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Optimization methods rooted in optimal control

science China(Information sciences) 2024年第12期67卷 272-280页

作者： Huanshui ZHANG Hongxia WANG Yeming XU Ziyuan GUO School of Electrical and Automation Engineering Shandong University of Science and Technology School of Control Science and Engineering Shandong University

In the paper, we investigate the optimization problem(OP) by applying the optimal control method. The optimization problem is reformulated as an optimal control problem(OCP) where the controller(iteration updating) is designed to minimize the sum of costs in the future time instant, which thus theoretically generates the “optimal algorithm”(fastest and most stable). By adopting the maximum principle and linearization with Taylor expansion, new algorithms are proposed. It is shown that the proposed algorithms have a superlinear convergence rate and thus converge more rapidly than the gradient descent;meanwhile, they are superior to Newton's method because they are not divergent in general and can be applied in the case of a singular or indefinite Hessian matrix. More importantly, the OCP method contains the gradient descent and the Newton's method as special cases, which discovers the theoretical basis of gradient descent and Newton's method and reveals how far these algorithms are from the optimal algorithm. The merits of the proposed optimization algorithm are illustrated by numerical experiments.

关键词： optimal control optimization methods optimization algorithm maximum principle superlinear convergence

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The optimal control theory——a scientific approach to fundamentally solving control problems

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science China(Information sciences) 2025年第1期68卷 389-391页

作者： Huanshui ZHANG School of Electrical and Automation Engineering Shandong University of Science and Technology School of Control Science and Engineering Shandong University

The maximum principle has bridged mathematical optimization to optimal control,ushering in significant developments and refinements in optimal control theory,notably during the 1960s with the advent of linear quadratic (LQ)control and linear quadratic estimation (LQE).This progression propelled optimal control theory into further advancements,encompassing stochastic control,robust/H-infinity control,model predictive control (MPC),networked control,and reinforcement learning *** control,established upon a rigorous mathematical foundation,extends static optimization theory to dynamic systems,exhibiting scientific essence,unity,and ***,since its inception,optimal control theory has served as an indispensable core role across all control-related domains,including communication-constrained control in networked systems,consensus control,cooperative control,and reinforcement learning control.

关键词： control optimal approach fundamentally problems scientific solving theory

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Deterministic learning-based neural output-feedback control for a class of nonlinear sampled-data systems

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science China(Information sciences) 2024年第9期67卷 164-183页

作者： Yu ZENG Fukai ZHANG Tianrui CHEN Cong WANG School of Automation Science and Engineering South China University of Technology School of Control Science and Engineering Shandong University

This study investigates the deterministic learning(DL)-based output-feedback neural control for a class of nonlinear sampled-data systems with prescribed performance(PP). Specifically, first, a sampleddata observer is employed to estimate the unavailable system states for the Euler discretization model of the transformed system dynamics. Then, based on the observations and backstepping method, a discrete neural network(NN) controller is constructed to ensure system stability and achieve the desired tracking performance. The noncausal problem encountered during the controller deduction process is resolved using a command filter. Moreover, the regression characteristics of the NN input signals are demonstrated with the observed states. This ensures that the radial basis function NN, based on DL theory, meets the partial persistent excitation condition. Subsequently, a class of discrete linear time-varying systems is proven to be exponentially stable, achieving partial convergence of neural weights to their optimal/actual values. Consequently, accurate modeling of unknown closed-loop dynamics is achieved along the system trajectory from the output-feedback control. Finally, a knowledge-based controller is developed using the modeling *** controller not only enhances the control performance but also ensures the PP of the tracking error. The effectiveness of the scheme is illustrated through simulation results.

关键词： deterministic learning neural networks adaptive neural control predefined performance nonlinear sampled-data systems

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Swarm intelligence:A survey of model classification and applications

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Chinese Journal of Aeronautics 2025年第3期38卷 163-182页

作者： Chao WANG Shuyuan ZHANG Tianhang MA Yuetong XIAO Michael Zhiqiang CHEN Lei WANG School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100191China School of Automation Nanjing University of Science and TechnologyNanjing 210094China

Swarm Intelligence (SI) is a collective behavior that emerges from interaction between individuals in a group. Typical SI includes fish schooling, ant foraging, bird migration, and so on. A great deal of models have been introduced to characterize the mechanism of SI. This article reviews several typical models and classifies them into four categories: self-driven particle models, with Boids model as the primary example;pheromone communication models, including the ant colony pheromone model which serves as the foundation for ant colony optimization;leadership decision models, utilizing the hierarchical dynamics model of pigeon flock as a prime instance;empirical research models, which employ the topological rule model of starling flock as a classic model. On this basis, each type of model is elaborated upon in terms of its typical model overview, applications, and model evaluation. More specifically, multi-agent swarm control, path optimization and obstacle avoidance, formation and consensus control, trajectory tracking in the dense crowd and social networks analysis are surveyed in the application of each category, respectively. Furthermore, the more precise and effective modeling techniques for leadership decision and empirical research models are described. Limitations and potential directions for further exploration in the study of SI are presented.

关键词： Swarm intelligence Ant colony optimization Self-driven particle models Pheromone communication models Leadership decision models Empirical research models

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A LODBO algorithm for multi-UAV search and rescue path planning in disaster areas

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Chinese Journal of Aeronautics 2025年第2期38卷 200-213页

作者： Liman Yang Xiangyu Zhang Zhiping Li Lei Li Yan Shi School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100191China

In disaster relief operations,multiple UAVs can be used to search for trapped *** recent years,many researchers have proposed machine le arning-based algorithms,sampling-based algorithms,and heuristic algorithms to solve the problem of multi-UAV path *** Dung Beetle Optimization(DBO)algorithm has been widely applied due to its diverse search patterns in the above ***,the update strategies for the rolling and thieving dung beetles of the DBO algorithm are overly simplistic,potentially leading to an inability to fully explore the search space and a tendency to converge to local optima,thereby not guaranteeing the discovery of the optimal *** address these issues,we propose an improved DBO algorithm guided by the Landmark Operator(LODBO).Specifically,we first use tent mapping to update the population strategy,which enables the algorithm to generate initial solutions with enhanced diversity within the search ***,we expand the search range of the rolling ball dung beetle by using the landmark ***,by using the adaptive factor that changes with the number of iterations.,we improve the global search ability of the stealing dung beetle,making it more likely to escape from local *** verify the effectiveness of the proposed method,extensive simulation experiments are conducted,and the result shows that the LODBO algorithm can obtain the optimal path using the shortest time compared with the Genetic Algorithm(GA),the Gray Wolf Optimizer(GWO),the Whale Optimization Algorithm(WOA)and the original DBO algorithm in the disaster search and rescue task set.

关键词： Unmanned aerial vehicle Path planning Meta heuristic algorithm DBO algorithm NP-hard problems

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Distributed velocity-free formation tracking control for clustered UAVs under virtual leader-follower framework

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science China(Technological sciences) 2024年第5期67卷 1538-1552页

作者： ZHANG ZhaoYu DUAN HaiBin School of Automation Science and Electrical Engineering Beihang UniversityBeijing100083China

The collective formation control problem of a cluster of rotorcraft unmanned aerial vehicles(UAVs)is investigated in this *** consensus tracking towards formation centroid with following UAVs forming a predefined configuration around the leader is considered as the *** prior studies,the information of the central reference trajectory,which is deemed as a virtual leader in the leader-follower topology,is not directly accessible for partial nodes through the communication ***,a novel distributed formation tracking control scheme is ***,a decentralized saturation observer is employed to estimate the reference acceleration signal of the virtual *** the absence of linear velocity measurement,two sliding manifolds are proposed by introducing the relative discrepancy terms of position and *** a smooth saturation operator in the form of a sigmoid function is applied to generate the command force ***,under the dilemma of constrained capabilities of the airborne sensors equipped on the rotorcrafts,the angular velocity is difficult to *** cascaded auxiliary attitude error systems are established on each rotorcraft system to synthesize the rotating torque with no need to require the angular velocity *** to the strong coupling and nonlinearity of the rotorcraft UAV system,the command angular velocity and the derivatives of command input are hard to *** a continuous nonlinear differentiator is proposed to work with the difficulties in deriving the explicit expression of system ***,a detailed stability analysis is conducted progressively on the angular control loop,reference trajectory observer loop,and the position control loop.A simulation scheme for a cluster of four rotorcraft UAVs tracking sinusoidal trajectory are presented and the formation control results are proven advantageous in comparison with the control protocol in previous literature.

关键词： distributed formation control unmanned rotorcraft clusters velocity-free tracking nonlinear differentiator

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Embedding prescribed-time adaptive control protocol unveiling distributed consensus in multirobot systems via directed topology

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science China(Information sciences) 2025年第2期68卷 383-384页

作者： Yonghao XIE Xinru MA Hengyu LI Shaorong XIE School of Computer Engineering and Science Shanghai University School of Mechatronic Engineering and Automation Shanghai University

Recently, multirobot systems(MRSs) have found extensive applications across various domains, including industrial manufacturing, collaborative formation of unmanned equipment, emergency disaster relief, and war scenarios [1]. These advancements are largely supported by the development of consistency control theory. However, traditional dynamicsfree models may cause instability in complex robotic systems. Lagrangian dynamics offers a better approach for modeling these systems, as it facilitates controller design and optimization analysis. Despite this, challenges persist with unknown parameters and nonlinear friction within the systems.

关键词： Microrobots

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Event-triggered leader-follower bipartite consensus control for nonlinear multi-agent systems under DoS attacks

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science China(Information sciences) 2025年第3期68卷 286-301页

作者： Wei SU Chaoxu MU Song ZHU Ben NIU Changyin SUN School of Control Science and Engineering Tianjin University School of Mathematics China University of Mining and Technology School of Control Science and Engineering Dalian University of Technology School of Automation Southeast University

Aiming at the consensus control problem of nonlinear multi-agent systems(MASs) under directed topology, a leader-follower bipartite consensus control strategy is proposed. This strategy takes into account the potential for denial-of-service(DoS) attacks and completely unknown system dynamics. Specifically, the bipartite consensus dynamics describes the cooperation and competition relationship between followers and the leader, that is, the follower chooses to move in accordance with or opposite to the leader according to its trajectory. In order to optimize the communication bandwidth and mitigate the impact of DoS attacks, the proposed consensus control scheme integrates the DoS attack detection mechanism and event-triggered mechanism. In addition, neural networks(NNs) are used to solve the nonlinear problem, and a speed function is designed to achieve the desired tracking performance, ensuring that all agents' tracking errors converge to a predefined set in a finite time. With the help of backstepping, graph theory, and Lyapunov stability theory, sufficient conditions for achieving bipartite consensus without Zeno behavior are established. Finally, the accuracy and feasibility of the theoretical analysis are verified by simulation cases.

关键词： multi-agent systems neural networks bipartite consensus event-trigger denial-of-service attack

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Adaptive admittance tracking control for interactive robot with prescribed performance

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Journal of Systems engineering and Electronics 2024年第2期35卷 444-450页

作者： MENG Qingrui LIN Yan School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100190China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China

An adaptive control approach is presented in this paper for tracking desired trajectories in interactive manipulators. The controller design incorporates prescribed performance functions (PPFs) to improve dynamic performance. Notably, the performance of the output error is confined in an envelope characterized by exponential convergence, leading to convergence to zero. This feature ensures a prompt response from admittance control and establishes a reliable safety framework for interactions. Simulation results provide practical insights,demonstrating the viability of the control scheme proposed in this paper.

关键词： prescribed performance admittance control adaptive control robots

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New results on finite-time stability and instability theorems for stochastic nonlinear time-varying systems

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science China(Information sciences) 2025年第2期68卷 186-199页

作者： Weihai ZHANG Liqiang YAO College of Electrical Engineering and Automation Shandong University of Science and Technology School of Mathematics and Information Science Yantai University

This paper studies finite-time stability and instability theorems in the probability sense for stochastic nonlinear timevarying systems. Firstly, a new sufficient condition is proposed to guarantee that the considered system has a global ***, we propose new finite-time stability and instability criteria that relax the constraints on LV(the infinitesimal operator of Lyapunov function V) by the uniformly asymptotically stable function. On the one hand, these obtained results make up for the shortcomings of the existing results. On the other hand, the new finite-time stability theorems can be viewed as natural extensions of the existing results and also allow LV to be indefinite(negative or positive) rather than just only allow LV < ***, some simulation examples verify the validity of the theoretical results.

关键词： stochastic nonlinear systems finite-time stability finite-timeinstability uniformly asymptotically stable function

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