Zhisheng Duan

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, 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.

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.

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.

Yicheng Lin, Bingxian Wu, Nan Bai et al.

This paper investigates the impact of approximation error in data-driven optimal control problem of nonlinear systems while using the Koopman operator. While the Koopman operator enables a simplified representation of nonlinear dynamics through a lifted state space, the presence of approximation error inevitably leads to deviations in the computed optimal controller and the resulting value function. We derive explicit upper bounds for these optimality deviations, which characterize the worst-case effect of approximation error. Supported by numerical examples, these theoretical findings provide a quantitative foundation for improving the robustness of data-driven optimal controller design.

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.

Yunxiao Ren, Dingguo Liang, Yuezu Lv et al.

This paper investigates the leader-following consensus problem for a class of multi-agent systems subject to adversarial attack-like external inputs. To address this, we formulate the robust leader-following control problem as a global coalitional min-max zero-sum game using differential game theory. Specifically, the agents' control inputs form a coalition to minimize a global cost function, while the attacks form an opposing coalition to maximize it. Notably, when these external adversarial attacks manifest as disturbances, the designed game-theoretic control policy systematically yields a robust $H_\infty$ control law. Addressing this problem inherently requires solving a high-dimensional generalized algebraic Riccati equation (GARE), which poses significant challenges for distributed computation and controller implementation. To overcome these challenges, we propose a two-fold approach. First, a decentralized computational strategy is devised to decompose the high-dimensional GARE into multiple uniform, lower-dimensional GAREs. Second, a dynamic average consensus-based decoupling algorithm is developed to resolve the inherent coupling structure of the robust control law, thereby facilitating its distributed implementation. Finally, numerical simulations on the formation control of multi-vehicle systems with feedback-linearized dynamics are conducted to validate the effectiveness of the proposed algorithms.

Xiaoxu Lyu, Guanghui Wen, Yuezu Lv et al.

This paper proposes a novel consensus-based distributed filter over directed graphs under the collectively observability condition. The distributed filter is designed using an augmented leader-following information fusion strategy, and the gain parameter is determined exclusively using local information. Additionally, the lower bound of the fusion step number is derived to ensure that the estimation error covariance remains uniformly upper-bounded. Furthermore, the lower bounds for the convergence rates of the steady-state performance gap between the proposed filter and the centralized filter are provided as the fusion step number approaches infinity. The analysis demonstrates that the convergence rate is at least as fast as exponential convergence, provided the communication topology satisfies the spectral norm condition. Finally, the theoretical results are validated through two simulation examples.

Ganghui Cao, Shimin Wang, Martin Guay et al.

This paper investigates parameter learning problems under deficient excitation (DE). The DE condition is a rank-deficient, and therefore, a more general evolution of the well-known persistent excitation condition. Under the DE condition, a proposed online algorithm is able to calculate the identifiable and non-identifiable subspaces, and finally give an optimal parameter estimate in the sense of least squares. In particular, the learning error within the identifiable subspace exponentially converges to zero in the noise-free case, even without persistent excitation. The DE condition also provides a new perspective for solving distributed parameter learning problems, where the challenge is posed by local regressors that are often insufficiently excited. To improve knowledge of the unknown parameters, a cooperative learning protocol is proposed for a group of estimators that collect measured information under complementary DE conditions. This protocol allows each local estimator to operate locally in its identifiable subspace, and reach a consensus with neighbours in its non-identifiable subspace. As a result, the task of estimating unknown parameters can be achieved in a distributed way using cooperative local estimators. Application examples in system identification are given to demonstrate the effectiveness of the theoretical results developed in this paper.