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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.

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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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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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Autonomous navigation method of satellite constellation based on adaptive forgetting factors

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Chinese Journal of Aeronautics 2024年第7期37卷 317-332页

作者： Dong WANG Jing YANG Kai XIONG School of Automation Science and Electrical Engineering Beihang UniversityBeijing 100191China Science and Technology on Space Intelligent Control Laboratory Beijing Institute of Control EngineeringBeijing 100094China

To address the problem that model uncertainty and unknown time-varying system noise hinder the filtering accuracy of the autonomous navigation system of satellite constellation,an autonomous navigation method of satellite constellation based on the Unscented Kalman Filter with Adaptive Forgetting Factors(UKF-AFF)is *** process noise covariance matrix is estimated online with the strategy that combines covariance matching and adaptive adjustment of forgetting *** adaptive adjustment coefficient based on squared Mahalanobis distance of state residual is employed to achieve online regulation of forgetting factors,equipping this method with more *** intersatellite direction vector obtained from photographic observations is introduced to determine the constellation satellite orbit together with the distance measurement to avoid rank deficiency *** that the number of available measurements varies online with intersatellite visibility in practical applications such as time-varying constellation configurations,the smooth covariance matrix of state correction determined by innovation and gain is adopted and constructed *** analysis of the proposed method is also *** effectiveness of the proposed method is verified by the Monte Carlo simulation and comparison *** estimation accuracy of constellation position and velocity of UKF-AFF is improved by 30%and 44%respectively compared to those of the extended Kalman filter,and the method proposed is also better than other several adaptive filtering methods in the presence of significant model uncertainty.

关键词： Constellation autonomous navigation Unscented Kalman filter Adaptive forgetting factor Model uncertainty Stability analysis

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Linear Quadratic Optimal control for Systems Governed by First-Order Hyperbolic Partial Differential Equations

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Journal of Systems science & Complexity 2024年第1期37卷 230-252页

作者： XUE Xiaomin XU Juanjuan ZHANG Huanshui School of Control Science and Engineering Shandong UniversityJinan 250061China College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266000China

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 *** 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 ***,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 *** 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.

关键词： Discretization-then-continuousization method first-order hyperbolic partial differential equations forward and backward partial difference equations linear quadratic optimal control.

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Time-varying formation tracking control of high-order multi-agent systems with multiple leaders and multiplicative noise

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science China(Information sciences) 2024年第12期67卷 191-207页

作者： Ruru JIA Xiaofeng ZONG Qing WANG College of Artificial Intelligence Nankai University School of Automation China University of Geosciences Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems School of Automation Science and Electrical Engineering Beihang University

This work discusses the time-varying formation(TVF) tracking control problem of high-order multi-agent systems(MASs) with multiple leaders and multiplicative measurement noise. With the help of Lyapunov function tools and stochastic analysis methods, the TVF tracking protocol with multiple leaders and multiplicative noise is developed based on the relative state measurements, where followers are driven to realize the target TVF while tracking the convex combination formed by multiple leaders. Then, the TVF tracking problem is converted into the mean square asymptotic stability problem of a stochastic differential equation(SDE); sufficient conditions related to the control gains are given by stabilizing the corresponding stochastic system. Moreover, a TVF tracking algorithm is presented to outline the steps of protocol ***, the theoretical results are illustrated in terms of simulation examples.

关键词： multi-agent systems multiple leaders multiplicative measurement noise stochastic differential equation formation tracking control

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Enhanced Tube-Based Event-Triggered Stochastic Model Predictive control With Additive Uncertainties

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IEEE/CAA Journal of Automatica Sinica 2025年第3期12卷 596-605页

作者： Chenxi Gu Xinli Wang Kang Li Xiaohong Yin Shaoyuan Li Lei Wang the School of Control Science and Engineering Shandong University IEEE the School of Electronic and Electrical Engineering University of Leeds the Qingdao University of Science and Technology the Department of Automation Shanghai Jiao Tong University the Key Laboratory of System Control and Information Processing Ministry of Education of China

This paper proposes an event-triggered stochastic model predictive control for discrete-time linear time-invariant(LTI) systems under additive stochastic disturbances. It first constructs a probabilistic invariant set and a probabilistic reachable set based on the priori knowledge of system *** with enhanced robust tubes, the chance constraints are then formulated into a deterministic form. To alleviate the online computational burden, a novel event-triggered stochastic model predictive control is developed, where the triggering condition is designed based on the past and future optimal trajectory tracking errors in order to achieve a good trade-off between system resource utilization and control performance. Two triggering parameters σ and γ are used to adjust the frequency of solving the optimization problem. The probabilistic feasibility and stability of the system under the event-triggered mechanism are also examined. Finally, numerical studies on the control of a heating, ventilation, and air conditioning(HVAC) system confirm the efficacy of the proposed control.

关键词： Event-triggered mechanism heating, ventilation, and air conditioning (HVAC) control probabilistic reachable set stochastic model predictive control

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Adaptive control of a Flexible Manipulator With Unknown Hysteresis and Intermittent Actuator Faults

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IEEE/CAA Journal of Automatica Sinica 2025年第1期12卷 148-158页

作者： Shouyan Chen Weitian He Zhijia Zhao Yun Feng Zhijie Liu Keum-Shik Hong School of Mechanical and Electrical Engineering Guangzhou University the School of Control Science and Engineering Shandong University IEEE the College of Electrical and Information Engineering Hunan University the National Engineering Research Center for Robot Visual Perception and Control Technology Hunan University the School of Intelligence Science and Technology University of Science and Technology Beijing (USTB) the Institute for Future the School of AutomationQingdao University the School of Mechanical Engineering Pusan National University

In this study, we consider a single-link flexible manipulator in the presence of an unknown Bouc-Wen type of hysteresis and intermittent actuator faults. First, an inverse hysteresis dynamics model is introduced, and then the control input is divided into an expected input and an error compensator. Second,a novel adaptive neural network-based control scheme is proposed to cancel the unknown input hysteresis. Subsequently,by modifying the adaptive laws and local control laws, a fault-tolerant control strategy is applied to address uncertain intermittent actuator faults in a flexible manipulator system. Through the direct Lyapunov theory, the proposed scheme allows the state errors to asymptotically converge to a specified interval. Finally,the effectiveness of the proposed scheme is verified through numerical simulations and experiments.

关键词： Adaptive control flexible manipulator intermittent actuator faults inverse hysteresis dynamics vibration control

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Security control for air-sea heterogeneous multiagent systems with cooperative-antagonistic interactions:An intermittent privacy preservation mechanism

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science China(Technological sciences) 2025年第4期68卷 179-192页

作者： Shoufeng YANG Hongjing LIANG Yingnan PAN Tieshan LI College of Control Science and Engineering Bohai UniversityJinzhou121013China School of Automation Engineering University of Electronic Science and Technology of ChinaChengdu611731China Laboratory of Electromagnetic Space Cognition and Intelligent Control Beijing100089China

antagonistic interactions,data security and transient-steady state performance of the system are two key *** ensure data security,an intermittent privacy preservation(IPP)mechanism is proposed for the first time.A novel setting time initial mask function and a novel intermittent mask function are *** can implement intermittent preservation for the system according to actual requirements,which solves the irreversibility problem after conventional mask disappears and balances control accuracy and system *** ensure transient-steady state performance,a novel error transformation function(ETF)is proposed and integrated into the predefined-time prescribed performance control *** to conventional hyperbolic tangent type ETFs,the proposed ETF can improve the convergence accuracy of errors under the same ***,a unified model of the air-sea HMASs is established,which improves the model accuracy compared with the simplified ***,the proposed IPP security control strategy is applied to the air-sea delivery mission to verify its feasibility and effectiveness.

关键词： air-sea heterogeneous multiagent systems(HMASs) security control intermittent privacy preservation(IPP) error transformation function(ETF)

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