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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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High-dimensional Steady-state Security Region Boundary Approximation in Power Systems Using Feature Non-linear Converter and Improved Oblique Decision Tree

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Journal of Modern Power Systems and Clean Energy 2024年第6期12卷 1786-1797页

作者： Yuxin Dai Jun Zhang Peidong Xu Tianlu Gao David Wenzhong Gao School of Electrical Engineering and Automation Wuhan UniversityWuhan 430072China Department of Electrical and Computer Engineering DenverUSA

The steady-state security region(SSR)offers ro-bust support for the security assessment and control of new power systems with high uncertainty and ***,accurately solving the steady-state security region boundary(SS-RB),which is high-dimensional,non-convex,and non-linear,presents a significant *** address this problem,this paper proposes a method for approximating the SSRB in power systems using the feature non-linear converter and improved oblique decision ***,to better characterize the SSRB,boundary samples are generated using the proposed sampling *** samples are distributed within a limited distance near the ***,to handle the high-dimensionality,non-convexity and non-linearity of the SSRB,boundary samples are converted from the original power injection space to a new fea-ture space using the designed feature non-linear ***-sequently,in this feature space,boundary samples are linearly separated using the proposed information gain rate based weighted oblique decision ***,the effectiveness and generality of the proposed sampling method are verified on the WECC 3-machine 9-bus system and IEEE 118-bus system.

关键词： Steady-state security region boundary sample generation feature non-linear conversion oblique decision tree

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Interference Suppression and Jitter Elimination Ability-Based Adaption Tracking Guidance for Robotic Fishes

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IEEE/CAA Journal of Automatica Sinica 2025年第1期12卷 126-137页

作者： Dongfang Li Jie Huang Rob Law Xin Xu Limin Zhu Edmond Q.Wu IEEE the School of Electrical Engineering and Automation Fuzhou University the Key Laboratory of System Control and Information Processing Ministry of Education the School of Electrical Engineering and Automation Fuzhou University 5G+Industrial Internet Institute Fuzhou University the University of Macau the College of Mechatronics and Automation National University of Defense Technology the School of Mechanical Engineering Shanghai Jiao Tong University the Department of Computer Science and Engineering Shanghai Jiao Tong University

This work presents an adaptive tracking guidance method for robotic fishes. The scheme enables robots to suppress external interference and eliminate motion jitter. An adaptive integral surge line-of-sight guidance rule is designed to eliminate dynamics interference and sideslip issues. Limited-time yaw and surge speed observers are reported to fit disturbance variables in the model. The approximation values can compensate for the system's control input and improve the robots' tracking ***, this work develops a terminal sliding mode controller and third-order differential processor to determine the rotational torque and reduce the robots' run jitter. Then, Lyapunov's theory proves the uniform ultimate boundedness of the proposed method. Simulation and physical experiments confirm that the technology improves the tracking error convergence speed and stability of robotic fishes.

关键词： Adaptive integral surge line-of-sight approximation robotic fish speed observer

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controllability of heterogeneous networked sampled-data systems

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Science China(Information Sciences) 2025年第3期68卷 302-318页

作者： Zixuan YANG Lin WANG Xiaofan WANG Guanrong CHEN Department of Automation Shanghai Jiao Tong University Key Laboratory of System Control and Information Processing Ministry of Education of China School of Mechatronic Engineering and Automation Shanghai University School of Electrical and Electronic Engineering Shanghai Institute of Technology Department of Electrical Engineering City University of Hong Kong

This study investigates the controllability of a general heterogeneous networked sampled-data system(HNSS) consisting of nonidentical node systems, where the inner coupling between any pair of nodes can be described by a unique *** signals on control and transmission channels are sampled and held by zero-order holders, and the control sampling period of each node can be different. Necessary and sufficient controllability conditions are developed for the general HNSS, using the Smith normal form and matrix equations, respectively. The HNSS in specific topology or dynamic settings is discussed subsequently with easier-to-verify conditions derived. These heterogeneous factors have been determined to independently or jointly affect the controllability of networked sampled-data systems. Notably, heterogeneous sampling periods have the potential to enhance the overall controllability, but not for systems with some special dynamics. When the node dynamics are heterogeneous,the overall system can be controllable even if it is topologically uncontrollable. In addition, in several typical heterogeneous sampled-data multi-agent systems, pathological sampling of single-node systems will necessarily cause overall uncontrollability.

关键词： network controllability sampled-data system heterogeneous system inner coupling multi-agent system

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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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Coordinated Frequency control for Isolated Power Systems with High Penetration of DFIG-Based Wind Power

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CSEE Journal of Power and Energy Systems 2024年第4期10卷 1399-1414页

作者： Xin Ding Wei Lin Jian Xu Yuanzhang Sun Liangzhong Yao Beilin Mao School of Electrical Engineering and Automation Wuhan UniversityWuhan 430072China Department of Electrical Engineering and Computer Science Case Western Reserve UniversityClevelandOH 44106 USA

This paper proposes a coordinated frequency control scheme for emergency frequency regulation of isolated power systems with a high penetration of wind *** proposed frequency control strategy is based on the novel nonlinear regulator theory,which takes advantage of nonlinearity of doubly fed induction generators(DFIGs)and generators to regulate the frequency of the power *** deviations and power imbalances are used to design nonlinear feedback controllers that achieve the reserve power distribution between generators and DFIGs,in various wind speed *** effectiveness and dynamic performance of the proposed nonlinear coordinated frequency control method are validated through simulations in an actual isolated power grid.

关键词： Frequency control isolated power systems nonlinear feedback nonlinear regulator theory wind power

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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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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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Event-based non-fragile state estimation for time-varying systems under deception attacks

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Science China(Information Sciences) 2025年第4期68卷 349-362页

作者： Xiao-Meng LI Tao ZOU Renquan LU Zhijia ZHAO School of Mechanical and Electrical Engineering Guangzhou University School of Automation Guangdong Hong Kong Joint Laboratory for Intelligent Decision and Cooperative ControlGuangdong University of Technology

This paper addresses the challenge of dynamic event-based non-fragile state estimation for discrete time-varying systems under deception attacks. These attacks involve injecting deceptive signals into the communication channel, which can consume limited network resources and disrupt system estimation tasks. To tackle this issue, the study introduces a comprehensive and realistic deception attack model that accounts for the various hard physical constraints. To mitigate the influence of these attacks and reduce communication demands, a dynamic event-triggered scheme that uses dynamic threshold parameters is developed. The main purpose of the addressed problem is to design an event-based non-fragile estimator that ensures the estimation error systems meet the H∞performance constraint over a finite horizon. The paper provides two key criteria to ensure the existence of the proposed estimator, leveraging stochastic analysis techniques. The desired estimator gains are determined using a recursive process of solving matrix inequalities. Finally, a numerical example illustrates the effectiveness of the developed event-based non-fragile estimator design method.

关键词： discrete time-varying systems deception attacks dynamic event-triggered mechanism finite horizon non-fragile estimation

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