This article explores the controllability robustness of simplicial complexes under both node-based and edge-based attacks. By considering network topology, dynamical properties, and higher order interactions, we propose a universal nodal dynamical model applicable to simplicial complexes of arbitrary dimensions. Quantitative analysis reveals that both the quantity and spatial distribution of 2-simplices play a pivotal role in regulating the robustness of network controllability. These results highlight the critical impact of second-order interaction structures on network robustness and suggest that the underlying mechanisms, such as higher order topological connectivity and dynamical synergy, can be extended to elucidate how higher dimensional $q$ -simplices ( $q\gt 2$ ) influence controllability robustness.

In this article, we reformulate the distributed optimal coordination problem for multi-agent systems to broaden its applicability across a wider range of coordination scenarios, thereby introducing a Generalized Distributed Optimal Coordination (GDOC) problem. In GDOC, the inter-agent relationships evolve from equality (consensus) to affinity (coordination), while local cost functions are unified as blends of parameters and shared basis functions, enabling cohesive network optimization. To address the GDOC problem, we propose a weak coupling hierarchical control framework for heterogeneous multi-agent systems. This framework consists of three layers: a signal generator, a tracking controller, and a speed regulator. For the generator, a transformed consensus protocol is designed for agents to estimate the global cost function and feasible set in a distributed manner, with the gradient projection method applied to minimize the objective function locally. For the controller, an observer-based output feedback control law is designed through system decomposition. For the regulator, a dynamic adaptive parameter is introduced to adjust the updating speed of the reference signal based on the agent’s relative tracking ability. The proposed framework not only preserves the universality of hierarchical control but also addresses the limitation of topdown structural open-loop control by introducing a regulator to form a bottom-up feedback loop. Finally, the effectiveness of the proposed framework is verified by Lyapunov stability theory analysis and simulation experiments. Note to Practitioners—In numerous task scenarios, the coordinated control of multi-agent systems involves solving optimization problems. This paper proposes GDOC to mathematically characterize these scenarios in a unified way, with the goal of controlling each agent’s output to converge towards the minimum point of the aggregate cost functions while maintaining preset inter-agent relationships. To achieve this, the affine transformation matrix is introduced to describe these inter-agent relationships under diverse coordination scenarios. Furthermore, the cost function adopts a form involving parameters and shared basis functions, facilitating interaction and iteration within the cost function. Correspondingly, an engineering-friendly control framework is proposed to address the GDOC problem. This framework consists of a reference signal generator, a tracking controller, and a speed regulator, each of which can be designed separately. The speed regulator is a new addition, aimed at adjusting the updating speed of signals according to the physical dynamic response capability of each agent, thereby establishing an indirect bottom-up feedback loop. This control framework can be applied to addressing GDOC problems in situations with switching cost functions and multiple solutions.

This paper is concerned with the study of robust distributed average tracking (DAT) algorithms for networked control systems in the presence of external disturbances or false data injection attacks (FDIAs). To eliminate the impacts of external disturbances and FDIAs, the technologies of disturbance-observer-based control (DOBC) and active disturbance rejection control (ADRC) are introduced into the context of DAT problems. First, for a class of external disturbances with known dynamics, we propose an anti-disturbance DAT (AD-DAT) algorithm, where a stand-alone disturbance observer based on the idea of DOBC is employed to estimate the disturbance and then to compensate it in the design of control inputs. The proposed AD-DAT algorithm can track the average of multiple time-varying reference signals with zero steady-state error and the accurate tracking is robust with respect to initialization constraints. Furthermore, for another class of FDIAs with unknown dynamics, we design an anti-attack DAT (AA-DAT) algorithm where the control input is based on the estimates of states instead of original states, and construct an extended state observer including a state observer and an FDIAs observer based on the idea of ADRC. The extended state observer plays a key role in estimating and eliminating the impact of FDIAs without compromising the accurate tracking performance. In addition, sufficient conditions are derived for the proposed two algorithms from a theoretical point of view to guarantee accurate average tracking. Finally, some numerical examples are given to illustrate the validity and effectiveness of the proposed algorithms.Note to Practitioners—This paper is motivated by the problem of robust distributed average tracking (DAT) for the time-varying centroid of the formation of a group of autonomous vehicles. The problem arises in the scenario where two groups of unmanned ground vehicles (UGVs) and unmanned aerial vehicles (UAVs) perform a combined surveillance-reconnaissance mission (where the UAVs aim to provide aerial coverage and early warning against threats for the UGVs, as shown in Fig. 1) in an uncertain environment where the external disturbances might exist or the FDIAs might be launched by adversaries. Obviously, the tracking accuracy of the target signal will be compromised in the presence of external disturbances or FDIAs. However, most existing works for disturbance rejection mainly focused on the static average consensus rather than the dynamic one even though a few works mentioned the DAT problem with only considering the case of external disturbances. Based on this, we propose an AD-DAT algorithm and an AA-DAT algorithm for the DAT problem based on the ideas of DOBC and ADRC, respectively. Numerical examples show that the proposed algorithms are able to estimate and eliminate the impacts of the external disturbances and the FDIAs, which implies that the algorithms can be implemented in practical scenarios. In future research, we will extend the results to more general scenarios in the presence of external disturbances and FDIAs.

We investigate the problem of distributed optimal formation control in Multi-Agent Systems (MAS) affected by multiplicative noise, with energy and time constraints. We develop a globally optimal distributed formation control algorithm to achieve the expected formation while minimizing a comprehensive cost function that includes formation errors, energy consumption, and network costs. Additionally, we derive lower bounds for the achievable completion time and the required energy levels, expressed in terms of the convergence error, and the second smallest and largest eigenvalues of the Laplacian matrix. These bounds set practical criteria for formation tasks with constraints on energy and time. Finally, we provide simulation results to validate the effectiveness of the proposed approach.

This paper investigates the average controllability of Laplacian dynamical networks characterized by an exponential degree distribution. We introduce a novel configuration network model with an exponential degree distribution, incorporating a degree distribution parameter to adjust the heterogeneity of the distribution. We thoroughly examine the impact of degree distribution and degree correlation on average controllability. Our results reveal that increased heterogeneity in degree distribution tends to enhance average controllability, particularly when edges connect nodes with higher degrees. Moreover, networks with high assortativity exhibit improved average controllability. Building on these findings, we propose two effective strategies for optimizing average controllability. These strategies offer valuable guidance for the design of optimal complex networks in practical settings.

This article investigates the distributed tracking problem of networked cyber-physical systems (CPSs), considering system uncertainties, output constraints, and false data injection (FDI) attacks. Notably, the FDI attacks modeled here are explicitly malicious, meaning they are designed to cause the system to violate prescribed output constraints. Motivated by the lack of constrained-control studies addressing situations where the reference signal does not meet the constraint, we introduce a new form of tracking error, termed barrier tracking error (BTE). It is valuable that any conventional control scheme can be combined with the BTE idea to deal with output constraints. Subsequently, a nonsingular finite-time controller is developed using the backstepping method and neural networks. It is worth mentioning that the controller employs an event-triggered quantized control strategy, effectively reducing the burden on channels and actuators. Finally, comprehensive stability analysis and simulations are provided.

Proper planning of charging infrastructure can significantly facilitate the popularization of electric vehicles and alleviate users’ mileage anxiety. Charging station siting and sizing are two key challenges in the planning with each of them being a complex optimization problem. In this paper, a multi-objective optimization approach is proposed to solve them together. First, considering that accurate charging demand estimation is crucial for planning, a traffic road network is established for this purpose. A Monte Carlo method is used to estimate the spatiotemporal distribution of charging demand in a region based on the probabilistic characteristics of user trips. Since uncoordinated charging not only increases the load but also leads to unstable operation of the local power system, a heuristic algorithm is proposed to coordinate charging scheduling. Then, based on the scheduled demand, this paper proposes a framework for the siting and sizing of charging stations to optimize the benefits for both operators and users by minimizing the construction, operation and maintenance costs, and the user’s detour time. As the given problem is a complex multi-objective combinatorial optimization problem, it is easy to fall into local optimum if traditional evolutionary algorithms are employed. Therefore, a multi-objective dynamic binary particle swarm optimization method is designed to solve this problem effectively. Finally, experimental simulations show that the proposed method outperforms the other comparative algorithms in terms of solution quality. A case study is presented to demonstrate the applicability and effectiveness of the proposed method in optimizing the location and capacity of charging stations.

Existing object-level SLAM methods often overlook the correspondence between semantic information and geometric features, resulting in a significant gap between them within SLAM frameworks. To tackle this issue, this paper proposes TiMoSLAM, a semantic-geometric tight-coupling monocular visual object SLAM system, which considers a rigorous correspondence between semantics and geometry across all steps of SLAM. Initially, a general Semantic Relation Graph (SRG) is developed to consistently represent semantic information alongside geometric features. Detailed analyses on complete constraints of the geometric feature combinations on estimation of 3D cuboid model are performed. Subsequently, a Compound Hypothesis Tree (CHT) is proposed to incrementally construct the object-specific SRG and concurrently estimate the 3D cuboid model of an object, ensuing semantic-geometric consistency in object representation and estimation. Special attention is given to the matching errors between geometric features and objects during the optimization of camera poses and object parameters. The effectiveness of this method is validated on various datasets, as well as in real-world environments.

This article investigates the problem of distributed optimization over multiagent networks with the global objective being the sum of a set of possibly nonconvex functions. Based on recent developments in distributed average tracking as well as distributed extremum seeking, a distributed bounded gradient-free optimization algorithm is proposed. It is shown that the proposed scheme is able to solve nonconvex optimization problems with arbitrary prescribed accuracy. The relationship between the optimization error and control parameters is established with the error bound’s explicit dependence on the bounds of agents’ control inputs, which clearly demonstrates a tradeoff between the optimization error and input bound. An illustrative example is included to validate the effectiveness of proposed scheme.

This article investigates an energy-efficient formation control problem for multiagent systems with sampled data and random packet losses. A Bernoulli stochastic variable is used to describe packet losses, which is defined relative to the transmission energy consumed by antennas. A distributed sampled-data formation control law is designed and some analytic sufficient conditions on the formation control are derived. It is revealed that the sampling period, control parameters, network topology, as well as the transmission energy used by sensors impose inherent limitations in achieving the formation. Also, a method for searching the minimum allowable transmission energy is presented. Finally, numerical simulations are shown for illustration and verification.

This article studies coordinated tracking of underactuated and uncertain autonomous surface vehicles (ASVs) via model-reference reinforcement learning control. It considered how model-reference control can be incorporated with reinforcement learning to address the challenges caused by model uncertainties and input underactuation, and how existing results may be employed to realize adaptive communication amongst ASVs. It is demonstrated that the proposed algorithm has a better performance over baseline control and effectively improves the training efficiency over reinforcement learning.

The time-varying economic dispatch over a network is considered where both the cost function and the equality constraint are time-varying. A distributed algorithm is first designed combing the prediction-correction framework and the consensus + innovations approach. In the prediction steps, the sensitivity analysis method is introduced to calculate the shift between the estimated and the exact optimization solution of the correction steps. Afterwards, the overall optimal errors in two steps are calculated by the sub-optimal analysis method. The convergence analysis shows that the dispatch errors are bounded and the convergence process is Q-linear. A dynamic prediction-correction algorithm is then presented to improve the accuracy at every time instant. Finally, numerical examples using the IEEE 118-bus system are presented to illustrate the validity of the algorithms.

The trace of the controllability Gramian quantifies the average controllability in all directions in the system state space. In this paper, we investigate the average controllability of a semistable networked system with Laplacian dynamics and derive upper and lower bounds on the trace of its pseudo-controllability Gramian matrix. We show that these bounds are solely determined by the network topology, which can be obtained without computing any higher-dimensional matrix. We find that a sparse or a scale-free network is easy to control in terms of the average controllability. We then investigate the effect of the edges with negative weights on the average controllability for a signed network with Laplacian dynamics. We find that a small number of negatively-weighted edges can significantly affect the average controllability of the signed network. We finally demonstrate that many real-world networks are easy to control via manipulating negatively-weighted edges.

This article studies the distributed average tracking (DAT) problem pertaining to a discrete-time linear time-invariant multiagent network, which is subject to, concurrently, input delays, random packet drops, and reference noise. The problem amounts to an integrated design of delay and a packet-drop-tolerant algorithm and determining the ultimate upper bound of the tracking error between agents' states and the average of the reference signals. The investigation is driven by the goal of devising a practically more attainable average tracking algorithm, thereby extending the existing work in the literature, which largely ignored the aforementioned uncertainties. For this purpose, a blend of techniques from Kalman filtering, multistage consensus filtering, and predictive control is employed, which gives rise to a simple yet comepelling DAT algorithm that is robust to the initialization error and allows the tradeoff between communication/computation cost and stationary-state tracking error. Due to the inherent coupling among different control components, convergence analysis is significantly challenging. Nevertheless, it is revealed that the allowable values of the algorithm parameters rely upon the maximal degree of an expected network, while the convergence speed depends upon the second smallest eigenvalue of the same network's topology. The effectiveness of the theoretical results is verified by a numerical example.

In this article, a class of distributed nonlinear placement problems is considered for a multicluster system. The task is to determine the positions of the agents in each cluster subject to the constraints on agent positions and the network topology. In particular, the agents in each cluster are placed to form the desired shape and minimize the sum of squares of the Euclidean lengths of the links amongst the center of each cluster and its corresponding cluster members. The problem is converted into a time-varying noncooperative game and then a distributed Nash equilibrium-seeking algorithm is designed based on a distributed observer method. A new iterative approach is employed to prove the convergence with the aid of the Lyapunov stability theorem. The effectiveness of the distributed algorithm is validated by numerical examples.

In this article, the distributed nonlinear placement problem for a class of multicluster Euler–Lagrange systems is considered. The problem is first converted into a time-varying noncooperative game. A distributed Nash equilibrium seeking algorithm composed of an auxiliary double-integrator system and a coordinated-tracking observer is designed to solve the problem. The convergence results are established by an iterative approach and the small gain theorem. The effectiveness of the algorithm is demonstrated via simulations.

This paper studies the inherent connection between dynamic region-following formation control (DRFFC) and distributed average tracking (DAT). We propose a fixed-gain DAT algorithm with robustness to initialization errors for linear multiagent systems, which is capable of achieving DAT with a zero tracking error for a large class of reference signals. In the case that the fixed gain cannot be chosen properly, we present an adaptive control gain design, under which each agent simply chooses its own gain and the restriction on knowing the upper bounds on the reference signals and their inputs is removed. We show that the proposed DAT algorithms can be employed to solve the DRFFC problem. This is an attempt on the applications of DAT algorithms to achieve distributed control; existing works most use DAT as distributed estimation algorithms. For single-integrator, double-integrator, higher-order linear dynamics, we derive the corresponding DRFFC algorithms from the DAT algorithm. Compared with existing DRFFC algorithms, the DAT-based DRFFC algorithms do not require the desired region to have a regular shape and is capable of generating a much richer formation behavior. Numerical examples are also included to show the validity of the derived results.