Modeling,optimization,and control for complex networked systems

Over the last decade, a succession of various complex systems has emerged in the field of automatic control, following the rapid development of information and communication technologies, such as manufacturing and production systems, robotics, spacecraft, smart grids, and intelligent transportation. The development of network technology brings many challenges for the modeling, control, and optimization of today’s complex systems, as well as their engineering applications. In recent years, some preliminary results have emerged on complex systems in network environments, ranging from academic research to industrial applications, including Antsaklis and Baillieul, ¹ Zhang et al., ² Zhang et al., ³ Zhu et al., ⁴ Hespanha et al., ⁵ Gupta and Chow. ⁶ More and more researchers are working on addressing various analysis and synthesis issues simultaneously, compensating for the deficiencies associated with this medium. Therefore, the main purpose of this special collection is to brief researchers on both the theory and practice of advances in modeling, optimization, and control for complex dynamic systems in network environments, especially on those developments that have been made in the field of engineering, and mechanical engineering in particular.

This special collection consists of 12 papers, all of which cover, but are not limited to, the proposed topics and can be divided into three groups. The first group mainly focuses on the issues of modeling and simulation analysis for mechanical systems in network environments, while the second addresses the issue of advanced control in complex networked systems. Finally, the third group is concerned with stability analysis and optimization for complex networked systems.

In the first group, the paper by Tian et al. ⁷ presents an omnidirectional mobile platform with six mecanum wheels, positing that an omnidirectional mobile platform with six mecanum wheels is more flexible and can reach the desired position more easily in narrow workspaces. The kinematic model for this platform is constructed and verified using four kinds of motion state in the simulation. The motion features of the platform corresponding to the cases of six and four wheels are discussed, and the authors demonstrate the advantages of the platform with six wheels. Moreover, thanks to the additional wheels, the developed platform can still move to the target position in the event of wheel failure. The simulation results are nearly identical to the results obtained by theoretical calculation, which implies the utility of the presented mathematical model.

The paper presented by Ma et al. ⁸ propose a support vector machine (SVM)-based recognition method to classify low-level wind shear images measured by laser detection and ranging. The partial scanning images are used to decrease the calculation time and to avoid wind field inversion.

Classification is performed via the SVM approach and the parameters are optimized using the K-fold cross-validation technique. The simulation results imply that the proposed approach is very significant for aircraft, providing advanced warning of low-level wind shear during takeoff and landing.

The last two papers in this group are concerned with experimental and numerical simulation research in real scenarios. In the paper by Liang et al., ⁹ an approach based on the hindrances cyclists encounter is proposed to be suitable for assessing the level of service and operational performance of dedicated bike lanes in China. A dynamic simulation model is developed to describe the characteristics of bicycle movement. In the paper by Zhi et al., ¹⁰ the spectral radius of extremal graphs for the unicyclic graphs is investigated using graft transformation and matching, and the upper bounds of the spectral radius of unicyclic graphs are obtained using the relations between degree and the second degree. The second group starts with a paper on finite-time controller design for coupled spacecraft formation with actuator saturation by Ye et al. ¹¹ This article investigates the consensus tracking control issue for a class of leader–follower spacecraft formation system, considering the occurrence of model uncertainties, external disturbances, and actuator saturation. A 6-degree-of-freedom (DOF) relative-coupled translational and rotational dynamics model is derived with the aid of exponential coordinates on the Lie group SE(3). A fast terminal sliding mode control law has then been developed to ensure the tracking control purpose within a specified time to avoid these shortcomings.

The next three papers in this group are also mainly focused on the issue of advanced control for complex systems. In the paper by Xu et al., ¹² by virtue of a combined cross-coupling error control method, a novel master–slave synchronization control strategy is proposed for a class of multi-layer and multi-axis systems. The obtained dynamic synchronization performance is better than that obtained via the minimum adjacent coupling control strategy, and the experimental results demonstrate the effectiveness of the developed control approaches.

In the paper by Zhao et al., ¹³ the authors investigate a strict passivity performance requirement to resolve a memory-based state feedback control issue in the delta domain for a class of Takagi–Sugeno fuzzy systems, and the corresponding nonlinear output is formulated as the passive output satisfying a prescribed strict passivity performance. The stability analysis and passivity criterion are dealt with via a fuzzy Lyapunov–Krasovskii functional approach, and the desired strictly passive memory–based controller is designed using the linear matrix inequality (LMI) technique.

The last paper in the second group, by Koo et al., ¹⁴ presents an event-triggered proportional–derivative control scheme for a class of Lur’e-type nonlinear networked control systems. Time-varying transmission delay with lower and upper delay bounds and nonlinearity with sector bounds are considered in the system. An event-triggering condition considering both state and state derivation is proposed to adjust the triggering dependency between them, which takes the form of LMIs. A rotational and translational actuator (RTAC) benchmark problem is studied to show the advantages of the proposed event-triggered control scheme.

In the last group, the first paper, by Wu et al., ¹⁵ is concerned with robust stability analysis for a class of uncertain neutral systems with mixed time-varying delays. A less conservative stability condition is derived by introducing a new Lyapunov–Krasovskii functional comprising a quadruple integral term, and the corresponding discrete and neutral delay-dependent stability criterion is given based on a delay-central point method and reciprocally convex combination approach. Several numerical examples are illustrated to show the superiority of the developed approach.

The other two papers in the group are concentrated on the practical application of optimization algorithms. In the paper by Lu et al., ¹⁶ a hierarchical framework is proposed to coordinate the optimization of timetables with an electronic multiple unit (EMU) circulation plan, and the space–time network-based problem illustration is presented. A special tree construction–based branch-and-bound algorithm is proposed to solve the electric motor train unit circulation planning (sub)model, and the quality of the EMU circulation plan is evaluated via the submodel. In the paper by Hong et al., ¹⁷ a simple and effective method is proposed to estimate the average convergence rate of clonal selection algorithms, by introducing the best individual transition probability matrix. Simulation experiments are conducted to validate the effectiveness and usability of the estimation approach.

The final paper in this group, by Xu, ¹⁸ applies the H∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delays and parameter uncertainties using the delta operator approach. The time-varying delays and parameter uncertainties are supposed to be of an internal-like type and a structured linear fractional form, respectively. A sufficient condition is derived with the help of the Lyapunov–Krasovskii functional in the delta domain.

As the Guest Editors of this special collection, we are soberly aware that the developments in the area of complex systems considering network-induced constraints cannot be comprehensively covered by these collected papers. Nevertheless, we hope that this special collection will motivate researchers to continue exploring some of challenges in this area, for either advances in theory or breakthroughs in practice.