It is with great pleasure and admiration that we celebrate the 60th birthday of Professor Lihua Xie, a distinguished researcher and visionary leader in the field of robust control and estimation. Prof. Xie’s remarkable journey, marked by outstanding achievements and groundbreaking contributions, has left an indelible mark on the world of engineering and academia.
Prof. Xie’s academic odyssey began at Nanjing University of Science and Technology, where he earned his bachelor’s and master’s degrees in 1983 and 1986, respectively. His pursuit of knowledge led him to the University of Newcastle, Australia, where he obtained his PhD in 1992. Since 1992, he has been a cornerstone of Nanyang Technological University (NTU), Singapore, currently serving as a distinguished professor in the School of Electrical and Electronic Engineering and as the Director of the Centre for Advanced Robotics Technology Innovation (CARTIN), NTU.
One of Prof. Xie’s pivotal contributions lies in the realm of robust control and estimation. His early work in the early 1990s addressed robust solutions for systems with parametric uncertainties, providing a profound understanding of how uncertainty influences control system performance. His pioneering research not only illuminated the impact of uncertainty but also offered effective strategies, particularly for parametric uncertainty, ensuring the robustness of control systems. Prof. Xie was among the first to develop robust estimation techniques for systems grappling with parametric uncertainties, influencing researchers globally since the 1990s.
In the past two decades, Prof. Xie, alongside his co-author, established a groundbreaking equivalence between quantized feedback and robust control. This breakthrough extended the applicability of existing robust control theory to the analysis and design of control systems operating under quantized feedback. His work also unraveled the intricate interplay among data rate, network topology, and agent dynamics in multi-agent consensus - a fundamental challenge in cooperative control. Prof. Xie’s research provided answers to crucial questions, such as determining the minimal data rate and network topology for multi-agent consensus, along with corresponding coding and decoding schemes.
The spectrum of Prof. Xie’s impact extends to compressive sensing, where he and his student established a phase transition relationship between sparsity and recoverability for complex signals. Their continuous compressive sensing algorithms and Vandermonde decomposition theory for multi-level Toeplitz matrices have found applications in array signal processing, marking another significant milestone in his illustrious career.
Beyond theoretical endeavors, Prof. Xie’s practical innovations have revolutionized localization and unmanned systems. His research group’s developments include a WiFi-based indoor positioning system, multi-modality sensor fusion technology, and a fully integrated navigation solution for UAVs. These innovations have found applications in diverse fields, from structure inspection and delivery using UAVs to a low-cost universal navigation system for AGVs in logistics and manufacturing.
In the realm of research and development leadership, Prof. Xie’s impact is equally profound. He is the founding Director of the Delta-NTU Corporate Laboratory for Cyber-physical Systems, which focuses on the development of smart manufacturing and smart learning technologies for industry. Additionally, Prof. Xie established the Centre for Advanced Robotics Technology Innovation, where he currently serves as the Director. The center’s mission is to pioneer advanced sensing and perception technologies, as well as collaborative robotics technologies, with applications in logistics, manufacturing, and elderly care.
As an accomplished researcher, Prof. Xie has demonstrated unparalleled dedication to serving the research community. His extensive editorial roles, including a founding Editor-inChief for Unmanned Systems and Associate Editor for Sciences China - Information Science, showcase his commitment to advancing scientific knowledge. He has played pivotal roles in various editorial boards, such as IET Book Series in Control and esteemed journals like IEEE Transactions on Automatic Control and Automatica.
Prof. Xie’s impact extends beyond editorial responsibilities; he has been a distinguished IEEE Distinguished Lecturer, a Board of Governors member for the IEEE Control System Society, and Vice President since January 2024. His leadership roles also include serving as General Chair of significant conferences, including the 62nd IEEE Conference on Decision and Control in December 2023.
His professional achievements, recognized by peers worldwide, include fellowships in the Academy of Engineering Singapore, the Institute of Electrical and Electronics Engineers (IEEE), International Federation of Automatic Control (IFAC), and the Chinese Automation Association (CAA).
In celebration of Prof. Xie’s 60th birthday, we invited 17 papers from friends and colleagues for this special issue. As editors, we extend our deepest gratitude to all the authors for their invaluable contributions. Special thanks to the Journal of Systems Science & Complexity editorial office, including Prof. Xiao-Shan Gao (Editor-in-Chief), Prof. Yanlong Zhao (Managing Editor), and Ms. Guoyun Wu (Editorial Director), for their steadfast support from the conception to the publication of this special issue.
On this momentous occasion, we express our profound appreciation for Prof. Lihua Xie for his unwavering commitment to advancing knowledge and look forward to the continued brilliance and innovation in the next chapters of his illustrious career.
Happy Birthday, Prof. Lihua Xie!

This paper focuses on optimizing an unknown cost function through extremum seeking (ES) control in the presence of a slow nonlinear dynamic sensor responsible for measuring the cost. In contrast to traditional perturbation-based ES control, which often suffers from sluggish convergence, the proposed method eliminates the time-scale separation between sensor dynamics and ES control by using the relative degree of the nonlinear sensor system. To improve the convergence rate, the authors incorporate high-frequency dither signals and a differentiator. To enhance the robustness with the existence of rapid disturbances, an off-the-shelf linear high-gain differentiator is applied. The first result demonstrates that, for any desired convergence rate, with properly tuned parameters for the proposed ES algorithm, the input of the cost function can converge to an arbitrarily small neighborhood of the optimal solution, starting from any initial condition within any given compact set. Furthermore, the second result shows the robustness of the proposed ES control in the presence of sufficiently fast, zero-mean periodic disturbances. Simulation results substantiate these theoretical findings.

This paper considers the problem of approximating the infinite-horizon value function of the discrete-time switched LQR problem. In particular, the authors propose a new value iteration method to generate a sequence of monotonically decreasing functions that converges exponentially to the value function. This method facilitates us to use coarse approximations resulting from faster but less accurate algorithms for further value iteration, and thus, the proposed approach is capable of achieving a better approximation for a given computation time compared with the existing methods. Three numerical examples are presented in this paper to illustrate the effectiveness of the proposed method.

In this paper, a distributed cooperative control protocol is presented to deal with actuator failures of multi-agent systems in the presence of connectivity preservation. With the developed strategy, each agent can track the reference trajectory of the leader in the presence of actuator failures, disturbances and uncertainties. The connectivity of the multi-agent system can always be ensured during the control process. To achieve the aforementioned control objectives, a potential function is introduced to the distributed adaptive fault-tolerant control algorithm to preserve the initial connected network among the agents. The uncertainty of the multi-agent system, which is allowed to be described by discontinuous functions, is approximated and compensated using the fuzzy logic system. The asymptotic stability of the closed-loop system is demonstrated through the use of Cellina’s approximate selection theorem of nonsmooth analysis. Due to the developed adaptive laws, the upper bound of the disturbance is allowed to be uncertain, which facilitates the implementation of the control scheme. Finally, simulation results are provided to verify the effectiveness of the proposed control scheme.

This paper studies the distributed Nash equilibrium seeking (DNES) problem for games whose action sets are compact and whose network graph is switching satisfying the jointly strongly connected condition. To keep the actions of all players in their action sets all the time, one has to resort to the projected gradient-based method. Under the assumption that the unique Nash equilibrium is the unique equilibrium of the pseudogradient system, an algorithm is proposed that is able to exponentially find the Nash equilibrium. Further, the authors also consider the distributed Nash equilibrium seeking problem for games whose actions are governed by high-order integrator dynamics and belong to some compact sets. Two examples are used to illustrate the proposed approach.

It is a significant research direction for highly complex musculoskeletal robots that how to develop the ability of motion learning and generalization. The cooperations of multiple brain regions are crucial to improving motion performance. Inspired by the neural mechanisms of structures, functions, and interconnections of basal ganglia and cerebellum, a biologically inspired integration model for motor learning of musculoskeletal robots is proposed. Based on the neural characteristics of the basal ganglia, the basal ganglia actor network, which mainly simulates the dorsal striatum, outputs motion commands, and the basal ganglia critic network, which simulates the ventral striatum, estimates actionstate values. Their network parameters are updated using the soft actor-critic method. Based on the sensorimotor prediction mechanism of the cerebellum, the cerebellum network evaluates the state feature extraction quality of the basal ganglia actor network and then updates the weights of its feature layer. This learning method is proven to converge to the optimal policy. Furthermore, drawing on the mechanism of dopaminergic dynamic regulation in the basal ganglia, the adaptive adjustment of target entropy and the dopaminergic experience replay are proposed to further improve the integration model, which contributes to the exploration-exploitation trade-off of motor learning. The bio-inspired integration model is validated on a musculoskeletal system. Experimental results indicate that this model can effectively control the musculoskeletal robot to accomplish the motion task from random starting locations to random target positions with high precision and robustness.

This paper presents a learning-based control policy design for point-to-point vehicle positioning in the urban environment via BeiDou navigation. While navigating in urban canyons, the multipath effect is a kind of interference that causes the navigation signal to drift and thus imposes severe impacts on vehicle localization due to the reflection and diffraction of the BeiDou signal. Here, the authors formulated the navigation control system with unknown vehicle dynamics into an optimal control-seeking problem through a linear discrete-time system, and the point-to-point localization control is modeled and handled by leveraging off-policy reinforcement learning for feedback control. The proposed learning-based design guarantees optimality with prescribed performance and also stabilizes the closed-loop navigation system, without the full knowledge of the vehicle dynamics. It is seen that the proposed method can withstand the impact of the multipath effect while satisfying the prescribed convergence rate. A case study demonstrates that the proposed algorithms effectively drive the vehicle to a desired setpoint under the multipath effect introduced by actual experiments of BeiDou navigation in the urban environment.

In this paper, the authors study the cooperative target-fencing problem for n-dimensional systems and a target with a general trajectory. Without using the velocity of the vehicles, a position feedback control law is proposed to fence the general target into the convex hull formed by the vehicles. Specifically, the dynamics of each vehicle is described by a double-integrator system. Two potential functions are designed to guarantee connectivity preservation of the communication network and collision avoidance among the vehicles. The proposed approach can deal with a target whose trajectory is any twice continuously differentiable function of time. The effectiveness of the result is verified by a numerical example.

Quantized feedback control is fundamental to system synthesis with limited communication capacity. In sharp contrast to the existing literature on quantized control which requires an explicit dynamical model, the authors study the quadratic stabilization and performance control problems with logarithmically quantized feedback in a direct data-driven framework, where the system state matrix is not exactly known and instead, belongs to an ambiguity set that is directly constructed from a finite number of noisy system data. To this end, the authors firstly establish sufficient and necessary conditions via linear matrix inequalities for the existence of a common quantized controller that achieves our control objectives over the ambiguity set. Then, the authors provide necessary conditions on the data for the solvability of the LMIs, and determine the coarsest quantization density via semi-definite programming. The theoretical results are validated through numerical examples.

The semi-tensor product (STP) of matrices is generalized to multidimensional arrays, called the compound product of hypermatrices. The product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general cases. Three different types of hyperdeterminants are introduced and certain properties are revealed. The Lie groups and Lie algebras corresponding to the hypermatrix products are constructed. Finally, these results are applied to dynamical systems.

This paper focuses on the performance of equalizer zero-determinant (ZD) strategies in discounted repeated Stackelberg asymmetric games. In the leader-follower adversarial scenario, the strong Stackelberg equilibrium (SSE) deriving from the opponents’ best response (BR), is technically the optimal strategy for the leader. However, computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states. To this end, the authors propose an equalizer ZD strategy, which can unilaterally restrict the opponent’s expected utility. The authors first study the existence of an equalizer ZD strategy with one-to-one situations, and analyze an upper bound of its performance with the baseline SSE strategy. Then the authors turn to multi-player models, where there exists one player adopting an equalizer ZD strategy. The authors give bounds of the weighted sum of opponents’s utilities, and compare it with the SSE strategy. Finally, the authors give simulations on unmanned aerial vehicles (UAVs) and the moving target defense (MTD) to verify the effectiveness of the proposed approach.

This paper is concerned with the optimal threshold selection and resource allocation problems of quantized identification, whose aims are improving identification efficiency under limited resources. Firstly, the first-order asymptotically optimal quantized identification theory is extended to the weak persistent excitation condition. Secondly, the characteristics of time and space complexities are established based on the Cram′er-Rao lower bound of quantized systems. On these basis, the optimal selection methods of fixed thresholds and adaptive thresholds are established under aperiodic signals, which answer how to achieve the best efficiency of quantized identification under the same time and space complexity. In addition, based on the principle of maximizing the identification efficiency under a given resource, the optimal resource allocation methods of quantized identification are given for the cases of fixed thresholds and adaptive thresholds, respectively, which show how to balance time and space complexity to realize the best identification efficiency of quantized identification.

This paper focuses on linear-quadratic (LQ) optimal control for a class of systems governed by first-order hyperbolic partial differential equations (PDEs). Different from most of the previous works, an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems. The contributions of this paper consist of the following aspects: 1) The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method. 2) A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed. Meanwhile, the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations (FBPDEs). 3) The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented. It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case, but also support the existing operator results and give a more convenient form of computation.

This paper investigates the cooperative adaptive optimal output regulation problem of continuous-time linear multi-agent systems. As the multi-agent system dynamics are uncertain, solving regulator equations and the corresponding algebraic Riccati equations is challenging, especially for high-order systems. In this paper, a novel method is proposed to approximate the solution of regulator equations, i.e., gradient descent method. It is worth noting that this method obtains gradients through online data rather than model information. A data-driven distributed adaptive suboptimal controller is developed by adaptive dynamic programming, so that each follower can achieve asymptotic tracking and disturbance rejection. Finally, the effectiveness of the proposed control method is validated by simulations.

Network localization serves as a fundamental component for enabling various position based operations in multi-agent systems, facilitating tasks like target searching and formation control by providing accurate position information for all nodes in the network. Network localization focuses on the challenge of determining the positions of nodes within a network, relying on the known positions of anchor nodes and internode relative measurements. Over the past few decades, distributed network localization has garnered significant attention from researchers. This paper aims to provide a review of main results and advancements in the field of distributed network localization, with a particular focus on the perspective of graph Laplacian. Owning to its favorable characteristics, graph Laplacian unifies various network localization, even when dealing with diverse types of internode relative measurements, into a unified protocol framework, which can be constructed by a linear method and ensure the global convergence.

This paper is devoted to event-triggered synchronization of delayed memristive neural networks with H_∞ and passivity performance. The aim is to guarantee the exponential synchronization and mixed H_∞ and passivity control for memristive neural networks by using event-triggered control. Firstly, a switching system is constructed under the event-triggered control strategy. Then, by adopting a piece-wise Lyapunov functional, a sufficient condition is established for the exponential synchronization and mixed H_∞ and passivity performance. Moreover, an event-triggered controller design scheme is proposed using matrix decoupling method. Finally, the effectiveness of the designed controller is exemplified by a numerical example.

This paper investigates the stability problem for sampled-data systems by adopting a refined semi-looped-functional, which is with the following two improvements. Firstly, the new functional term is with a new integral vector η₀, which contains sampling information of the systems and associates two commonly used vectors. Secondly, the vector η₀ is combined into various zero equations for processing the functional, especially where a new equation is derived from η₀. Based on the refined functional, further stability results for sampled-data systems are obtained. And the effectiveness of the results is numerically verified through two examples at the end.

In this paper, the authors consider how to design defensive countermeasures against DoS attacks for remote state estimation of multiprocess systems. For each system, a sensor will measure its state and transmits the data packets through an unreliable channel which is vulnerable to be jammed by an attacker. Under limited communication bandwidth, only a subset of sensors are allowed for data transmission, and how to select the optimal one to maximize the accuracy of remote state estimation is the focus of the proposed work. The authors first formulate this problem as a Markov decision process and investigate the existence of optimal policy. Moreover, the authors demonstrate the piecewise monotonicity structure of optimal policy. Given the difficulty of obtaining an optimal policy of large-scale problems, the authors develop a suboptimal heuristic policy based on the aforementioned policy structure and Whittle’s index. Moreover, a closed form of the indices is derived in order to reduce implementation complexity of proposed scheduling policy and numerical examples are provided to illustrate the proposed developed results.

Mobile Edge Computing (MEC) provides communication and computational capabilities for the industrial Internet, meeting the demands of latency-sensitive tasks. Nevertheless, traditional model-driven task offloading strategies face challenges in adapting to situations with unknown network communication status and computational capabilities. This limitation becomes notably significant in complex industrial networks of high-speed railway. Motivated by these considerations, a data and model-driven task offloading problem is proposed in this paper. A redundant communication network is designed to adapt to anomalous channel states when tasks are offloaded to edge servers. The link switching mechanism is executed by the train according to the attributes of the completed task. The task offloading optimization problem is formulated by introducing data-driven prediction of communication states into the traditional model. Furthermore, the optimal strategy is achieved by employing the informer-based prediction algorithm and the quantum particle swarm optimization method, which effectively tackle real-time optimization problems due to their low time complexity. The simulations illustrate that the data and model-driven task offloading strategy can predict the communication state in advance and increase the cost and robustness of the system.

The multi-UAV adversary swarm defense (MUASD) problem is to defend a static base against an adversary UAV swarm by a defensive UAV swarm. Decomposing the problem into task assignment and low-level interception strategies is a widely used approach. Learning-based approaches for task assignment are a promising direction. Existing studies on learning-based methods generally assume decentralized decision-making architecture, which is not beneficial for conflict resolution. In contrast, centralized decision-making architecture is beneficial for conflict resolution while it is often detrimental to scalability. To achieve scalability and conflict resolution simultaneously, inspired by a self-attention-based task assignment method for sensor target coverage problem, a scalable centralized assignment method based on self-attention mechanism together with a defender-attacker pairwise observation preprocessing (DAP-SelfAtt) is proposed. Then, an imperative-priori conflict resolution (IPCR) mechanism is proposed to achieve conflict-free assignment. Further, the IPCR mechanism is parallelized to enable efficient training. To validate the algorithm, a variant of proximal policy optimization algorithm (PPO) is employed for training in scenarios of various scales. The experimental results show that the proposed algorithm not only achieves conflict-free task assignment but also maintains scalability, and significantly improve the success rate of defense.