we study the occasions when wheeled mobile robots and underactuated surface vessels can maintain the RTI or P-RTI formation. Finally, the results of the simulation and experiment are presented so as to exhibit the RTI and P-RTI formation intuitively.

Further Improvements on Non-Negative Edge Consensus of Networked Systems

In this article, the non-negative edge consensus problem is addressed for positive networked systems with undirected graphs using state-feedback protocols. In contrast to existing results, the major contributions of this work included: 1) significantly improved criteria of consequentiality and non-negativity, therefore leading to a linear programming approach and 2) necessary and sufficient criteria giving rise to a semidefinite programming approach. Specifically, an improved upper bound is given for the maximum eigenvalue of the Laplacian matrix and the (out-) in-degree of the degree matrix, and an improved consensuability and non-negativevity condition is obtained. The sufficient condition presented only requires the number of edges of a nodal network without the connection topology. Also, with the introduction of slack matrix variables, two equivalent conditions of consensuability and non-negativevity are obtained. In the conditions, the system matrices, controller gain, as well as Lyapunov matrices are separated, which is helpful for parameterization. Based on the results, a semidefinite programming algorithm for the controller is readily developed. Finally, a comprehensive analytical and numerical comparison of three illustrative examples is conducted to show that the proposed results are less conservative than the existing work.

A Novel Resilient Control Scheme for a Class of Markovian Jump Systems With Partially Unknown Information

In the complex practical engineering systems, many interferences and attacking signals are inevitable in industrial applications. This article investigates the reinforcement learning (RL)-based resilient control algorithm for a class of Markovion jump systems with completely unknown transition probability information. Based on the Takagi-Sugeno logical structure, the resilient control problem of the nonlinear Markovion systems is converted into solving a set of local dynamic games, where the control policy and attacking signal are considered as two rival players. Combining the potential learning and forecasting abilities, the new integral RL (IRL) algorithm is designed via system data to compute the zero-sum games without using the information of stationary transition probability. Besides, the matrices of system dynamics can also be partially unknown, and the new architecture requires less transmission and computation during the learning process. The stochastic stability of the system dynamics under the developed overall resilient control is guaranteed based on the Lyapunov theory. Finally, the designed IRL-based resilient control is applied to a typical multimode robot arm system, and implementing results demonstrate the practicality and effectiveness.

Fixed-Time Event-Triggered Output Consensus Tracking of High-Order Multiagent Systems Under Directed Interaction Graphs

This article investigates the problem of fixed-time event-triggered output consensus tracking for high-order multiagent systems (MASs) under directed interaction graphs. First, a fixed-time event-triggered distributed observer and triggering functions are proposed. Next, fixed-time convergence of the presented distributed observer is proved by the Lyapunov function approach, and an analysis is conducted to show the proposed distributed observer excludes zeno behavior. Then, an event-triggered adaptive dynamic surface fixed-time controller is designed to stabilize the tracking error system. Finally, simulation results are given to show the effectiveness and superiority of the consensus scheme developed. The contribution of this article is to present a novel event-triggered fixed-time distributed observer and a novel fixed-time controller, which can reduce frequency of communication and control update, avoid continuous monitor, exclude zeno behavior, eliminate the effect of mismatched disturbance caused by observation error, and achieve practical fixed-time output consensus tracking of high-order MAS under directed interaction graphs.

Distributed Finite-Time Secondary Frequency and Voltage Control for Islanded Microgrids With Communication Delays and Switching Topologies

This article is concerned with the distributed secondary frequency and voltage control for islanded microgrids. First, the distributed secondary control problem is formulated by taking both communication delays and switching topologies into account. Second, by using an Artstein model reduction method, a novel delay-compensated distributed control scheme is proposed to restore frequencies of each distributed generator (DG) to a reference level in finite time, while achieving active power sharing in prescribed finite-time regardless of initial deviations generated from primary control. Third, a distributed finite-time controller is developed to regulate voltages of all DGs to a reference level. Fourth, the proposed idea is also applied to deal with the finite-time consensus for first-order multiagent systems. Finally, case studies are carried out, demonstrating the effectiveness, the robustness against load changes, and the plug-and-play capability of the proposed controllers.

Formation Tracking Control and Obstacle Avoidance of Unicycle-Type Robots Guaranteeing Continuous Velocities

In this paper, we addressed the problem of controlling the position of a group of unicycle-type robots to follow in formation a time-varying reference avoiding obstacles when needed. We propose a kinematic control scheme that, unlike existing methods, is able to simultaneously solve the both tasks involved in the problem, effectively combining control laws devoted to achieve formation tracking and obstacle avoidance. The main contributions of the paper are twofold: first, the advantages of the proposed approach are not all integrated in existing schemes, ours is fully distributed since the formulation is based on consensus including the leader as part of the formation, scalable for a large number of robots, generic to define a desired formation, and it does not require a global coordinate system or a map of the environment. Second, to the authors' knowledge, it is the first time that a distributed formation tracking control is combined with obstacle avoidance to solve both tasks simultaneously using a hierarchical scheme, thus guaranteeing continuous robots velocities in spite of activation/deactivation of the obstacle avoidance task, and stability is proven even in the transition of tasks. The effectiveness of the approach is shown through simulations and experiments with real robots.