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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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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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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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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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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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Multimode Design and Analysis of an Integrated Leg-Arm Quadruped Robot with Deployable Characteristics

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Chinese Journal of Mechanical engineering 2024年第3期37卷 41-61页

作者： Fuqun Zhao Yifan Wu Xinhua Yang Xilun Ding Kun Xu Sheng Guo Xiaodong Jin School of Mechanical Engineering and Automation Beihang UniversityBeijing 100191China School of Mechanical Electronic and Control EngineeringBeijing Jiaotong UniversityBeijing 100044China

To improve locomotion and operation integration, this paper presents an integrated leg-arm quadruped robot(ILQR) that has a reconfigurable joint. First, the reconfigurable joint is designed and assembled at the end of the legarm chain. When the robot performs a task, reconfigurable configuration and mode switching can be achieved using this joint. In contrast from traditional quadruped robots, this robot can stack in a designated area to optimize the occupied volume in a nonworking state. Kinematics modeling and dynamics modeling are established to evaluate the mechanical properties for multiple modes. All working modes of the robot are classified, which can be defined as deployable mode, locomotion mode and operation mode. Based on the stability margin and mechanical modeling, switching analysis and evaluation between each mode is carried out. Finally, the prototype experimental results verify the function realization and switching stability of multimode and provide a design method to integrate and perform multimode for quadruped robots with deployable characteristics.

关键词： Quadruped robot Multimode design Mode switching Locomotion Operation

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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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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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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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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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