Zhongkui Li

Zhongkui Li, Guanghui Wen, Zhisheng Duan et al.

This paper addresses the distributed consensus protocol design problem for multi-agent systems with general linear dynamics and directed communication graphs. Existing works usually design consensus protocols using the smallest real part of the nonzero eigenvalues of the Laplacian matrix associated with the communication graph, which however is global information. In this paper, based on only the agent dynamics and the relative states of neighboring agents, a distributed adaptive consensus protocol is designed to achieve leader-follower consensus for any communication graph containing a directed spanning tree with the leader as the root node. The proposed adaptive protocol is independent of any global information of the communication graph and thereby is fully distributed. Extensions to the case with multiple leaders are further studied.

Zhongkui Li, Wei Ren, Xiangdong Liu et al.

This paper considers the distributed consensus problems for multi-agent systems with general linear and Lipschitz nonlinear dynamics. Distributed relative-state consensus protocols with an adaptive law for adjusting the coupling weights between neighboring agents are designed for both the linear and nonlinear cases, under which consensus is reached for all undirected connected communication graphs. Extensions to the case with a leader-follower communication graph are further studied. In contrast to the existing results in the literature, the adaptive consensus protocols here can be implemented by each agent in a fully distributed fashion without using any global information.

Zhongkui Li, Xiangdong Liu, Wei Ren et al.

This paper considers the distributed consensus problem of multi-agent systems with general continuous-time linear dynamics. Two distributed adaptive dynamic consensus protocols are proposed, based on the relative output information of neighboring agents. One protocol assigns an adaptive coupling weight to each edge in the communication graph while the other uses an adaptive coupling weight for each node. These two adaptive protocols are designed to ensure that consensus is reached in a fully distributed fashion for any undirected connected communication graphs without using any global information. A sufficient condition for the existence of these adaptive protocols is that each agent is stabilizable and detectable. The cases with leader-follower and switching communication graphs are also studied.

Zhongkui Li, Zhisheng Duan, Lihua Xie et al.

This paper considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous- and discrete-time multi-agent systems, based on the relative states of neighboring agents and a subset of absolute states of the agents. It is shown for both the continuous- and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the $H_\infty$ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust $H_\infty$ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed.

Zhongkui Li, Xiangdong Liu, Mengyin Fu et al.

This paper addresses the global consensus problems of a class of nonlinear multi-agent systems with Lipschitz nonlinearity and directed communication graphs, by using a distributed consensus protocol based on the relative states of neighboring agents. A two-step algorithm is presented to construct a protocol, under which a Lipschitz multi-agent system without disturbances can reach global consensus for a strongly connected directed communication graph. Another algorithm is then given to design a protocol which can achieve global consensus with a guaranteed $H_\infty$ performance for a Lipschitz multiagent system subject to external disturbances. The case with a leader-follower communication graph is also discussed. Finally, the effectiveness of the theoretical results is demonstrated through a network of single-link manipulators.

Zhongkui Li, Zhisheng Duan, Guanrong Chen

This paper concerns the consensus of discrete-time multi-agent systems with linear or linearized dynamics. An observer-type protocol based on the relative outputs of neighboring agents is proposed. The consensus of such a multi-agent system with a directed communication topology can be cast into the stability of a set of matrices with the same low dimension as that of a single agent. The notion of discrete-time consensus region is then introduced and analyzed. For neurally stable agents, it is shown that there exists an observer-type protocol having a bounded consensus region in the form of an open unit disk, provided that each agent is stabilizable and detectable. An algorithm is further presented to construct a protocol to achieve consensus with respect to all the communication topologies containing a spanning tree. Moreover, for the case where the agents have no poles outside the unit circle,an algorithm is proposed to construct a protocol having an origin-centered disk of radius $δ$ ($0<δ<1$) as its consensus region, where $δ$ has to further satisfy a constraint related to the unstable eigenvalues of a single agent for the case where each agent has a least one eigenvalue outside the unit circle. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.

Yuezu Lv, Zhongkui Li, Zhisheng Duan et al.

This paper addresses the distributed consensus protocol design problem for linear multi-agent systems with directed graphs and external unmatched disturbances. A novel distributed adaptive consensus protocol is proposed to achieve leader-follower consensus for any directed graph containing a directed spanning tree with the leader as the root node. It is noted that the adaptive protocol might suffer from a problem of undesirable parameter drift phenomenon when bounded external disturbances exist. To deal with this issue, a distributed robust adaptive consensus protocol is designed to guarantee the ultimate boundedness of both the consensus error and the adaptive coupling weights in the presence of external disturbances. Both adaptive protocols are fully distributed, relying on only the agent dynamics and the relative states of neighboring agents.

Bin Cheng, Zhongkui Li

This paper considers the distributed event-triggered consensus problem for general linear multi-agent networks. Both the leaderless and leader-follower consensus problems are considered. Based on the local sampled state or local output information, distributed adaptive event-triggered protocols are designed, which can ensure that consensus of the agents is achieved and the Zeno behavior is excluded by showing that the interval between any two triggering events is lower bounded by a strictly positive value. Compared to the previous related works, our main contribution is that the proposed adaptive event-based protocols are fully distributed and scalable, which do not rely on any global information of the network graph and are independent of the network's scale. In these event-based protocols, continuous communications are not required for either control laws updating or triggering functions monitoring.

Yu Zhao, Yongfang Liu, Zhongkui Li et al.

This paper studies the distributed average tracking problem for multiple time-varying signals generated by linear dynamics, whose reference inputs are nonzero and not available to any agent in the network. In the edge-based framework, a pair of continuous algorithms with, respectively, static and adaptive coupling strengths are designed. Based on the boundary layer concept, the proposed continuous algorithm with static coupling strengths can asymptotically track the average of multiple reference signals without the chattering phenomenon. Furthermore, for the case of algorithms with adaptive coupling strengths, average tracking errors are uniformly ultimately bounded and exponentially converge to a small adjustable bounded set. Finally, a simulation example is presented to show the validity of theoretical results.

Zhongkui Li, Jie Chen

In this paper, we study the robust consensus problem for a set of discrete-time linear agents to coordinate over an uncertain communication network, which is to achieve consensus against the transmission errors and noises resulted from the information exchange between the agents. We model the network by means of communication links subject to multiplicative stochastic uncertainties, which are susceptible to describing packet dropout, random delay, and fading phenomena. Different communication topologies, such as undirected graphs and leader-follower graphs, are considered. We derive sufficient conditions for robust consensus in the mean square sense. This results unveil intrinsic constraints on consensus attainment imposed by the network synchronizability, the unstable agent dynamics, and the channel uncertainty variances. Consensus protocols are designed based on the state information transmitted over the uncertain channels, by solving a modified algebraic Riccati equation.

Zhongkui Li, Zhisheng Duan

This paper addresses the distributed attitude synchronization problem of multiple spacecraft with unknown inertia matrices. Two distributed adaptive controllers are proposed for the cases with and without a virtual leader to which a time-varying reference attitude is assigned. The first controller achieves attitude synchronization for a group of spacecraft with a leaderless communication topology having a directed spanning tree. The second controller guarantees that all spacecraft track the reference attitude if the virtual leader has a directed path to all other spacecraft. Simulation examples are presented to illustrate the effectiveness of the results.

Yuezu Lv, Zhongkui Li, Zhisheng Duan et al.

This paper studies output feedback consensus protocol design problems for linear multi-agent systems with directed graphs. We consider both leaderless and leader-follower consensus with a leader whose control input is nonzero and bounded. We propose a novel sequential observer design approach, which makes it possible to design fully distributed adaptive output feedback protocols that the existing methods fail to accomplish. With the sequential observer architecture, we show that leaderless consensus can be achieved for any strongly connected directed graph in a fully distributed manner, whenever the agents are stabilizable and detectable. For the case with a leader of bounded control input, we further present novel distributed adaptive output feedback protocols, which include nonlinear functions to deal with the effect of the leaders's nonzero control input and are able to achieve leader-follower consensus for any directed graph containing a directed spanning tree with the leader as the root.

Bin Cheng, Yuezu Lv, Zhongkui Li et al.

This paper studies the consensus control problem faced with three essential demands, namely, discrete control updating for each agent, discrete-time communications among neighboring agents, and the fully distributed fashion of the controller implementation without requiring any global information of the whole network topology. Noting that the existing related results only meeting one or two demands at most are essentially not applicable, in this paper we establish a novel framework to solve the problem of fully distributed consensus with discrete communication and control. The first key point in this framework is the design of controllers that are only updated at discrete event instants and do not depend on global information by introducing time-varying gains inspired by the adaptive control technique. Another key point is the invention of novel dynamic triggering functions that are independent of relative information among neighboring agents. Under the established framework, we propose fully distributed state-feedback event-triggered protocols for undirected graphs and also further study the more complexed cases of output-feedback control and directed graphs. Finally, numerical examples are provided to verify the effectiveness of the proposed event-triggered protocols.

Zhongkui Li, Zhisheng Duan

This paper addresses the distributed consensus design problem for linear multi-agent systems with directed communication graphs and external disturbances. Both the cases with strongly connected communication graphs and leader-follower graphs containing a directed spanning tree with the leader as the root are discussed. Distributed adaptive consensus protocols based on the relative states of neighboring agents are designed, which can ensure the ultimate boundedness of the consensus error and adaptive gains in the presence of external disturbances. The upper bounds of the consensus error are further explicitly given. Compared to the existing consensus protocols, the merit of the adaptive protocols proposed in this paper is that they can be computed and implemented in a fully distributed fashion and meanwhile are robust with respect to external disturbances.

Qisheng Zhao, Meng Guo, Hengxuan Du et al.

Multi-robot systems can be extremely efficient for accomplishing team-wise tasks by acting concurrently and collaboratively. However, most existing methods either assume static task features or simply replan when environmental changes occur. This paper addresses the challenging problem of coordinating multi-robot systems for collaborative tasks involving dynamic and moving targets. We explicitly model the uncertainty in target motion prediction via Conformal Prediction(CP), while respecting the spatial-temporal constraints specified by Linear Temporal Logic (LTL). The proposed framework (UMBRELLA) combines the Monte Carlo Tree Search (MCTS) over partial plans with uncertainty-aware rollouts, and introduces a CP-based metric to guide and accelerate the search. The objective is to minimize the Conditional Value at Risk (CVaR) of the average makespan. For tasks released online, a receding-horizon planning scheme dynamically adjusts the assignments based on updated task specifications and motion predictions. Spatial and temporal constraints among the tasks are always ensured, and only partial synchronization is required for the collaborative tasks during online execution. Extensive large-scale simulations and hardware experiments demonstrate substantial reductions in both the average makespan and its variance by 23% and 71%, compared with static baselines.

Huaiyi Mu, Yujie Tang, Jie Song et al.

This paper investigates distributed zeroth-order optimization for smooth nonconvex problems, targeting the trade-off between convergence rate and sampling cost per zeroth-order gradient estimation in current algorithms that use either the $2$-point or $2d$-point gradient estimators. We propose a novel variance-reduced gradient estimator that either randomly renovates a single orthogonal direction of the true gradient or calculates the gradient estimation across all dimensions for variance correction, based on a Bernoulli distribution. Integrating this estimator with gradient tracking mechanism allows us to address the trade-off. We show that the oracle complexity of our proposed algorithm is upper bounded by $O(d/ε)$ for smooth nonconvex functions and by $O(dκ\ln (1/ε))$ for smooth and gradient dominated nonconvex functions, where $d$ denotes the problem dimension and $κ$ is the condition number. Numerical simulations comparing our algorithm with existing methods confirm the effectiveness and efficiency of the proposed gradient estimator.

Yicheng Lin, Bingxian Wu, Nan Bai et al.

The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This raises a distinct and fundamental question on optimality robustness, specifically, how uncertainties affect the optimal solution itself. To address this problem, we adopt a unified analysis-to-design perspective for systematically quantifying and improving optimality robustness. At the analysis level, we derive explicit upper bounds on the deviations of both the value function and the optimal controller, where uncertainties from multiple sources are systematically integrated into a unified norm-bounded representation. At the design level, we develop a robustness-aware optimal control methodology that provably reduces such optimality deviations, thereby enhancing robustness while explicitly revealing a quantitative trade-off between nominal optimality and robustness. As for practical implementation aspect, we further propose a tractable policy iteration algorithm, whose well-posedness and convergence are established via vanishing viscosity regularization and elliptic partial differential equation (PDE) techniques. Numerical examples validate the theoretical findings and demonstrate the effectiveness of proposed methodology.

Junfeng Chen, Yuxiao Zhu, An Zhuo et al.

Robot swarms promise scalable assistance in complex and hazardous environments. Task planning lies at the core of human-swarm collaboration, translating the operator's intent into coordinated swarm actions and helping determine when validation or intervention is required during execution. In long-horizon missions under dynamic scenarios, however, reliable task planning becomes difficult to maintain: emerging events and changing conditions demand continual adaptation, and sustained operator oversight imposes substantial cognitive burden. Existing LLM-based planning tools can support plan generation, yet they remain susceptible to invalid task orderings and infeasible robot actions, resulting in frequent manual adjustment. Here we introduce a neuro-symbolic framework for long-horizon human-swarm collaboration that tightly melds verifiable task planning with context-grounded LLM reasoning. We formalize mission goals and operational rules as temporal logic formulas and admissible task orderings as task automata. Conditioned on these formal constraints and live perceptual context, LLMs generate executable subtask sequences that satisfy mission rules and remain grounded in the current scene. An uncertainty-aware scheduler then assigns subtasks across the heterogeneous swarm to maximize parallelisms while remaining resilient to disruptions. An event-triggered interaction protocol further limits operator involvement to sparse, high-level confirmation and guidance. Deployment on a heterogeneous robotic fleet yields similar results while remaining robust to hardware-specific actuation and communication uncertainties. Together, these results support a formal and scalable paradigm for reliable and low-overhead human-swarm collaboration in dynamic environments

Yuda Chen, Meng Guo, Zhongkui Li

Online collision-free trajectory generation within a shared workspace is fundamental for most multi-robot applications. However, many widely-used methods based on model predictive control (MPC) lack theoretical guarantees on the feasibility of underlying optimization. Furthermore, when applied in a distributed manner without a central coordinator, deadlocks often occur where several robots block each other indefinitely. Whereas heuristic methods such as introducing random perturbations exist, no profound analyses are given to validate these measures. Towards this end, we propose a systematic method called infinite-horizon model predictive control with deadlock resolution. The MPC is formulated as a convex optimization over the proposed modified buffered Voronoi with warning band. Based on this formulation, the condition of deadlocks is formally analyzed and proven to be analogous to a force equilibrium. A detection-resolution scheme is proposed, which can effectively detect deadlocks online before they even happen. Once detected, it utilizes an adaptive resolution scheme to resolve deadlocks, under which no stable deadlocks can exist under minor conditions. In addition, the proposed planning algorithm ensures recursive feasibility of the underlying optimization at each time step under both input and model constraints, is concurrent for all robots and requires only local communication. Comprehensive simulation and experiment studies are conducted over large-scale multi-robot systems. Significant improvements on success rate are reported, in comparison with other state-of-the-art methods and especially in crowded and high-speed scenarios.