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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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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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Torque Ripple and Acoustic Noise Suppression for Sensorless PMSM Drive Based on Biaxial Random Signal Injection

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IEEE Transactions on Transportation Electrification 2025年第3期11卷 7287-7299页

作者： Qian, Zhe Li, Xin Wang, Qunjing Deng, Wenzhe Sun, Zehui Chen, Qixu Anhui University School of Electrical Engineering and Automation National Engineering Laboratory of Energy-Saving Motor and Control Technology Hefei230601 China Anhui University School of Electrical Engineering and Automation Hefei230601 China Anhui University School of Electrical Engineering and Automation National Engineering Laboratory of Energy-Saving Motor and Control Technology Anhui Collaborative Innovation Center of Industrial Energy-Saving and Power Quality Control Hefei230601 China

Signal injection method shows good performance in estimating the rotor position of permanent magnet synchronous motor (PMSM) at low speed, while the traditional uniaxial fixedphase signal injection (UFPSI) method will produce extra torque ripple and noise. This paper proposes a novel sensorless PMSM drive method based on biaxial random phase signal injection (BRPSI), which can simultaneously suppress both torque ripple and noise. To achieve this, an additional injected q-axis voltage, with its amplitude calculated in real time to satisfy different operating conditions, is used to counteract the torque ripple induced by the injected d-axis voltage. Meanwhile, the phase of the injected voltages is randomly switched to achieve a smooth current power spectral density (PSD) and attenuated noise level. The effectiveness of the proposed method is verified on a rapid control prototyping (RCP) platform, which demonstrates that the proposed method exhibits good speed and position tracking performance while simultaneously suppressing the torque ripples and noise caused by the injected signals. © 2015 IEEE.

关键词： Permanent magnets

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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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Constrained Networked Predictive control for Nonlinear Systems Using a High-Order Fully Actuated System Approach

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IEEE/CAA Journal of Automatica Sinica 2025年第2期12卷 478-480页

作者： Yi Huang Guo-Ping Liu Yi Yu Wenshan Hu the School of Electrical Engineering and Automation Wuhan University IEEE the Center for Control Science and Technology Southern University of Science and Technology the Department of Electrical and Electronic Engineering The Hong Kong Polytechnic University

Dear Editor,In this letter, a constrained networked predictive control strategy is proposed for the optimal control problem of complex nonlinear highorder fully actuated (HOFA) systems with noises. The method can effectively deal with nonlinearities, constraints, and noises in the system, optimize the performance metric, and present an upper bound on the stable output of the system.

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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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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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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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